show y = c e^(y/x) is soln to dy/dx = (y^2) / (xy - X^2)

sunny1324

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Jul 12, 2008
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show that y=c e ^ (y/x) is a solution to dy/dx = (y^2) / (xy - X^2)

i need help solving this problem please. here's how i did it:

dy/dx = c e ^(y/x) (-y/(x^2) + 1/x dy/dx)
dy/dx = c e ^(y/x) (- y +x / (x^2) )
c = y/ (e ^ (y/x) )
dy/dx = (-y^2 + xy)/ (x^2)

please tell me where my mistake is and how can i fix it

thanks a lot
 
"y/dx = c e ^(y/x) (- y +x / (x^2) ) "

You lost "dy/dx" somewhere.
 
sunny1324 said:
show that y=c e ^ (y/x) is a solution to dy/dx = (y^2) / (xy - X^2)

i need help solving this problem please. here's how i did it:

dy/dx = c e ^(y/x) (-y/(x^2) + 1/x dy/dx)

dy/dx = y * (-y/(x^2) + 1/x dy/dx)

dy/dx - y/x * dy/dx = - y^2/x^2
 
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