JEE Main 2022 · 29 Jul · Shift 1 · Mathematics Q7

← JEE Main 2022 · 29 Jul · Shift 1

MathematicsSingle correct+4 / -1Question 7 of 90

Let the solution curve $y=y(x)$ of the differential equation $\left(1+e^{2x}\right)\left(\dfrac{dy}{dx}+y\right)=1$ pass through the point $\left(0,\dfrac\pi2\right)$ . Then, $\displaystyle\lim_{x\to\infty}e^xy(x)$ is equal to :

\dfrac\pi4

\dfrac{3\pi}4

\dfrac\pi2

\dfrac{3\pi}2

Answer and worked solution

Official answer: B

Integrate. $\dfrac d{dx}(e^xy)=\dfrac{e^x}{1+e^{2x}}$ , so $e^xy=\tan^{-1}e^x+C$ ; at $x=0$ , $\frac\pi2=\frac\pi4+C$ .

Limit $\frac\pi2+\frac\pi4=\frac{3\pi}4$ .

(B)

Topics:Linear first-order equations Limits

← Previous question Next question →

JEE Main 2022 · 29 Jul · Shift 1, Mathematics question 7