Exercise
$\frac{dy}{dx}=\frac{y}{x\left(x-x^3\right)}$
Step-by-step Solution
Learn how to solve problems step by step online. Solve the differential equation dy/dx=y/(x(x-x^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(x-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\frac{1}{y}dy and replace the result in the differential equation.
Solve the differential equation dy/dx=y/(x(x-x^3))
Final answer to the exercise
$y=\frac{C_1\sqrt{x+1}e^{\frac{1}{-x}}}{\sqrt{-x+1}}$