Exercise
$y'=\frac{xy}{y^2-1}$
Step-by-step Solution
Learn how to solve problems step by step online. Solve the differential equation y^'=(xy)/(y^2-1). Rewrite the differential equation using Leibniz notation. 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}\left(y^2-1\right)dy. 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 y^'=(xy)/(y^2-1)
Final answer to the exercise
$\frac{1}{2}y^2-\ln\left|y\right|=\frac{1}{2}x^2+C_0$