How to Solve Second Order ODE with 1 boundary condition for y and 1 non-zero boundary condition for y'

I'm not sure if MatLab has a built in function to handle this.

To clarify, I'm working with the simple ODE: y''+ay=0 (a is a known constant) and have the following coundary conditions:

1) y(0)=50

2) y'(L)=0 (L is a known constant)

As far as I can tell, ode45 is only applicable for initial value problems and bvp4c requires both boundary conditions to be for y, not y'. I was thiking MatLab would have a built in function to handle this, but I'm not sure at this point.

Answer 1

[Torsten]

If you convert your second order equation to a system of first-order equations

y1' = y2
y2' = -a*y1

you can use bvp4c to set boundary conditions for y1 (which is y) at x=0 and for y2 (which is y') at x=L.

[Osman Qamar]

Got it, thanks!