Question

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

Answer 1

Find the homogeneous solution first:

Using characteristic Equation:

\[m^2 - 1 = 0\]

m = -1 ,-1

Answer 2

m = 1 and -1 Sorry..

Answer 3

For 1 and -1 solution is given by:

\(y_c = Ae^x + Be^{-x}\)

Answer 4

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

Answer 5

particular solution is Ae^x + Bxe^x

Answer 6

No I think.

Answer 7

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

Answer 8

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

Answer 9

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.

Answer 10

ok,

Answer 11

ok lets solve it

Answer 12

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

Answer 13

ok @vamgadu