Question

(again)Solve by Laplace transform:
\[\frac{d^2y}{dx^2} + a \frac{dy}{dx} - 2a^2y=0\]
y(0)=6, y'(0) = 0

Answer 1

\[\frac{d^2y}{dx^2} + a \frac{dy}{dx} - 2a^2y=0\]\[sY'-0 +a(sY-6)-2a^2Y=0\]\[s(sY-6) +a(sY-6)-2a^2Y=0\]\[(s^2+as-2a^2)Y=6a+6s\]\[Y=\frac{6a+6s}{(s+2a)(s-a)}\]So far so good? Or...??