how to write to solve this type of system of equations ?

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NIRUPAM SAHOO
NIRUPAM SAHOO 2021년 9월 11일
댓글: NIRUPAM SAHOO 2021년 9월 12일
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NIRUPAM SAHOO
NIRUPAM SAHOO 2021년 9월 12일
please anyone solve this . here u and v are functions of r.

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답변(2개)

Wan Ji
Wan Ji 2021년 9월 12일
Hey friend
Just expand the left items of the two equations, extract u'' and v'', then an ode45 solver is there for you.

Walter Roberson
Walter Roberson 2021년 9월 12일
편집: Walter Roberson 2021년 9월 12일
I was not able to figure out what is being raised to 10/9 . I used squiggle instead.
syms u(r) v(r)
syms N squiggle real
assume(r, 'real')
du = diff(u);
dv = diff(v);
left1 = diff(r^(N-1)*du^3)
left1(r) = 
right1 = r^(N-1) * sqrt(u) * sqrt(v) / (3*r^(2/3) * sqrt(1 + 9*squiggle^(10/9)/(10*(3*N-2)^(1/3))))
right1(r) = 
left2 = diff(r^(N-1)*dv^3)
left2(r) = 
right2 = r^(N-1) * u * v / (3*r^(2/3))
right2(r) = 
eqn1 = left1 == right1
eqn1(r) = 
eqn2 = left2 == right2
eqn2(r) = 
ic = [u(0) == 1, v(0) == 1, du(0) == 0, dv(0) == 0]
ic = 
sol = dsolve([eqn1, eqn2, ic])
Warning: Unable to find symbolic solution.
sol = [ empty sym ]
string(eqn1)
ans = "3*r^(N - 1)*diff(u(r), r)^2*diff(u(r), r, r) + r^(N - 2)*(N - 1)*diff(u(r), r)^3 == (r^(N - 1)*u(r)^(1/2)*v(r)^(1/2))/(3*r^(2/3)*((9*squiggle^(10/9))/(10*(3*N - 2)^(1/3)) + 1)^(1/2))"
string(eqn2)
ans = "3*r^(N - 1)*diff(v(r), r)^2*diff(v(r), r, r) + r^(N - 2)*(N - 1)*diff(v(r), r)^3 == (r^(N - 1)*u(r)*v(r))/(3*r^(2/3))"
string(ic)
ans = 1×4 string array
"u(0) == 1" "v(0) == 1" "subs(diff(u(r), r), r, 0) == 0" "subs(diff(v(r), r), r, 0) == 0"
Lack of a symbolic solution means that you would have to do numeric solutions -- but you cannot do a numeric solution to infinity, and you certainly would not get a formula out of it.
  댓글 수: 5
NIRUPAM SAHOO
NIRUPAM SAHOO 2021년 9월 12일
syms p(t) m(t) t Y
Eqns = [diff((t^(100-1))*(diff(p(t),t))) == (t^(100-1))*(t-1)*exp(t)*p(t)*m(t);
diff((t^(100-1))*(diff(m(t),t))) == (t^(100-1))*(t-1)*exp(t)*p(t)^(1/2)*m(t)^(1/2)]
[DEsys,Subs] = odeToVectorField(Eqns);
DEFcn = matlabFunction(DEsys, 'Vars',{t,Y});
tspan = [0,100];
y0 = [0 0 0 0];
[t,Y] = ode45(DEFcn, tspan, y0);
plot(t,Y)
## i write this but the graph does not shows . please help me

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