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Cant solve diff-eq with substitution

  1. Jan 17, 2005 #1
    Use subs [tex]y=xv[/tex] to show that [tex](x^2+y^2)+2xy\frac{dy}{dx}=0, x>0[/tex] is [tex] x^3+3xy^2=k[/tex] where k is a constant.

    I played around with this at school and if memory serves me correct i got something similar to [tex]\frac{dx}{dv}=\frac{-3}{2xv}-\frac{1}{2}[/tex] and after that i decided i wasnt on the right path and stopped. Need a little help here ! :smile:
     
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  3. Jan 17, 2005 #2

    arildno

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    x is to remain the independent variable; v(x) is the dependent variable which replaces y(x)
     
  4. Jan 17, 2005 #3
    What is v? Is v a function or a constant??
     
  5. Jan 17, 2005 #4

    arildno

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    v is defined as the function:
    [tex]v(x)=\frac{y(x)}{x}[/tex]
     
  6. Jan 17, 2005 #5

    HallsofIvy

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    If y= xv, then dy/dx= x dv/dx+ v. Put that into your equation and replace y by xv and see what happens.
     
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