Help please, I cant use Dsolve and dont understand why :(

Hi,

I really need help with this error please. I do not know what is causing it, in my opinion I have 4 variables and 4 equations, it should work fine.

Thanks in advance.

[Paul]

ode3 and ode4 aren't differential equations. Are you intending that ode3 and ode4 should subsitute into ode2?

[Sebastian Morales]

I thought that dsolve worked for differential and algebraic equations. Do I always need to separate the equationsto solve them. Dsolve for differential and subs for algebraic?

Answer 1

[Walter Roberson]

syms o_r(r) o_t(r) e_r(r) e_t(r)
e_t = o_t - o_r

e_t(r) = 

e_r = o_r - o_t

e_r(r) = 

ode1 = diff(o_r.*r) == o_t

ode1(r) = 

ode2 = diff(e_t.*r) == e_r

ode2(r) = 

temp1 = ode1(r) - o_r(r)

temp1 = 

ode1b = lhs(temp1)/r == rhs(temp1)/r

ode1b = 

temp2 = simplify(subs(ode2, lhs(ode1b), rhs(ode1b)))

temp2(r) = 

ode2b = simplify((temp2(r) - o_t(r))/r)

ode2b = 

odes = [ode1b; ode2b]

odes = 

sol = dsolve(odes)

sol = struct with fields:
    o_t: C1/2 - C2/r^2
    o_r: C1/2 + C2/r^2

[Sebastian Morales]

I tried to do it like this with your feedbacks, but it can not solve the eqn system.

If I got it right, what you are doing is separating the diff() on one side and replacing it later, in a way you are helping Matlab to solve the problem. Is there no Matlab comand that can solve it automatically?

clc
E=210000;
v=0.4;
syms o_r(r) o_t(r) e_r(r) e_t(r )

eqn1 = e_t == (o_t - v.*o_r)./E

eqn1(r) = 

eqn2 = e_r == (o_r - v.*o_t)./E

eqn2(r) = 

ode1 = diff(o_r*r) == o_t

ode1(r) = 

ode2 = diff(e_t*r) == e_r

ode2(r) = 

ode2b= simplify(subs(ode2,[lhs(eqn1),lhs(eqn2)],[rhs(eqn1),rhs(eqn2)]))

ode2b(r) = 

odes = [ode1; ode2b]

odes(r) = 

sol = dsolve(odes)

Warning: Unable to find symbolic solution.

 
sol =
 
[ empty sym ]
 

[Walter Roberson]

Is there no Matlab comand that can solve it automatically?

NO

[Sebastian Morales]

Okay. Thank you :)

[Walter Roberson]

E=210000;
v=0.4;
syms o_r(r) o_t(r) e_r(r) e_t(r )

eqn1 = e_t == (o_t - v.*o_r)./E

eqn1(r) = 

eqn2 = e_r == (o_r - v.*o_t)./E

eqn2(r) = 

ode1 = diff(o_r*r) == o_t

ode1(r) = 

ode1b = (ode1 - o_r)/r

ode1b(r) = 

ode2 = diff(e_t*r) == e_r

ode2(r) = 

ode2b = (ode2 - e_t)/r

ode2b(r) = 

odes = [ode1b; ode2b]

odes(r) = 

sol = dsolve(odes)

sol = struct with fields:
    e_t: C2/r + int(e_r(r), r, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true)/r
    o_r: C1/r + int(o_t(r), r, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true)/r

You cannot resolve more than this without additional information that allows e_r and o_t to be defined.