Verifying solutions of ODEs

f1player

Junior Member
Joined
Feb 25, 2005
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Verify that the given function is a solution of the differential equation:

x^2 + y^2 = cy ; y' = (2xy)/(x^2 - y^2)

Here's what i've done:

Implicit differentiation on LHS: 2x + 2y(dy/dx) = c

The c im assuming is just a constant??

Now however i manipulate that i cant make it equal to y' = (2xy)/(x^2 - y^2)
 
f1player said:
Verify that the given function is a solution of the differential equation:

x^2 + y^2 = cy ; y' = (2xy)/(x^2 - y^2)

Here's what i've done:

Implicit differentiation on LHS: 2x + 2y(dy/dx) = c(dy/dx)
2x = c(dy/dx) - 2y(dy/dx)
2x/(c - 2y) = dy/dx
2xy/(cy - 2y<sup>2</sup>) = dy/dx
2xy/(x<sup>2</sup> + y<sup>2</sup> - 2y<sup>2</sup>) = dy/dx
2xy/(x<sup>2</sup> - y<sup>2</sup>) = dy/dx


The c im assuming is just a constant??

Now however i manipulate that i cant make it equal to y' = (2xy)/(x^2 - y^2)
 
Yeah thanks for that quick reply. I knew i stuffed up the constant in that.
 
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