Exercise
$x\cdot\frac{dy}{dx}=\frac{1-x^3}{y^2}$
Step-by-step Solution
Learn how to solve differential equations problems step by step online. Solve the differential equation xdy/dx=(1-x^3)/(y^2). Group the terms of the differential equation. Move the terms of the y variable to the left side, and the terms of the x variable to the right side of the equality. Simplify the expression \frac{1}{x}\left(1-x^3\right)dx. Integrate both sides of the differential equation, the left side with respect to y, and the right side with respect to x. Solve the integral \int y^2dy and replace the result in the differential equation.
Solve the differential equation xdy/dx=(1-x^3)/(y^2)
Final answer to the exercise
$y=\sqrt[3]{3\left(\ln\left(x\right)+\frac{-x^{3}}{3}+C_0\right)}$