Exercise
$\frac{dy}{dx}=\frac{\left(x+1\right)y^5}{x^2\left(2y^3-y\right)}$
Step-by-step Solution
Learn how to solve problems step by step online. Solve the differential equation dy/dx=((x+1)y^5)/(x^2(2y^3-y)). 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}{y^5}\left(2y^3-y\right)dy. Simplify the expression \left(x+1\right)\frac{1}{x^2}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 differential equation dy/dx=((x+1)y^5)/(x^2(2y^3-y))
Final answer to the exercise
$\frac{-6y^{2}+1}{3y^{3}}=\ln\left|x\right|+\frac{1}{-x}+C_0$