Math Help - Quick Simple homogenous equation help

1. Quick Simple homogenous equation help

If i have the function:

$\frac{d^2u}{dx^2} + 4u = f(x)$

What would the homogenous equation be?

2. Originally Posted by signature
If i have the function:

$\frac{d^2u}{dx^2} + 4u = f(x)$

What would the homogenous equation be?

$\frac{d^2u}{dx^2} + 4u = 0$

3. so $U(x)=a\sin(2x)+b\cos(2x)$ for all a,b.