Can someone please help me! I know I'm messing something up but I'm not sure where! The question is:
Find a particular solution of the differential equation

(-5/4)y''−2y'+y=2xe^(4x)
using the Method of Undetermined Coefficients (primes indicate derivatives with respect to x).

Question

Can someone please help me! I know I'm messing something up but I'm not sure where! The question is:
Find a particular solution of the differential equation

(-5/4)y''−2y'+y=2xe^(4x)
using the Method of Undetermined Coefficients (primes indicate derivatives with respect to x).

anonymous · Answer

i found r to be -2 and(2/5) hihc i then found the complementary solution to be yc=c1e^(2/5x)+c2e^-2x

yp=Ae^x +Be^x

anonymous · Answer

y'p=the same thing as yp and so does y''p(x)

anonymous · Answer

then i plugged it in and ended up with e^x ((-9/4)A-(9/4)B)=2xe^x

anonymous · Answer

which i assume is  wrong because I cannot solve for the variable

phi · Answer

shouldn't it be
$$ y_p=Axe^{4x} +Be^{4x} $$

anonymous · Answer

omg yes! thanks!