Find the general solution of the following nonhomogeneous second order differential equation: y" - 4y = e^2x

Solution is

Step-by-step explanation:

the given equation y''-4y can be written as

The Complementary function thus becomes

y=c_{1}e^{m_{1}x}+c_{2}e^{m_{2}x}

where are the roots of the

The roots of are +2,-2 Thus the comlementary function becomes

here are arbitary constants

Now the Particular Integral becomes using standard formula

Hence the solution is = Complementary function + Particular Integral

Thus Solution becomes