Could someone tell me the steps of solving this 2nd order differential equation? (x^2)y'' - x y' + y = 8(x^3) Is it Euler's equations for the left side and method of undertermined coeffficients for the right side? Thanks!!!

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Could someone tell me the steps of solving this 2nd order differential equation? (x^2)y'' - x y' + y = 8(x^3) Is it Euler's equations for the left side and method of undertermined coeffficients for the right side? Thanks!!!

Mathematics
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the A.E. is D^2 - D +1 =0 D= 1+- SQRT(3) i/ 2 yc= e^1/2 (C1 cos sqrt(3)/2 + C2 sin sqrt(3)/2)
particular solution = 1/ (D^2 - D +1) * 8(x^3)
sry an error in typing. yc= e^1/2 (C1 cos sqrt(3)/2 x + C2 sin sqrt(3)/2 x)

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ah again yc= e^1/2 x (C1 cos sqrt(3)/2 x + C2 sin sqrt(3)/2 x)
why did you write: D^2 - D +1 =0 at the very beginning? Did you divide both sides by x squared?
this is auxiliary equation
yeah but you can't just ignore the x squared right? i know the quadratic formula but i am not sure if this is the case here
still there buddy?
ok give me a sec...
so here we go...
put z=logx and xD=theta , x^2D^2= theta (theta -1)
1 sec
Your way may work but I don't think I've seen it in class...it's gotta be easier than we think
ok
thanks a lot though
you've been super helpful
no prob... i wish i cud help u a lot more.. :(

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