The general solution of the differential equation d^2y/dx^2 - 4 dy/dx + 4y = 0 is?
The general solution of the differential equation d^2y/dx^2 - 4 dy/dx + 4y = 0 is?
Explanation
The given differential equation is a second-order linear homogeneous equation with constant coefficients. The characteristic equation is:
r^2 - 4r + 4 = 0
which has a repeated root r = 2. Therefore, the general solution is:
y = (c1 + c2x)e^2x
where c1 and c2 are arbitrary constants.