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solve a system of equations symbolically with R2018a
조회 수: 14 (최근 30일)
이전 댓글 표시
>> eqn1='(Fa0*x1)/0.1*(9.05*(1-x1))*(27.8-9.05*x1))==3785'
eqn1 =
'(Fa0*x1)/0.1*(9.05*(1-x1))*(27.8-9.05*x1))==3785'
>> eqn2='(Fa0*(x2-x1))/0.1*(9.05*(1-x2))*(27.8-9.05*x2))==3785'
eqn2 =
'(Fa0*(x2-x1))/0.1*(9.05*(1-x2))*(27.8-9.05*x2))==3785'
>> eqn3='(Fa0*(0.95-x2))/0.1*(9.05*(1-0.95))*(27.8-9.05*0.95))==3785'
eqn3 =
'(Fa0*(0.95-x2))/0.1*(9.05*(1-0.95))*(27.8-9.05*0.95))==3785'
>> solT=solve(eqn1,eqn2,eqn3,x1,x2,Fa0)
Error using solve>getEqns (line 418)
List of equations must not be empty.
Error in solve (line 226)
[eqns,vars,options] = getEqns(varargin{:});
답변 (1개)
Walter Roberson
2019년 7월 16일
You are using R2018b or later. solve() no longer accepts character vectors for equations.
Furthermore, each of your equations has an extra ) before the ==
댓글 수: 5
Katy Skillings
2019년 7월 16일
Great thank you so much. Do you have any suggestions on easily solving the three equations for the three unknowns?
Walter Roberson
2019년 7월 17일
syms x1 x2 Fa0
eqn1=(Fa0*x1)/0.1*(9.05*(1-x1))*(27.8-9.05*x1)==3785
eqn2=(Fa0*(x2-x1))/0.1*(9.05*(1-x2))*(27.8-9.05*x2))==3785
eqn3=(Fa0*(0.95-x2))/0.1*(9.05*(1-0.95))*(27.8-9.05*0.95)==3785
solT=solve(eqn1,eqn2,eqn3,x1,x2,Fa0)
>> solT.x1
ans =
(107661970999629286757214701029303*root(z^9 + (876723486400000*z^8)/202893300079 + (12991106484046625280000000000*z^7)/2166615327207744284539 + (76083178071679839453913088000000000000000*z^6)/23136407038890612331350973009399 + (150940543804112324360187616985088000000000000000000000*z^5)/247064314531132675315834249803401104970659 + (4108029355821456200801735089921720320000000000000000000000000*z^4)/343483880984367044317267039965926223597613351999 - (2813441280502164056685917619200458752000000000000000000000000000000*z^3)/2638299689840923267400928133978279323453268156704319 - (1047142599503041327543418476239519744000000000000000000000000000000000000*z^2)/20264779917668131616906528997087163483444552711645874239 - (129725245369116609526016420075945328640000000000000000000000000000000000000000*z)/155653774547608918949459049226626502716337609378151960029759 - 5609740340286123655179088435716554752000000000000000000000000000000000000000000000/1195576642300184106450794957109718167364189177633585204988578879, z, 1)^3)/8428946514850326118400000000000000 - (644190362043358247516937331*root(z^9 + (876723486400000*z^8)/202893300079 + (12991106484046625280000000000*z^7)/2166615327207744284539 + (76083178071679839453913088000000000000000*z^6)/23136407038890612331350973009399 + (150940543804112324360187616985088000000000000000000000*z^5)/247064314531132675315834249803401104970659 + (4108029355821456200801735089921720320000000000000000000000000*z^4)/343483880984367044317267039965926223597613351999 - (2813441280502164056685917619200458752000000000000000000000000000000*z^3)/2638299689840923267400928133978279323453268156704319 - (1047142599503041327543418476239519744000000000000000000000000000000000000*z^2)/20264779917668131616906528997087163483444552711645874239 - (129725245369116609526016420075945328640000000000000000000000000000000000000000*z)/155653774547608918949459049226626502716337609378151960029759 - 5609740340286123655179088435716554752000000000000000000000000000000000000000000000/1195576642300184106450794957109718167364189177633585204988578879, z, 1)^2)/34795849219164160000000000 + (3293149117549712670845262908619636589173*root(z^9 + (876723486400000*z^8)/202893300079 + (12991106484046625280000000000*z^7)/2166615327207744284539 + (76083178071679839453913088000000000000000*z^6)/23136407038890612331350973009399 + (150940543804112324360187616985088000000000000000000000*z^5)/247064314531132675315834249803401104970659 + (4108029355821456200801735089921720320000000000000000000000000*z^4)/343483880984367044317267039965926223597613351999 - (2813441280502164056685917619200458752000000000000000000000000000000*z^3)/2638299689840923267400928133978279323453268156704319 - (1047142599503041327543418476239519744000000000000000000000000000000000000*z^2)/20264779917668131616906528997087163483444552711645874239 - (129725245369116609526016420075945328640000000000000000000000000000000000000000*z)/155653774547608918949459049226626502716337609378151960029759 - 5609740340286123655179088435716554752000000000000000000000000000000000000000000000/1195576642300184106450794957109718167364189177633585204988578879, z, 1)^4)/352525553134900379648000000000000000000000 + (511416579648121617198722263673655024478773699*root(z^9 + (876723486400000*z^8)/202893300079 + (12991106484046625280000000000*z^7)/2166615327207744284539 + (76083178071679839453913088000000000000000*z^6)/23136407038890612331350973009399 + (150940543804112324360187616985088000000000000000000000*z^5)/247064314531132675315834249803401104970659 + (4108029355821456200801735089921720320000000000000000000000000*z^4)/343483880984367044317267039965926223597613351999 - (2813441280502164056685917619200458752000000000000000000000000000000*z^3)/2638299689840923267400928133978279323453268156704319 - (1047142599503041327543418476239519744000000000000000000000000000000000000*z^2)/20264779917668131616906528997087163483444552711645874239 - (129725245369116609526016420075945328640000000000000000000000000000000000000000*z)/155653774547608918949459049226626502716337609378151960029759 - 5609740340286123655179088435716554752000000000000000000000000000000000000000000000/1195576642300184106450794957109718167364189177633585204988578879, z, 1)^5)/9435998894077156681318400000000000000000000000000 + (6383621944075290460970391272167949096639525163797*root(z^9 + (876723486400000*z^8)/202893300079 + (12991106484046625280000000000*z^7)/2166615327207744284539 + (76083178071679839453913088000000000000000*z^6)/23136407038890612331350973009399 + (150940543804112324360187616985088000000000000000000000*z^5)/247064314531132675315834249803401104970659 + (4108029355821456200801735089921720320000000000000000000000000*z^4)/343483880984367044317267039965926223597613351999 - (2813441280502164056685917619200458752000000000000000000000000000000*z^3)/2638299689840923267400928133978279323453268156704319 - (1047142599503041327543418476239519744000000000000000000000000000000000000*z^2)/20264779917668131616906528997087163483444552711645874239 - (129725245369116609526016420075945328640000000000000000000000000000000000000000*z)/155653774547608918949459049226626502716337609378151960029759 - 5609740340286123655179088435716554752000000000000000000000000000000000000000000000/1195576642300184106450794957109718167364189177633585204988578879, z, 1)^6)/63142993704454431891783680000000000000000000000000000000 + (703558362212137899332129394101759976766459179357552489*root(z^9 + (876723486400000*z^8)/202893300079 + (12991106484046625280000000000*z^7)/2166615327207744284539 + (76083178071679839453913088000000000000000*z^6)/23136407038890612331350973009399 + (150940543804112324360187616985088000000000000000000000*z^5)/247064314531132675315834249803401104970659 + (4108029355821456200801735089921720320000000000000000000000000*z^4)/343483880984367044317267039965926223597613351999 - 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(2813441280502164056685917619200458752000000000000000000000000000000*z^3)/2638299689840923267400928133978279323453268156704319 - (1047142599503041327543418476239519744000000000000000000000000000000000000*z^2)/20264779917668131616906528997087163483444552711645874239 - (129725245369116609526016420075945328640000000000000000000000000000000000000000*z)/155653774547608918949459049226626502716337609378151960029759 - 5609740340286123655179088435716554752000000000000000000000000000000000000000000000/1195576642300184106450794957109718167364189177633585204988578879, z, 1))/275828638800776000000 - 13659982847852236349/3498414423099010
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(644190362043358247516937331*root(z^9 + (876723486400000*z^8)/202893300079 + (12991106484046625280000000000*z^7)/2166615327207744284539 + (76083178071679839453913088000000000000000*z^6)/23136407038890612331350973009399 + (150940543804112324360187616985088000000000000000000000*z^5)/247064314531132675315834249803401104970659 + (4108029355821456200801735089921720320000000000000000000000000*z^4)/343483880984367044317267039965926223597613351999 - (2813441280502164056685917619200458752000000000000000000000000000000*z^3)/2638299689840923267400928133978279323453268156704319 - (1047142599503041327543418476239519744000000000000000000000000000000000000*z^2)/20264779917668131616906528997087163483444552711645874239 - (129725245369116609526016420075945328640000000000000000000000000000000000000000*z)/155653774547608918949459049226626502716337609378151960029759 - 5609740340286123655179088435716554752000000000000000000000000000000000000000000000/1195576642300184106450794957109718167364189177633585204988578879, z, 2)^2)/34795849219164160000000000 + (3293149117549712670845262908619636589173*root(z^9 + (876723486400000*z^8)/202893300079 + (12991106484046625280000000000*z^7)/2166615327207744284539 + (76083178071679839453913088000000000000000*z^6)/23136407038890612331350973009399 + (150940543804112324360187616985088000000000000000000000*z^5)/247064314531132675315834249803401104970659 + (4108029355821456200801735089921720320000000000000000000000000*z^4)/343483880984367044317267039965926223597613351999 - 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Walter Roberson
2019년 7월 17일
