Transforming a Differential Equation: Tips and Tricks

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In summary, the conversation is about converting a general solution to a differential into a more simplified form. The desired form is y = (x^(-2))[c+-((c^2) + x^5)^(1/2)]. The participants discuss using the quadratic formula to solve for y and realizing it is a simple conversion.
  • #1
discoverer02
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I need to put this general solution to a differential in the following form:

My solution is in the form (-x^3)(y^(-1)) + (x^2)y = C

It needs to be in the form y = (x^(-2))[c+-((c^2) + x^5)^(1/2)]

I've been noodling around with it for a while and it's not working out for me. Does anyone something I can factor out or multiply by that will put it into a friendlier form?

Thanks.
 
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  • #2
You've got:
[tex]\frac{-x^3}{y}+x^2y=C[/tex]
[tex]-x^3=Cy-x^2y^2[/tex]
Which is a quadratic equation in [tex]y[/tex].
[tex]x^2y^2-Cy-x^3=0[/tex]
Apply the quadratic formula, and you should get there.
 
  • #3
Multiply through by y and you have a quadratic equation in the y variable.

cookiemonster
 
  • #4
Thanks.

I should have seen this. It's a no brainer. Where was my brain last night?[zz)]
 

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