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 (π/2, 0 ) , then the value of e y (π/6 ) is equal to

Mathematics · Differential Equations

JEE Main 2024 — 6 April, Shift 2 — Question 30

If the solution $y(x)$ of the given differential equation $\left(e^{y}+1\right) \cos x d x+e^{y} \sin x d y=0$ passes through the point

$\left(\frac{\pi}{2}, 0\right)$ , then the value of $e^{y\left(\frac{\pi}{6}\right)}$ is equal to $\qquad$

Numerical answer — enter this value.

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

$\Rightarrow \mathrm{d}\left(\left(\mathrm{e}^{\mathrm{y}}+1\right) \sin \mathrm{x}\right)=0$

$\left(e^{y}+1\right) \sin x=C$

It passes through $\left(\frac{\pi}{2}, 0\right)$

$\Rightarrow \mathrm{c}=2$

Now, $x=\frac{\pi}{6}$

$\Rightarrow \mathrm{e}^{\mathrm{y}}=3$

Answer key and solution verified before publishing.

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