Question

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!!!

Answer 1

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)

Answer 2

particular solution = 1/ (D^2 - D +1) * 8(x^3)

Answer 3

sry an error in typing.
yc= e^1/2 (C1 cos sqrt(3)/2 x + C2 sin sqrt(3)/2 x)

Answer 4

ah again
yc= e^1/2 x (C1 cos sqrt(3)/2 x + C2 sin sqrt(3)/2 x)

Answer 5

why did you write: D^2 - D +1 =0 at the very beginning? Did you divide both sides by x squared?

Answer 6

this is auxiliary equation

Answer 7

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

Answer 8

still there buddy?

Answer 9

ok give me a sec...

Answer 10

so here we go...

Answer 11

put z=logx and xD=theta , x^2D^2= theta (theta -1)

Answer 12

1 sec

Answer 13

Your way may work but I don't think I've seen it in class...it's gotta be easier than we think

Answer 14

ok

Answer 15

thanks a lot though

Answer 16

you've been super helpful

Answer 17

no prob... i wish i cud help u a lot more.. :(