JEE Main 2019 · Mathematics · Differential Equations · hard

If y=y(x) solves x dy/dx=x+y for x>0 with y(1)=2, then y(e) is

Single correct option

y=y(x)

solves

x\,\dfrac{dy}{dx}=x+y

for

x>0

with

y(1)=2

, then

y(e)

Show answer and solution

Answer: (B) $3e$

Write

y'-\dfrac yx=1

; integrating factor

\dfrac1x

. Then

\dfrac{d}{dx}\left(\dfrac yx\right)=\dfrac1x\Rightarrow\dfrac yx=\ln x+C

y(1)=2

gives

C=2

, so

y=x\ln x+2x

and

y(e)=e+2e=3e

Original question written in the JEE Main 2019 pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake