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problem on differential equations (higher order)

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 solve y"-y = xe^(3x)
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find the complementary function
observe the R.H.S and the C.F.
since the RHS is different from the RHS use the
pattern of (Ax+B)e^(3x) for the particular integral
differentiate twice and the substitute in the given equation
to find A and B
answer and  some steps are given below
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(trig. formulae) 





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