Find the general solution of the following differential equation: xdy/dx + y = y^2 ​

Question

Find the general solution of the following differential equation:

x\(\frac{dy}{dx}\) + y = y²

Answer 1

⇒ x.\(\frac{dy}{dx}\) + y = y²

Integrating on both the sides,

Comparing coefficients in both the sides,

A = - 1, B = 1

RHS:

\(\int\frac{1}{x}dx\)

\(\int\frac{1}{x}dx\) = log x + log c

Therefore the solution of the given differential equation is