New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Differential Equations question

2021 · 25 Jul · Shift 1 · Q38

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

PYQ Library
JEE Main
Mathematics
Differential Equations
2021 · 25 Jul · Shift 1 · Q38

Differential Equations question

2021 · 25 Jul · Shift 1 · Q38

JEE MainMathematicsDifferential EquationsNumerical+4 / −1

Let y = y(x) be solution of the following differential equation

{e^y}{{dy} \over {dx}} - 2{e^y}\sin x + \sin x{\cos ^2}x = 0,y\left( {{\pi \over 2}} \right) = 0

If

y(0) = {\log _e}(\alpha + \beta {e^{ - 2}})

, then

4(\alpha + \beta )

is equal to

\underline{\hspace{2cm}}

.

Numerical answer

More from Differential Equations

Let y = y(x) be the solution of the differential equation xdy = (y + x3 cosx)dx with y( $π$ ) = 0, then $y (\frac{π}{2})$ is equal to :2021 · MCQ
Let y = y(x) be a solution curve of the differential equation $(y + 1) tan^{2} x d x + tan x d y + y d x = 0$ , $x \in (0, \frac{π}{2})$ . If $x \to 0 + lim x y (x) = 1$ , then the value of $y (\frac{π}{4})$ …2021 · MCQ
Let y(x) be the solution of the differential equation 2x2 dy + (ey $-$ 2x)dx = 0, x > 0. If y(e) = 1, then y(1) is equal to :2021 · MCQ
The rate of growth of bacteria in a culture is proportional to the number of bacteria present and the bacteria count is 1000 at initial time t = 0. The number of bacteria is increased by 20% in 2 hours. If the population of bacteria is…2021 · MCQ
The difference between degree and order of a differential equation that represents the family of curves given by $y^{2} = a (x + \frac{a}{2})$ , a > 0 is .2021 · Numerical
If y = y(x) is the solution of the equation $e^{s i n y} cos y \frac{d y}{d x} + e^{s i n y} cos x = cos x$ , y(0) = 0; then $1 + y (\frac{π}{6}) + \frac{3}{2} y (\frac{π}{3}) + \frac{1}{2} y (\frac{π}{4})$ …2021 · Numerical
Let y = y(x) be the solution of the differential equation $\frac{d y}{d x} = 2 (y + 2 sin x - 5) x - 2 cos x$ such that y(0) = 7. Then y( $π$ ) is equal to :2021 · MCQ
Let us consider a curve, y = f(x) passing through the point ( $-$ 2, 2) and the slope of the tangent to the curve at any point (x, f(x)) is given by f(x) + xf'(x) = x2. Then :2021 · MCQ