NDA 2025 Maths · Mathematics · Differential Equations · medium

Find the general solution of the equation xdy/dx+y=x^2 for x>0.

Single correct option

Find the general solution of the equation

x\dfrac{dy}{dx}+y=x^2

for

x>0

Show answer and solution

Answer: (C) $xy=\dfrac{x^3}3+C$

The left side is

\frac{d}{dx}(xy)

, so

\frac{d}{dx}(xy)=x^2

and

xy=\frac{x^3}3+C

, i.e.

y=\frac{x^2}3+\frac Cx

. The option

y=\frac{x^3}{3}+C

ignores the product

xy

xy=\frac{x^2}2+C

integrates

x

instead of

x^2

, and

y=x^2+C

is not a solution.

Original question written in the NDA 2025 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake