Question content area top

Part $1$

A general solution$$ y$($x$)$ of a homogeneous$$ second$-$order differential equation

a y prime prime plus b y prime plus cy equals $0$ay$+$by$+$cy$=0$

with constant coefficients is given. Find such an equation.

y left parenthesis x right parenthesis equals c $1$ e Superscript $2$ x Baseline plus c $2$ e Superscript negative $2$ x