1

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 ____

2

JEE Main 2021 (Online) 27th July Morning Shift

Numerical

+4

-1

If $$y = y(x),y \in \left[ {0,{\pi \over 2}} \right)$$ is the solution of the differential equation $$\sec y{{dy} \over {dx}} - \sin (x + y) - \sin (x - y) = 0$$, with y(0) = 0, then $$5y'\left( {{\pi \over 2}} \right)$$ is equal to ______________.

Your input ____

3

JEE Main 2021 (Online) 25th July Evening Shift

Numerical

+4

-1

Out of Syllabus

Let a curve y = f(x) pass through the point (2, (log

_{e}2)^{2}) and have slope $${{2y} \over {x{{\log }_e}x}}$$ for all positive real value of x. Then the value of f(e) is equal to ______________.Your input ____

4

JEE Main 2021 (Online) 25th July Morning Shift

Numerical

+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 ______________.

Your input ____

Questions Asked from Differential Equations (Numerical)

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