I am given this equation: $$ y''(x) y(x) - 4 y(x) = -4e^{4x} $$ And I am asked to start off by finding the solution to the homogeneous equation.
First, I am confused as to why the above equation is said to be constant coefficient. Wouldn't the $y''(x)$ being multiplied to $y(x)$ mean that it is not a constant coefficient equation? But, our teacher did not teach us how to solve for equation that are not constant coefficient, and strictly said that we will not look at those equations now.
I went on to solve for the homogeneous solution by equating the right hand side of the equation to zero. I got the characteristic equation: $q^2 -4=0$, $\longrightarrow$ $q=+2$ or $-2$.
So, i then got that the general homog. solution is: $Ae^{2t} + Be^{-2t}$, for $A,B$ constants.
But, this is wrong.