- #1

FeynmanIsMyHero

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I'm having trouble with this ODE:

*y' + 4xy - y^2 = 4x^2 - 7*

*=> y' = 4x^2 - 4xy + y^2 - 7*

= (2x - y)^2 - 7

=> x(dv/dx) + v = (2x-vx)^2 - 7

= x^2(2-v)^2 - 7

= (2x - y)^2 - 7

=> x(dv/dx) + v = (2x-vx)^2 - 7

= x^2(2-v)^2 - 7

I assume this ODE is of the homogeneous type, so I've substituted

*v=y/x*and gotten thus far, but, what's the next step?