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petapan123
Help please Find a particular solution of the given equation: y"-5'+2y=(2-6x-2x^2) e^x
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?
to get you started, always solve the characteristic equation r^2 -5r +2 = 0 \[r = \frac{5 \pm \sqrt{17}}{2}\]
As for the particular solution, as a guess, try \[y_p=e^x(Ax^2+Bx+C)\]
You might need "variation of parameters" here.