Step-by-step Solution

Solve the differential equation $\frac{dy}{dx}=\frac{y^2-1}{x^2-1}$

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Step-by-step explanation

Problem to solve:

$\frac{dy}{dx}=\frac{\left(y^2-1\right)}{\left(x^2-1\right)}$

Learn how to solve differential equations problems step by step online.

$\frac{1}{y^2-1}dy=\frac{1}{x^2-1}dx$

Unlock this full step-by-step solution!

Learn how to solve differential equations problems step by step online. Solve the differential equation dy/dx=(y^2-1)/(x^2-1). 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. Integrate both sides, the left side with respect to y, and the right side with respect to x. Solve the integral \int\frac{1}{y^2-1}dy and replace the result in the differential equation. Solve the integral \int\frac{1}{x^2-1}dx and replace the result in the differential equation.

Final Answer

$-\frac{1}{2}\ln\left(y+1\right)+\frac{1}{2}\ln\left(y-1\right)=\frac{1}{2}\ln\left(\frac{x-1}{x+1}\right)+C_0$

Problem Analysis