Consider the following second order differential equation:

y'' - 2y' + y = (e^x) / 1+ (x^2)

a) Find two linearly independent solutions of the corresponding homogeneous differential equation y'' - 2y + y = 0. Use the Wronskian to show that they are linearly independent.

b) Use variation of parameters to find the general solution of the equation
y'' - 2y' + y = (e^x) / 1+ (x^2)

Question

Consider the following second order differential equation:

y'' - 2y' + y = (e^x) / 1+ (x^2)

a) Find two linearly independent solutions of the corresponding homogeneous differential equation y'' - 2y + y = 0. Use the Wronskian to show that they are linearly independent.

b) Use variation of parameters to find the general solution of the equation 
y'' - 2y' + y = (e^x) / 1+ (x^2)

anonymous · Answer

try "show steps" http://www.wolframalpha.com/input/?i=y%27%27+-+2y%27+%2B+y+%3D+%28e^x%29+%2F+%281%2B+%28x^2%29%29