# Homogeneous linear ODEs with Constant Coefficients

#### Jester

##### Well-known member
MHB Math Helper
But $y = \sin x$ could work. For example,

$y'' + y = 0$

has as one solution $y = \sin x$.

#### dwsmith

##### Well-known member
But $y = \sin x$ could work. For example,

$y'' + y = 0$

has as one solution $y = \sin x$.
As long as the boundaries aren't $y'(0) = 0$ and $y'\left(\frac{\pi}{2}\right) = 0$ then y = 0.

But $y = A\sin x + B\cos x = e^0\left(A\sin x + B\cos x\right)$ is also a solution of the non boundary value problem.