D^2y/dx^2+4dy/dx-12y=cos2x

If you're solving for x, you'd move all the terms containing x to the left side of the equation:

d^2y/dx^2+4y/x-12y-cos^2 (x) + sin^2 (x) = 0

If you're solving for y, you'd simplify both sides of the equation, then isolating the variable:

y=xcos (2x)