anonymous
  • anonymous
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
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
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)
anonymous
  • anonymous
particular solution = 1/ (D^2 - D +1) * 8(x^3)
anonymous
  • anonymous
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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anonymous
  • anonymous
ah again yc= e^1/2 x (C1 cos sqrt(3)/2 x + C2 sin sqrt(3)/2 x)
anonymous
  • anonymous
why did you write: D^2 - D +1 =0 at the very beginning? Did you divide both sides by x squared?
anonymous
  • anonymous
this is auxiliary equation
anonymous
  • anonymous
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
anonymous
  • anonymous
still there buddy?
anonymous
  • anonymous
ok give me a sec...
anonymous
  • anonymous
so here we go...
anonymous
  • anonymous
put z=logx and xD=theta , x^2D^2= theta (theta -1)
anonymous
  • anonymous
1 sec
anonymous
  • anonymous
Your way may work but I don't think I've seen it in class...it's gotta be easier than we think
anonymous
  • anonymous
ok
anonymous
  • anonymous
thanks a lot though
anonymous
  • anonymous
you've been super helpful
anonymous
  • anonymous
no prob... i wish i cud help u a lot more.. :(

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