Exercise
$3y^2x\frac{dy}{dx}=1-2x^3$
Step-by-step Solution
Learn how to solve problems step by step online. Solve the differential equation 3y^2xdy/dx=1-2x^3. 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(1-2x^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 \int3y^2dy and replace the result in the differential equation.
Solve the differential equation 3y^2xdy/dx=1-2x^3
Final answer to the exercise
$y=\sqrt[3]{\ln\left(x\right)-\frac{2}{3}x^{3}+C_0}$