# DE Boundary Condition Problem

1. Oct 15, 2011

### Lancelot59

I'm asked to determine if for the solution
$$y=c_{1}e^{x}cos(x)+c_{2}e^{x}sin(x)$$
for:
$$y"-2y'+2y=0$$

whether a member of the family can be found that satisfies the boundary conditions:
$$y(0)=1$$, $$y'(\pi)=0$$

Not quite sure what to do here. The examples in my book give boundary conditions for the same function, not derivatives.

When I put the first condition into y, I got c1=1, then substituting that result into the derivative condition I found c2=-1. So I found the constants, does this mean that there is a member of the family that can satisfy the boundary condition? For some reason I think there should be a Wronskian involved.

2. Oct 16, 2011

### HallsofIvy

Staff Emeritus
Yes, there is a member of the family that satisfies the boundary condition and you found it:
$$y(x)= e^x cos(x)- e^x sin(x)$$

Last edited: Oct 16, 2011
3. Oct 16, 2011

### Lancelot59

Alright, thanks for the help!