If the solution y(x) of the given differential equation passes through the point , then the value of is equal to _________. [2024]

STUDY MATERIALS
COURSES
MORE
SUCCESS STORY
ADMISSION
STORE

Back

JEE ADVANCE

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

JEE MAIN

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

NEET

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

BITSAT

CLASS XI - XII

CLASS XI - XII

CBSE BOARD

CLASS IX

CLASS X

CLASS XI

CLASS XII

CLASS VI

CLASS VII

CLASS VIII

UP BOARD

CLASS IX
CLASS X
CLASS XI
CLASS XII

CLASS IX

CLASS X

CLASS XI

CLASS XII

CUET

CRASH COURSE

CRASH COURSE

Courses

CLASSROOM COURSES
ONLINE COURSES

ONLINE COURSES

More

Solution

Q.
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 $e^{y (\frac{π}{6})}$ is equal to _________. [2024]

Ans.
(3)

Givem, $(e^{y} + 1) \cos x d x + e^{y} \sin x d y = 0$

$\Rightarrow d (e^{y} \sin x) + \cos x d x = 0 \Rightarrow e^{y} \sin x + \sin x = C$

The curve passes through $(\frac{π}{2}, 0)$

$\Rightarrow C = 2 \Rightarrow e^{y} \sin x + \sin x = 2$

$\Rightarrow (e^{y (\frac{π}{6})} \frac{1}{2} + \frac{1}{2}) = 2 \Rightarrow e^{y (\frac{π}{6})} + 1 = 4 \Rightarrow e^{y (\frac{π}{6})} = 3$ .

Want Us to Email you About Special Offers & Updates?