Hi guys,
I've been having a hard time solving this system of ODEs:
[math]\frac{dM(s)}{ds}=D\cdot w(s)[/math][math]\frac{dw(s)}{ds}=w(s)\cdot M(s)\cdot \frac{1}{s^2}[/math]
where D is a positive constant, s>0 and the boundary conditions are:
[math]M(s_1)=\sigma M(s_2)=\sigma_2[/math]
I've already tried transforming it into a 2nd order diff. equation, but it doesn't work because M''(s) becomes a function of w(s) and I can't solve it. It's also not possible to express it in matrix notation to find eigenvalues and eigenvectors since w(s)*M(s) are stuck together in the second equation. My last hope was to divide one equation by the other and try to solve the ODE dw/dM, but also ended up with bad results...
can someone help me?
I've been having a hard time solving this system of ODEs:
[math]\frac{dM(s)}{ds}=D\cdot w(s)[/math][math]\frac{dw(s)}{ds}=w(s)\cdot M(s)\cdot \frac{1}{s^2}[/math]
where D is a positive constant, s>0 and the boundary conditions are:
[math]M(s_1)=\sigma M(s_2)=\sigma_2[/math]
I've already tried transforming it into a 2nd order diff. equation, but it doesn't work because M''(s) becomes a function of w(s) and I can't solve it. It's also not possible to express it in matrix notation to find eigenvalues and eigenvectors since w(s)*M(s) are stuck together in the second equation. My last hope was to divide one equation by the other and try to solve the ODE dw/dM, but also ended up with bad results...
can someone help me?