# Math Help - 4th order DE

1. ## 4th order DE

$\frac{d^4y}{dx^4}-7\frac{d^2y}{dx^2}-18y=0$

$m^4e^{mx}-7m^2e^{mx}-18e^{mx} = 0$

$(m^4-7m^2-18)(e^{mx}) = 0$

$(m-3)(m+3)(m^2+2) = 0$

$m = 3, -3, \sqrt{2}i, -\sqrt{2}i$

Then, $y=c_1e^{3x}+c_2e^{-3x}+c_3cos(\sqrt{2}x)+c_4sin(\sqrt{2}x)+c_5cos(\sq rt{2}x)-c_6sin(\sqrt{2}x)$

2. remove the last two terms from your solution and then it's correct