Question

Help please

Find a particular solution of the given equation:

y"-5'+2y=(2-6x-2x^2) e^x

Answer 1

this would be more help than i could give
http://www.wolframalpha.com/input/?i=y%27%27-5y%27%2B2y+%3D+2e^x%281-3x-x^2%29
if you register with site you can see step-by-step solution
also to get particular solution you need initial values?

Answer 2

to get you started, always solve the characteristic equation
r^2 -5r +2 = 0
\[r = \frac{5 \pm \sqrt{17}}{2}\]

Answer 3

As for the particular solution, as a guess, try
\[y_p=e^x(Ax^2+Bx+C)\]

Answer 4

You might need "variation of parameters" here.