What is the best substitution for solving this ODE?

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SUMMARY

The discussion focuses on solving the ordinary differential equation (ODE) given by x²y' + 2xy = 5y³. The user struggles with finding an appropriate substitution and attempts to manipulate the equation by moving terms and dividing by x². The suggested approach involves recognizing the equation as a Bernoulli differential equation, which can be solved using the substitution y = vx, where v is a function of x. This substitution simplifies the equation and allows for further analysis and solution.

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So I am trying to figure out what substitution to use for the following ODE substitution:
x^2*y' + 2xy = 5y^3; I initially moved the 2xy to the right but to no avail because when I tried to divide through by x^2 (to clear the left), I struggle to get the y/x format on the right. If the solution is obvious, I apologize, but we get zip examples in class and apparently I'm not good enough to figure this out on my own.
 
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Try dividing by x2 and then http://en.wikipedia.org/wiki/Bernoulli_differential_equation" :wink:.
 
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