The solution of the equation d y d x = ^2 y is : - Vidyadip

MCQ

The solution of the equation $\frac{d y}{d x}=\cos ^2 y$ is :

A
$x+\tan y=c$
✓
$\tan y=x+c$
C
$\sin y+x=c$
D
$\sin y-x=c$

✓

Answer

Correct option: B.

$\tan y=x+c$

(B)
$
\begin{aligned}
\frac{d y}{d x} & =\cos ^2 y \\
\Rightarrow \quad \frac{1}{\cos ^2 y} d y & =d x \Rightarrow \sec ^2 y d y=d x
\end{aligned}
$
Hence
$
\begin{aligned}
\int \sec ^2 y d y & =\int d x \\
\tan y & =x+c
\end{aligned}
$
Therefore the correct choice is (B).

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