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(2813441280502164056685917619200458752000000000000000000000000000000*z^3)/2638299689840923267400928133978279323453268156704319 - (1047142599503041327543418476239519744000000000000000000000000000000000000*z^2)/20264779917668131616906528997087163483444552711645874239 - (129725245369116609526016420075945328640000000000000000000000000000000000000000*z)/155653774547608918949459049226626502716337609378151960029759 - 5609740340286123655179088435716554752000000000000000000000000000000000000000000000/1195576642300184106450794957109718167364189177633585204988578879, z, 9)^6)/63142993704454431891783680000000000000000000000000000000 + (703558362212137899332129394101759976766459179357552489*root(z^9 + (876723486400000*z^8)/202893300079 + (12991106484046625280000000000*z^7)/2166615327207744284539 + (76083178071679839453913088000000000000000*z^6)/23136407038890612331350973009399 + (150940543804112324360187616985088000000000000000000000*z^5)/247064314531132675315834249803401104970659 + (4108029355821456200801735089921720320000000000000000000000000*z^4)/343483880984367044317267039965926223597613351999 - (2813441280502164056685917619200458752000000000000000000000000000000*z^3)/2638299689840923267400928133978279323453268156704319 - (1047142599503041327543418476239519744000000000000000000000000000000000000*z^2)/20264779917668131616906528997087163483444552711645874239 - (129725245369116609526016420075945328640000000000000000000000000000000000000000*z)/155653774547608918949459049226626502716337609378151960029759 - 5609740340286123655179088435716554752000000000000000000000000000000000000000000000/1195576642300184106450794957109718167364189177633585204988578879, z, 9)^7)/9559849246854400988416049152000000000000000000000000000000000000 + (396296674606146645530500829518543553646142187501647739204239*root(z^9 + (876723486400000*z^8)/202893300079 + (12991106484046625280000000000*z^7)/2166615327207744284539 + (76083178071679839453913088000000000000000*z^6)/23136407038890612331350973009399 + (150940543804112324360187616985088000000000000000000000*z^5)/247064314531132675315834249803401104970659 + (4108029355821456200801735089921720320000000000000000000000000*z^4)/343483880984367044317267039965926223597613351999 - (2813441280502164056685917619200458752000000000000000000000000000000*z^3)/2638299689840923267400928133978279323453268156704319 - (1047142599503041327543418476239519744000000000000000000000000000000000000*z^2)/20264779917668131616906528997087163483444552711645874239 - (129725245369116609526016420075945328640000000000000000000000000000000000000000*z)/155653774547608918949459049226626502716337609378151960029759 - 5609740340286123655179088435716554752000000000000000000000000000000000000000000000/1195576642300184106450794957109718167364189177633585204988578879, z, 9)^8)/23157778815580100954339037465804800000000000000000000000000000000000000000 - (139017318585762447971847*root(z^9 + (876723486400000*z^8)/202893300079 + (12991106484046625280000000000*z^7)/2166615327207744284539 + (76083178071679839453913088000000000000000*z^6)/23136407038890612331350973009399 + (150940543804112324360187616985088000000000000000000000*z^5)/247064314531132675315834249803401104970659 + (4108029355821456200801735089921720320000000000000000000000000*z^4)/343483880984367044317267039965926223597613351999 - (2813441280502164056685917619200458752000000000000000000000000000000*z^3)/2638299689840923267400928133978279323453268156704319 - (1047142599503041327543418476239519744000000000000000000000000000000000000*z^2)/20264779917668131616906528997087163483444552711645874239 - (129725245369116609526016420075945328640000000000000000000000000000000000000000*z)/155653774547608918949459049226626502716337609378151960029759 - 5609740340286123655179088435716554752000000000000000000000000000000000000000000000/1195576642300184106450794957109718167364189177633585204988578879, z, 9))/275828638800776000000 - 13659982847852236349/3498414423099010
>> vpa(solT.x1)
ans =
3.0357213552334732731457027523516 + 0.0057708150473315784314972680001142i
3.0357213552334732731457027523516 - 0.0057708150473315784314972680001142i
-0.066172688730812314034716339121309
1.1009658497172078556813780942382
0.03189275258759005950150696592886
1.0071597729247286803574536258657
-0.0018153581457940921327392971755925
3.0710092676143639617828665903711
1.0009873068254378108401376768815
However, you must question how meaningful it is to give an exact solution for equations involving inexact numbers such as 9.05, which represents the complete range [9.045, 9.055)
Katy Skillings
2019년 7월 17일
Thank you. I attempted solving another way and got this answer as well but was intimidated by the lengthy answer. What is vpa?
Walter Roberson
2019년 7월 17일
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