Bernouilli ODE (where is my mistake?)

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SUMMARY

The discussion centers on solving the ordinary differential equation (ODE) given by x²y' + 2xy - y³ = 0. The user identifies their mistake in the initial approach and successfully applies the substitution v = y⁻², transforming the equation into a linear form. The resulting equation is v' + (4/x)v = -2/x², which is now ready for further analysis and solution using standard techniques for linear ODEs.

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justaboy
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found my mistake... thanks
 
Last edited:
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justaboy said:

Homework Statement


Solve the ODE
[tex]x^2y'+2xy-y^3=0[/tex]



The Attempt at a Solution



[tex]x^2y'+2xy-y^3=0[/tex]
Substitution:
[tex]v=y^-2[/tex]
V makes the equation linear:
[tex]v'-4\frac{v}{x}=-2x^{-2}[/tex]

I get:

[tex]v'+\frac{4}{x} v=-\frac{2}{x^2}[/tex]
 

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