QJEEM17Ma65e1: JEE Main 2017 Mathematics - Class 12 JEEM17Ma65e1 Solution: If ( 2 + sin ⁡ x ) d y d x + ( y + 1 ) cos ⁡ x = 0 and y(0) =…

Question

Verified Solution • 2025–26 Session moderate

If

(2 + \sin x) \frac{d y}{d x} + (y + 1) \cos x = 0

and y(0) = 1,

then

y (\frac{π}{2})

is equal to :

Accepted Answer

(2 + \sin x) \frac{d y}{d x} + (y + 1) \cos x = 0

\Rightarrow

\frac{d}{d x} (2 + \sin x) (y + 1) = 0

On integrating, we get

(2 + sin x) (y + 1) = C

At x = 0, y = 1 we have

(2 + sin 0) (1 + 1) = C

\Rightarrow

C = 4

\Rightarrow

(y + 1) = \frac{4}{2 + \sin x}

\Rightarrow

y =

\frac{4}{2 + \sin x} - 1

Now

y (\frac{π}{2}) = \frac{4}{2 + \sin \frac{π}{2}} - 1

=

\frac{4}{3} - 1

=

\frac{1}{3}

Step-by-Step Verified Solution