Exact Equations

The 1st order ODE:

(6xy - y^3)dx + (4y + 3x^2 - 3xy^2)dy = 0

is exact as:

Partials

Solutions to the ODE are given implicitly by:

2y^2 + 3x^2y - xy^3 = C

The slope field and several solution curves are shown below:

Slope field and solution curves

C = −6, −4, −2, 0, 2, 4, 6, 8, 10, 12


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