\left(y + \left(3 x^2\right) y + x^2\right) dx + \left(x + x^3\right) dy = 0

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$\left(y+3x^2y+x^2\right)dx+\left(x+x^3\right)dy=0$

Learn how to solve problems step by step online. \left(y + \left(3 x^2\right) y + x^2\right) dx + \left(x + x^3\right) dy = 0. Math interpretation of the question. The differential equation \left(y+3x^2y+x^2\right)dx+\left(x+x^3\right)dy=0 is exact, since it is written in the standard form M(x,y)dx+N(x,y)dy=0, where M(x,y) and N(x,y) are the partial derivatives of a two-variable function f(x,y) and they satisfy the test for exactness: \displaystyle\frac{\partial M}{\partial y}=\frac{\partial N}{\partial x}. In other words, their second partial derivatives are equal. The general solution of the differential equation is of the form f(x,y)=C. Using the test for exactness, we check that the differential equation is exact. Integrate M(x,y) with respect to x to get.