NDA 2025 Maths · Mathematics · Differential Equations · medium

If dy/dx=1+y^2 and y(0)=0, then y((π)/(4)) is equal to

Single correct option

\dfrac{dy}{dx}=1+y^2

and

y(0)=0

, then

y\left(\dfrac\pi4\right)

is equal to

Show answer and solution

Answer: (A) $1$

Separate variables:

\frac{dy}{1+y^2}=dx

, so

\tan^{-1}y=x+C

. From

y(0)=0

C=0

, so

y=\tan x

and

y\left(\frac\pi4\right)=1

. The value

\frac\pi4

\tan^{-1}y

rather than

y

, and

0

is the initial value. Verify:

\frac{d}{dx}\tan x=\sec^2x=1+\tan^2x

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