New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Differential Equations question

2025 · 28 Jan · Shift 1 · Q39

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

PYQ Library
JEE Main
Mathematics
Differential Equations
2025 · 28 Jan · Shift 1 · Q39

Differential Equations question

2025 · 28 Jan · Shift 1 · Q39

JEE MainMathematicsDifferential EquationsMCQ+4 / −1

Let for some function

\mathrm{y}=f(x), \int_0^x t f(t) d t=x^2 f(x), x\gt 0

and

f(2)=3

. Then

f(6)

is equal to

A
1
B
6
C
2
D
3

More from Differential Equations

If $y = y (x)$ is the solution of the differential equation, $4 - x^{2} \frac{d y}{d x} = ((sin^{- 1} (\frac{x}{2}))^{2} - y) sin^{- 1} (\frac{x}{2}), - 2 \leq x \leq 2, y (2) = \frac{π ^{2} - 8}{4}$ …2025 · Numerical
Let y = y(x) be the solution of the differential equation : $cos x (lo g_{e} (cos x))^{2} d y + (sin x - 3 y sin x lo g_{e} (cos x)) d x = 0$ , x ∈ (0, $\frac{π}{2}$ ). If $y (\frac{π}{4})$ = $- \frac{1}{l o g _{e} 2}$ , then $y (\frac{π}{6})$ …2025 · MCQ
If for the solution curve $y = f (x)$ of the differential equation $\frac{d y}{d x} + (tan x) y = \frac{2 + s e c x}{( 1 + 2 s e c x ) ^{2}}$ , $x \in (\frac{- π}{2}, \frac{π}{2}), f (\frac{π}{3}) = \frac{3}{10}$ , then $f (\frac{π}{4})$ …2025 · MCQ
Let $y = y (x)$ be the solution of the differential equation $\frac{d y}{d x} = 2 x (x + y)^{3} - x (x + y) - 1, y (0) = 1$ . Then, $(\frac{1}{2} + y (\frac{1}{2}))^{2}$ equals :2024 · MCQ
If $x = x (t)$ is the solution of the differential equation $(t + 1) d x = (2 x + (t + 1)^{4}) dt, x (0) = 2$ , then, $x (1)$ equals .2024 · Numerical
Let $α$ be a non-zero real number. Suppose $f : R \to R$ is a differentiable function such that $f (0) = 2$ and $x \to - \infty lim f (x) = 1$ . If $f^{'} (x) = α f (x) + 3$ , for all $x \in R$ …2024 · MCQ
If $\frac{d x}{d y} = \frac{1 + x - y ^{2}}{y}, x (1) = 1$ , then $5 x (2)$ is equal to .2024 · Numerical
If the solution $y = y (x)$ of the differential equation $(x^{4} + 2 x^{3} + 3 x^{2} + 2 x + 2) d y - (2 x^{2} + 2 x + 3) d x = 0$ satisfies $y (- 1) = - \frac{π}{4}$ , then $y (0)$ is equal to :2024 · MCQ