Question

solve the differential equation (x^2logx)dy/dx =2y​

Answer 1

Step-by-step explanation:

We have,

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

$\implies \frac{dy}{2y} = \frac{dx}{ {x}^{2} log(x) }$

Integrating both sides, we have,

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

Let log(x) = t

=> dx = x dt

$\implies \frac{1}{2} log(y) = \int \: \frac{x \: dt}{x^{2} \:. t}$

$\implies \frac{1}{2} log(y) = \int \frac{dt}{ {e}^{t} t}$