Solve the following nonhomogeneous equations y y 6y 2x y

Solve the following nonhomogeneous equations y\" + y\' - 6y = 2x y\" + 3y\' - 4y = e2x y\" + 4y = 3sin 2x Solve the following nonhomogeneous equations y\" + y\' - 6y = 2x y\" + 3y\' - 4y = e2x y\" + 4y = 3sin 2x

Solution

a.)y(x) = c_1 e^(-3 x)+c_2 e^(2 x)-x/3-1/18
b.)y(x) = c_1 e^(-4 x)+c_2 e^x-(e^2 x)/4-(3 e^2)/16