Question

Plugging in 4e^(2x) into (d^2 *y)/(dx^2) - 4y should produce 0. I must be plugging it into the wrong area or something because I am not getting 0

Answer 1

I believe what they mean is plug \(4e^{2x}\)into \(y\):\[
\frac{d^2y}{dx^2} = \frac{d^2}{dx^2}\bigg(4e^{2x}\bigg) = \frac{d}{dx}\bigg(8e^{2x}\bigg) = 16e^{2x}
\]And \[
4y = 4(4e^{2x}) =16e^{2x}
\]So \[
\frac{d^2y}{dx^2} - 4y = 16e^{2x}- 16e^{2x}=0

\]