Question

P
solve the differential equation
dy /dx =y(x^2-1)/x(y^2-1)​

Answer 1

Step-by-step explanation:

We have,

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

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

$\implies \int \big(y - \frac{1}{y} \big) dy = \int\big(x - \frac{1}{x} \big) dx$

$\implies \frac{ {y}^{2} }{2} - ln(y) = \frac{ {x}^{2} }{2} - ln(x) + c$