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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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
yeah or you can use vartiation of parameters
anonymous
  • anonymous
thanks but how do you solve for the left side of the equation which now looks: y'' - (1/x) y' + y/(xsquared) = 8x
anonymous
  • anonymous
you leave the left side as it is and solve for the characteristic equation using cauchy eulers

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anonymous
  • anonymous
and i would use variation of parametesr after because i actually don't think undetermined coefficients work
anonymous
  • anonymous
so apply euler right off the bat to the left side which is : y'' - 2y' + y = 0 and use variation of parameters to get the particular solution?
anonymous
  • anonymous
yes but when you apply variation of parameters remember to get a coefficient of 1 on y'' so that your g(t)=x
anonymous
  • anonymous
what do you mean by getting a coefficient of 1 on y''?
anonymous
  • anonymous
because the form to use variation of parameters is y''+q(t)y'+p(t)y=g(t)
anonymous
  • anonymous
yeahh my bad...thanks a lot
anonymous
  • anonymous
Could you verbally tell me the steps of solving this system of differential equations as well? Thanks!!! x'= x-y+z y'= x+y-z z'= 2x-y
anonymous
  • anonymous
you take the laplace of each equation and then cancel to try to get X Y or Z by itself and then inverse laplace that to solve for that and plug back in to solve for other two.. it's an algebraic nightmare so i suggest you use wolfram to help simplify things :P
anonymous
  • anonymous
Okok thanks at least i know how to attack it now. Thanks a lot. Do you engineers use DE everyday?
anonymous
  • anonymous
DE is probably one of the most useful maths compared to the other ones. But technically I haven't even taken my DE course yet, I just learned it on my own right now. I have it next semester, so I can plan on skipping class :P. And it does show up quite a bit in engineering, though in real life, most DE are most likely solved by a computer. It is still crucial to understand how they work and the meaning behind them though
nikvist
  • nikvist
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anonymous
  • anonymous
what method is that nikvist? i've never seen that method before =o
nikvist
  • nikvist
this is the product rule
anonymous
  • anonymous
why is y = xz?
nikvist
  • nikvist
this is substitution \[y(x)=x\cdot z(x)\]
nikvist
  • nikvist
replace x=0 in starting differential equation, you will get y=0 \[\Rightarrow\quad y(x)=x\cdot z(x)\]
anonymous
  • anonymous
thanks a lot! do you know how to use power series here instead?
anonymous
  • anonymous
yeah i know product rule is involved but isnt there a name for the method?
anonymous
  • anonymous
spacenight: what he did is called "reduction of order" but in order to do that we needed to know 1 of the 2 solutions. He just assumed y1(x) = x here.
anonymous
  • anonymous
so i don't think he started off the right way
anonymous
  • anonymous
http://www.physicsforums.com/showthread.php?t=151779
anonymous
  • anonymous
lol oh yeah i know reduction of order, i just didnt know why y=xz is an assumed solution.. hm that's weird, i'd prefer to just do it the other way, that's how it was done in our homework for us

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