# Solving First order ODEs simultaneously

조회 수: 1 (최근 30일)
Valerie . 2023년 9월 28일
댓글: Valerie . 2023년 9월 29일
Hello, needed help figuring out why I cannot obtain a solution. I'm sure this is a solvable solution however I keep getting a warning saying no solution is found. Is there any mistake I'm making in the code?
Everything is a constant except E, Sr(t) & Er(t).
% Rigorous Solution Case #1
syms Sr(t) Er(t) E;
E = Ea - Er(t);
Unrecognized function or variable 'Ea'.
ode2a = diff(Sr(t),t) == -(k1*(Ea - Er(t))*Sr(t)) + krev1*Er(t);
ode3a = diff(Er,t) == (k1*(Ea - Er(t))*Sr(t)) - (krev1+k2)*Er(t);
odes = [ode2a; ode3a];
cond1 = Sr(0) == Sa;
cond2 = Er(0) == 0;
conds = [cond1; cond2];
[SrSol(t),ErSol(t)] = dsolve(odes,conds)
##### 댓글 수: 4이전 댓글 2개 표시이전 댓글 2개 숨기기
Walter Roberson 2023년 9월 28일
Ea = 123; %just to have SOME value
k1 = 42; %just to have SOME value
k2 = 13; %just to have SOME value
krev1 = 48; %just to have SOME value
Sa = 5; %just to have SOME value
% Rigorous Solution Case #1
syms Sr(t) Er(t) E;
E = Ea - Er(t);
ode2a = diff(Sr(t),t) == -(k1*(Ea - Er(t))*Sr(t)) + krev1*Er(t);
ode3a = diff(Er,t) == (k1*(Ea - Er(t))*Sr(t)) - (krev1+k2)*Er(t);
eqns = [ode2a; ode3a];
cond1 = Sr(0) == Sa;
cond2 = Er(0) == 0;
conds = [cond1; cond2];
[eqs,vars] = reduceDifferentialOrder(eqns, [Sr(t), Er(t)])
eqs =
vars =
[M,F] = massMatrixForm(eqs,vars)
M =
F =
f = M\F
f =
odefun = odeFunction(f,vars)
odefun = function_handle with value:
@(t,in2)[in2(2,:).*4.8e+1-in2(1,:).*5.166e+3+in2(2,:).*in2(1,:).*4.2e+1;in2(2,:).*-6.1e+1+in2(1,:).*5.166e+3-in2(2,:).*in2(1,:).*4.2e+1]
InitConditions = double(rhs(conds)) %watch out for order though!
InitConditions = 2×1
5 0
[T, Y] = ode45(odefun, [0 0.01], InitConditions);
subplot(2,1,1); plot(T, Y(:,1)); title(string(vars(1)))
subplot(2,1,2); plot(T, Y(:,2)); title(string(vars(2)))
%that almost looks like the initial conditions are reversed.
%what happens if we try reversing the conditions?
[Tr, Yr] = ode45(odefun, [0 0.01], flipud(InitConditions));
figure
subplot(2,1,1); plot(Tr, Yr(:,1)); title(string(vars(1)))
subplot(2,1,2); plot(Tr, Yr(:,2)); title(string(vars(2)))
Valerie 2023년 9월 28일
Thank you so much!

댓글을 달려면 로그인하십시오.

### 채택된 답변

Torsten 2023년 9월 28일
이동: Torsten 님. 2023년 9월 28일
I'm quite sure there is no analytical solution for your system of ODEs since the right-hand sides are nonlinear in the unknown functions (term Er(t)*Sr(t)).
##### 댓글 수: 7이전 댓글 5개 표시이전 댓글 5개 숨기기
Sam Chak 2023년 9월 28일
Wolfram Mathematica uses DSolve. 😅
Valerie 2023년 9월 29일
@Sam Chak I rage quit mathematica this week and is how I eneded up on MATLAB lol but thank you!

댓글을 달려면 로그인하십시오.

### 카테고리

Help CenterFile Exchange에서 Ordinary Differential Equations에 대해 자세히 알아보기

### Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by