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