# Question:How can I solve this set of two ordinary differential equations?

## Question:How can I solve this set of two ordinary differential equations?

Maple

Dear All

Hi

I want to solve a set of two ordinary differential equations by means of Maple. I can not unfortunately perform it as a non-numeric method. It is worth mentioning that by the following commands, Maple returns a solution presented as a DESol form, which is not useful for me. Note that functions C2_U0[i](theta) and C2_V0[i](theta) are obtained in terms of  C1_U0[i](theta) and C1_V0[i](theta) by using boundary conditions bc1_U0[i] and bc1_V0[i] at radius r=a. So, I should determine unknown functions C1_U0[i](theta) and C1_V0[i](theta) by using boundary conditions bc2_U0[i] and bc2_V0[i] at radius r=b. It should be noted that f_U0[i](r,theta) and f_V0[i](r,theta) are known for i=1,2,3,...

On the other hands, It is much better if it is possible to decouple two coupled differential equations to two individual differential equations.

Best wishes.

U0[i]:=unapply(f_U0[i](r,theta)+C1_U0[i](theta)+C2_U0[i](theta)*r,r,theta):

V0[i]:=unapply(f_V0[i](r,theta)+C1_V0[i](theta)+C2_V0[i](theta)*r,r,theta):

bc1_U0[i]:=U0[i](r,theta)=0;

bc2_U0[i]:=subs(r=b,A11(r,theta))*diff(U0[i](r,theta),r)+subs(r=b,A12(r,theta))*(U0[i](r,theta)/r+diff(V0[i](r,theta),theta)/r)=0;

bc1_V0[i]:=V0[i](r,theta)=0;

bc2_V0[i]:=(diff(U0[i](r,theta),theta)/r+diff(V0[i](r,theta),r)-V0[i](r,theta)/r)=0;

C2_U0[i]:=unapply(solve(subs(r=a,bc1_U0[i]),C2_U0[i](theta)),theta);

C2_V0[i]:=unapply(solve(subs(r=a,bc1_V0[i]),C2_V0[i](theta)),theta);

ans_bc[i]:=dsolve({subs(r=b,bc2_U0[i]),subs(r=b,bc2_V0[i])},{C1_U0[i](theta),C1_V0[i](theta)});

﻿