New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Differential Equations question

2015 · Shift 1 · Q28

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

PYQ Library
JEE Advanced
Mathematics
Differential Equations
2015 · Shift 1 · Q28

Differential Equations question

2015 · Shift 1 · Q28

JEE AdvancedMathematicsDifferential EquationsMultiple correct+4 / −2

Let

y(x)

be a solution of the differential equation

\left( {1 + {e^x}} \right)y' + y{e^x} = 1.

If

y(0)=2

, then which of the following statement is (are) true?

A
$y(-4)=0$
B
$y(-2)=0$
C
$y(x)$ has a critical point in the interval $(-1, 0)$
D
$y(x)$ has no critical point in the interval $(-1,0)$

More from Differential Equations

Consider the family of all circles whose centres lie on the straight line $y = x,$ If this family of circle is represented by the differential equation $P y^{''} + Q y^{'} + 1 = 0,$ where $P, Q$ are functions of $x, y$ and $y^{'}$ $(h er e y^{'} = \frac{d y}{d x}, y^{''} = \frac{d ^{2} y}{d x ^{2}})$ …2015 · Multiple correct
The function $y = f (x)$ is the solution of the differential equation $\frac{d y}{d x} + \frac{x y}{x ^{2} - 1} = \frac{x ^{4} + 2 x}{1 - x ^{2}}$ in $(- 1, 1)$ satisfying $f (0) = 0$ . Then $- \frac{3}{2} \int \frac{3}{2} f (x) d (x)$ …2014 · MCQ
A curve passes through the point $(1, \frac{π}{6})$ . Let the slope of the curve at each point $\frac{y}{x} + sec (\frac{y}{x}), x > 0.$ be $\frac{y}{x} + sec (\frac{y}{x}), x > 0.$ Then the equation of the curve is2013 · MCQ
If $y (x)$ satisfies the differential equation $y^{'} - y t an x = 2 x sec x$ and $y (0) = 0,$ then2012 · Multiple correct
Let $f : [1, \infty) \to [2, \infty)$ be a differentiable function such that $f (1) = 2$ . If $6 1 \int x f (t) d t = 3 x f (x) - x^{3} - 5$ for all $x \geq 1$ , then the value of f(2) is .2011 · Numerical
Let $y^{'} (x) + y (x) g^{'} (x) = g (x), g^{'} (x), y (0) = 0, x \in R,$ where $f^{'} (x)$ denotes $\frac{df ( x )}{d x}$ and $g (x)$ is a given non-constant…2011 · Numerical
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