(adsbygoogle = window.adsbygoogle || []).push({}); X*U'_{x}+Y*U'_{y}=U

{U=1-x^{2}}

{y=1}

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dx/x=dy/y=du/u

[tex]\int[/tex]dx/x=[tex]\int[/tex]dy/y

ln|x|=ln|y|+ln|c_{1}|

x/y=c_{1}

[tex]\int[/tex]dx/x=[tex]\int[/tex]du/u

ln|x|=ln|u|+ln|c_{2}|

x/u=c_{2}

[tex]\Phi[/tex](x/u , x/y)=0

x/u=[tex]\phi[/tex](x/y)

now i use the conditions

{U=1-x^{2}}

{y=1}

x/(1-x^{2})=[tex]\phi[/tex](x)=x/u

and all i get is U=1-x^{2}but i already know that

the correct answer is u=(y^{2}-x^{2})/y

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# Homework Help: Partial differentail equation

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