Obtain the general solution using undetermined coefficients method (differential equations): (D^2 - 1) y = 8xe^x

Question

Obtain the general solution using undetermined coefficients method (differential equations):   (D^2 - 1) y = 8xe^x

anonymous · Answer

Find the homogeneous solution first:

Using characteristic Equation:

$$m^2 - 1 = 0$$

m = -1 ,-1

anonymous · Answer

m = 1 and -1 Sorry..

anonymous · Answer

For 1 and -1 solution is given by:

$y_c = Ae^x + Be^{-x}$

anonymous · Answer

Now make a guess what will you take for particular solution???

anonymous · Answer

particular solution is Ae^x + Bxe^x

anonymous · Answer

No I think.

anonymous · Answer

no. the homogeneous solution is Ae^x+Be^-x

anonymous · Answer

You can't take because there is already $e^x$ in the homogeneous solution..

anonymous · Answer

now , obtain the particular solution by substituting , A(x) and B(x) in place of A and B. and then substituting this in the original equation.

anonymous · Answer

ok,

anonymous · Answer

ok lets solve it

anonymous · Answer

@sami-21 , I advise not to post solutions.

anonymous · Answer

ok @vamgadu