The integrating factor of the differential equation \(x\displaystyle\frac{dy}{dx} - y = 2x^2\) is :
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(\displaystyle\frac{1}{x}\)
Dividing by x puts the equation in the standard linear form \(\frac{dy}{dx} + Py = Q\):
\( \displaystyle \frac{dy}{dx} - \frac{1}{x}\,y = 2x \)
So \(P = -\frac{1}{x}\), and the integrating factor is
\( \displaystyle e^{\int P\,dx} = e^{-\int \frac{1}{x}\,dx} \)
\( \displaystyle = e^{-\log x} = \frac{1}{x} \)
NCERT (2026-27 edition):
Linear Differential Equations
