# Exact equations

First determine if the equation is exact. If it is exact, find the general solution, or at least a relation that defines the solutions implicitly:

[cos(x^2 + y) - 3xy^2]y' + 2x cos(x^2 + y) - y^3=0

https://brainmass.com/math/basic-algebra/exact-equations-implicit-differentiation-13774

#### Solution Preview

To find whether it is exact or not we shall rewrite it as:

[cos(x^2 + y) - 3xy^2]dy+[2x cos(x^2 + y) - y^3]dx=0

Then

p(x,y)=2x cos(x^2 + y) - y^3

Q(x,y)=cos(x^2 + y) - 3xy^2

The derivative of P wrt y would ...

#### Solution Summary

This shows how to find if an equation is exact. The implicit differentiation is provided.

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