The question specifies the auxiliary eqution given is (D^2 + D - 2) = (e^x)/(x)
the method of variation of parameter must be used to find the particular solution to the right hand function. then finally the general soultion should be stated.
variation of paremeters formula.
yp = -y1∫y2 * g(x)/ (w(y1 , y2))
+ y2∫y1 * g(x)/ (w(y1 , y2))
The Attempt at a Solution
i had solved the complementary function and had gotten yc = c1e-x + c2e-2x. then after applying the formula for variation of parameters i had gotten e-x*lnx/3 - e-2x/3 * ∫e3x / x
i cannot obtain an integral for ∫e3x / x i dont think it can be done have tried various mathods eg by parts, there are no suitable substitutions is it that there is no integral for the expression? i.e. it cannot be integrated.