New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Differential Equations question

2011 · Shift 2 · Q32

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

PYQ Library
JEE Advanced
Mathematics
Differential Equations
2011 · Shift 2 · Q32

Differential Equations question

2011 · Shift 2 · Q32

JEE AdvancedMathematicsDifferential EquationsNumerical+4 / −1

Let

y'\left( x \right) + y\left( x \right)g'\left( x \right) = g\left( x \right),g'\left( x \right),y\left( 0 \right) = 0,x \in R,

where

f'(x)

denotes

{{df\left( x \right)} \over {dx}}

and

g(x)

is a given non-constant differentiable function on

R

with

g(0)=g(2)=0.

Then the value of

y(2)

is

Numerical answer

More from Differential Equations

Match the statements/expressions in Column I with the open intervals in Column II : Includes table2009 · MCQ
Match the statements/expressions in Column I with the values given in Column II: Includes table2009 · MCQ
Let a solution $y = y (x)$ of the differential equation, $x x^{2} - 1 d y - y y^{2} - 1 d x = 0$ satify $y (2) = \frac{2}{3} .$ STATEMENT-1 : $y (x) = sec (sec^{- 1} x - \frac{π}{6})$ …2008 · MCQ
For all x > 0, let y₁(x), y₂(x), and y₃(x) be the functions satisfying $\frac{d y _{1}}{d x} - (sin x)^{2} y_{1} = 0, y_{1} (1) = 5, \frac{d y _{2}}{d x} - (cos x)^{2} y_{2} = 0, y_{2} (1) = \frac{1}{3}, \frac{d y _{3}}{d x} - \frac{( 2 - x ^{3} )}{x ^{3}} y_{3} = 0, y_{3} (1) = \frac{3}{5 e},$ …2025 · Numerical
Let $y (x)$ be the solution of the differential equation $x^{2} \frac{d y}{d x} + x y = x^{2} + y^{2}, x > \frac{1}{e}$ satisfying $y (1) = 0$ . Then the value of $2 \frac{( y ( e ) ) ^{2}}{y ( e ^{2} )}$ is .2025 · Numerical
Let $f (x)$ be a continuously differentiable function on the interval $f (1) = 2$ such that $f (1) = 2$ and $t \to x lim \frac{t ^{10} f ( x ) - x ^{10} f ( t )}{t ^{9} - x ^{9}} = 1$ for each $x > 0$ . Then, for all $x > 0, f (x)$ is equal…2024 · MCQ
Let $f : [1, \infty) \to R$ be a differentiable function such that $f (1) = \frac{1}{3}$ and $3 1 \int x f (t) d t = x f (x) - \frac{x ^{3}}{3}, x \in [1, \infty)$ . Let $e$ denote the base of the natural logarithm. Then the value…2023 · MCQ
For $x \in R$ , let $y (x)$ be a solution of the differential equation $(x^{2} - 5) \frac{d y}{d x} - 2 x y = - 2 x (x^{2} - 5)^{2}$ such that $y (2) = 7$ . Then the maximum value of the function $y (x)$ is :2023 · Numerical