Solving a Nonlinear Differential Equation

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URGENT: Differential Equation

Homework Statement

Use suitable substitutions to solve the following equation:

y' + xy = y^3

Homework Equations

dy/dx + P(x)y = Q(x)

I(x) = e^(integral(P(x)dx)

y = (Integral of(I(x)Q(x)))/I(x)

The Attempt at a Solution

dy/dx + xy = y^3

P(x) = x, Q(x) = y^3

I(x) = e^((x^2)/2)

y = (integral of (e^((x^2)/2))*y^3)/(e^((x^2)/2))

**This is not a multi-variable calculus class.

 

[mark126]

Hello, my professor just replied regarding this question, I no longer need help. Thanks though!