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Differential Equations problem 2

  • Thread starter Mastur
  • Start date
  • #1
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Homework Statement


[itex]2(2x^2+y^2)dx-xydy=0[/itex]

Homework Equations


[itex]let x = yv[/itex]

[itex]dx = ydv+vdy[/itex]

The Attempt at a Solution


[itex](4v^2y^2+2y^2)(ydv+vdy)-vy^2dy=0[/itex]

[itex]4v^2y^3dv+4v^3y^2dy+2y^3dv+2vy^2dy-vy^2dy=0[/itex]

[itex]4v^2y^3dv+2y^3dv+4v^3y^2dy+vy^2dy=0[/itex]

[itex]2y^3(2v^2+1)dv+y^2(4v^3+v)dy=0[/itex]
dividing all sides by y2
[itex]2y(2v^2+1)dv+(4v^3+v)dy=0[/itex]
combining all ydys and vdvs
[itex]\frac{(2v^2+1)dv}{(4v^3+v)}+\frac{dy}{2y}=0[/itex]

[itex]\int{\frac{(2v^2dv)}{4v^3+v}}+\int{\frac{dv}{4v^3+v}}+\int{\frac{dy}{2y}}=0[/itex]

Err.. I don't know what to do next.. I can only integrate the 3rd integral..:frown:
 

Answers and Replies

  • #2
Dick
Science Advisor
Homework Helper
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Two words. Partial fractions.
 
  • #3
41
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Naa, my memory.. I always forgot those!

Thank you very much for reminding! :biggrin:

I'll try to review first that partial fraction. It seems like I have forgotten the process of it already.
 

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