# Non-linear ODE solution

#### idontknow

$$\displaystyle y''+2y=3e^x$$.

#### romsek

Math Team
$s^2 + 2 = 0\\ s = \pm i\sqrt{2}\\ y_h(x) = c_0 \cos(\sqrt{2}x) + c_1 \sin(\sqrt{2}x)$

$y_p(x) = c_2 e^x\\ c_2e^x + 2c_2 e^x = 3e^x\\ c_2 = 1\\ y_p(x) = e^x\\ y(x) = y_h(x) + y_p(x) = c_0 \cos(\sqrt{2}x) + c_1 \sin(\sqrt{2}x) + e^x$

This is a linear diff eq. It just has a driving function.