JEE Main 2026 · 2 Apr · Shift 1 · Mathematics Q17

← JEE Main 2026 · 2 Apr · Shift 1

MathematicsSingle correct+4 / -1Question 17 of 75

If the curve $y=f(x)$ passes through the point $(1,e)$ and satisfies the differential equation $dy=y\left(2+\log_ex\right)dx$ , $x>0$ , then $f(e)$ is equal to :

e^e

e^{e^2}

e^{2e}

e^{2^e}

Answer and worked solution

Official answer: C

Separate. $\dfrac{dy}y=(2+\ln x)\,dx$ , so $\ln y=x+x\ln x+C$ .

Constant. At $(1,e)$ : $1=1+C$ , so $C=0$ .

Value. $\ln f(e)=e+e=2e$ , so $f(e)=e^{2e}$ .

(C)

Topics:Variable separable

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JEE Main 2026 · 2 Apr · Shift 1, Mathematics question 17