1

JEE Main 2022 (Online) 26th June Morning Shift

Numerical

+4

-1

Let the solution curve y = y(x) of the differential equation

$$(4 + {x^2})dy - 2x({x^2} + 3y + 4)dx = 0$$ pass through the origin. Then y(2) is equal to _____________.

Your input ____

2

JEE Main 2022 (Online) 26th June Morning Shift

Numerical

+4

-1

Let $$S = (0,2\pi ) - \left\{ {{\pi \over 2},{{3\pi } \over 4},{{3\pi } \over 2},{{7\pi } \over 4}} \right\}$$. Let $$y = y(x)$$, x $$\in$$ S, be the solution curve of the differential equation $${{dy} \over {dx}} = {1 \over {1 + \sin 2x}},\,y\left( {{\pi \over 4}} \right) = {1 \over 2}$$. If the sum of abscissas of all the points of intersection of the curve y = y(x) with the curve $$y = \sqrt 2 \sin x$$ is $${{k\pi } \over {12}}$$, then k is equal to _____________.

Your input ____

3

JEE Main 2021 (Online) 27th August Morning Shift

Numerical

+4

-1

Out of Syllabus

If $${y^{1/4}} + {y^{ - 1/4}} = 2x$$, and

$$({x^2} - 1){{{d^2}y} \over {d{x^2}}} + \alpha x{{dy} \over {dx}} + \beta y = 0$$, then | $$\alpha$$ $$-$$ $$\beta$$ | is equal to __________.

$$({x^2} - 1){{{d^2}y} \over {d{x^2}}} + \alpha x{{dy} \over {dx}} + \beta y = 0$$, then | $$\alpha$$ $$-$$ $$\beta$$ | is equal to __________.

Your input ____

4

JEE Main 2021 (Online) 27th July Evening Shift

Numerical

+4

-1

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

^{$$\alpha$$x + y}dx; $$\alpha$$ $$\in$$ N. If y(log_{e}2) = log_{e}2 and y(0) = log_{e}$$\left( {{1 \over 2}} \right)$$, then the value of $$\alpha$$ is equal to _____________.Your input ____

Questions Asked from Differential Equations (Numerical)

Number in Brackets after Paper Indicates No. of Questions

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