New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Differential Equations question

2024 · 4 Apr · Shift 2 · Q57

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

PYQ Library
JEE Main
Mathematics
Differential Equations
2024 · 4 Apr · Shift 2 · Q57

Differential Equations question

2024 · 4 Apr · Shift 2 · Q57

JEE MainMathematicsDifferential EquationsNumerical+4 / −1

Let

y=y(x)

be the solution of the differential equation

(x+y+2)^2 d x=d y, y(0)=-2

. Let the maximum and minimum values of the function

y=y(x)

in

\left[0, \frac{\pi}{3}\right]

be

\alpha

and

\beta

, respectively. If

(3 \alpha+\pi)^2+\beta^2=\gamma+\delta \sqrt{3}, \gamma, \delta \in \mathbb{Z}

, then

\gamma+\delta

equals

\underline{\hspace{2cm}}

.

Numerical answer

More from Differential Equations

If $y = y (x)$ is the solution of the differential equation $\frac{d y}{d x} + 2 y = sin (2 x), y (0) = \frac{3}{4}$ , then $y (\frac{π}{8})$ is equal to :2024 · MCQ
The differential equation of the family of circles passing through the origin and having centre at the line $y = x$ is :2024 · MCQ
Let $y = y (x)$ be the solution of the differential equation $\frac{d y}{d x} + \frac{2 x}{( 1 + x ^{2} ) ^{2}} y = x e^{\frac{1}{( 1 + x ^{2} )}}; y (0) = 0.$ Then the area enclosed by the curve $f (x) = y (x) e^{- \frac{1}{( 1 + x ^{2} )}}$ …2024 · Numerical
Let $y = y (x)$ be the solution of the differential equation $(2 x lo g_{e} x) \frac{d y}{d x} + 2 y = \frac{3}{x} lo g_{e} x, x > 0$ and $y (e^{- 1}) = 0$ . Then, $y (e)$ is equal to2024 · MCQ
Let $y = y (x)$ be the solution of the differential equation $(1 + x^{2}) \frac{d y}{d x} + y = e^{t a n^{- 1} x}$ , $y (1) = 0$ . Then $y (0)$ is2024 · MCQ
Suppose the solution of the differential equation $\frac{d y}{d x} = \frac{( 2 + α ) x - β y + 2}{β x - 2 α y - ( β γ - 4 α )}$ represents a circle passing through origin. Then the radius of this circle is :2024 · MCQ
If the solution $y (x)$ of the given differential equation $(e^{y} + 1) cos x d x + e^{y} sin x d y = 0$ passes through the point $(\frac{π}{2}, 0)$ , then the value of $e^{y (\frac{π}{6})}$ …2024 · Numerical
Let $f (x)$ be a positive function such that the area bounded by $y = f (x), y = 0$ from $x = 0$ to $x = a > 0$ is $e^{- a} + 4 a^{2} + a - 1$ . Then the differential equation, whose general solution is $y = c_{1} f (x) + c_{2}$ , where $c_{1}$ and $c_{2}$ are arbitrary…2024 · MCQ