Question

Find a general solution for the differential equation
-􀀀y'' = 6x + x cos x
(a) using the method of undetermined coefficients.
(b) using variation of parameters.
(c) using the D-operator method.

Answer 1

I have determined that the Variation of parameters may not work because the auxillary equation
\[-m ^{2}= 0\]
will give me
\[y _{c}=c _{1}+c _{2}x\]
and making my Wronsikian = 0 OR AM I WRONG?

I got it correctly using the D-Operator method
It is the method of undet coeffs that is bringing me down! I tried both superposition and the Annihilator approch but I cant seem to crack it.

Answer 2

heres a reference:
http://tutorial.math.lamar.edu/Classes/DE/VariationofParameters.aspx

i think the Wronsikian would be 1 not 0
f(x) = 1 , g(x) = x
W = fg' + f'g = 1

Answer 3

looks like you need to split this
y'' = 6x
y'' = xcosx

and then use this as a guide

http://math.stackexchange.com/questions/747990/general-solution-to-a-second-order-nonhomogeneous-differential-equation/748061#748061

Answer 4

thank you guys