New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Differential Equations question

2025 · 3 Apr · Shift 2 · Q33

Guest · try one question or challengeGuest · try one question or challenge

PYQ Library
JEE Main
Mathematics
Differential Equations
2025 · 3 Apr · Shift 2 · Q33

Differential Equations question

2025 · 3 Apr · Shift 2 · Q33

JEE MainMathematicsDifferential EquationsMCQ+4 / −1

Let

y=y(x)

be the solution of the differential equation

\frac{d y}{d x}+3\left(\tan ^2 x\right) y+3 y=\sec ^2 x, y(0)=\frac{1}{3}+e^3

. Then

y\left(\frac{\pi}{4}\right)

is equal to :

A
$\frac{4}{3}$
B
$\frac{2}{3}+e^3$
C
$\frac{4}{3}+e^3$
D
$\frac{2}{3}$

More from Differential Equations

If a curve $y = y (x)$ passes through the point $(1, \frac{π}{2})$ and satisfies the differential equation $(7 x^{4} cot y - e^{x} cosec y) \frac{d x}{d y} = x^{5}, x \geq 1$ , then at $x = 2$ …2025 · MCQ
Let $y = y (x)$ be the solution curve of the differential equation $x (x^{2} + e^{x}) d y + (e^{x} (x - 2) y - x^{3}) d x = 0, x > 0$ , passing through the point $y (2)$ . Then $y (2)$ is equal to :2025 · MCQ
Let y = y(x) be the solution of the differential equation $(x^{2} + 1) y^{'} - 2 x y = (x^{4} + 2 x^{2} + 1) cos x$ , $y (0) = 1$ . Then $- 3 \int 3 y (x) d x$ is :2025 · MCQ
Let $f (x) = x - 1$ and $g (x) = e^{x}$ for $x \in R$ . If $\frac{d y}{d x} = (e^{- 2 x} g (f (f (x))) - \frac{y}{x})$ , $y (0) = 0$ , then $y (1)$ is2025 · MCQ
Let $x = x (y)$ be the solution of the differential equation $y^{2} d x + (x - \frac{1}{y}) d y = 0$ . If $x (1) = 1$ , then $x (\frac{1}{2})$ is :2025 · MCQ
Let $f (x)$ be a real differentiable function such that $f (0) = 1$ and $f (x + y) = f (x) f^{'} (y) + f^{'} (x) f (y)$ for all $x, y \in R$ . Then $\sum_{n = 1}^{100} lo g_{e} f (n)$ is equal to :2025 · MCQ
Let $f : R \to R$ be a twice differentiable function such that $f (x + y) = f (x) f (y)$ for all $x, y \in R$ . If $f^{'} (0) = 4 a$ and $f$ satisfies $f^{''} (x) - 3 a f^{'} (x) - f (x) = 0, a > 0$ …2025 · MCQ
If $x = f (y)$ is the solution of the differential equation $(1 + y^{2}) + (x - 2 e^{t a n^{- 1} y}) \frac{d y}{d x} = 0, y \in (- \frac{π}{2}, \frac{π}{2})$ with $f (0) = 1$ , then $f (\frac{1}{3})$ …2025 · MCQ