Search any question & find its solution
Question:
Answered & Verified by Expert
The solution of the differential equation $x \frac{d y}{d x}=\cot y$ is
Options:
Solution:
1898 Upvotes
Verified Answer
The correct answer is:
$x \cos y=c$
Given, $x \frac{d y}{d x}=\cot y$
$$
\Rightarrow \quad \tan y d y=\frac{d x}{x}
$$
On integrating, we get
$$
\begin{array}{ll}
\Rightarrow & \int \tan y d y=\int \frac{d x}{x} \\
\Rightarrow & \log \sec y=\log x+\log c_1 \\
\Rightarrow & \log \sec y=\log x \cdot c_1 \\
\Rightarrow & \sec y=x \cdot c_1 \\
\Rightarrow & x \cos y=c, \\
\text { where } c=\frac{1}{c_1}
\end{array}
$$
$$
\Rightarrow \quad \tan y d y=\frac{d x}{x}
$$
On integrating, we get
$$
\begin{array}{ll}
\Rightarrow & \int \tan y d y=\int \frac{d x}{x} \\
\Rightarrow & \log \sec y=\log x+\log c_1 \\
\Rightarrow & \log \sec y=\log x \cdot c_1 \\
\Rightarrow & \sec y=x \cdot c_1 \\
\Rightarrow & x \cos y=c, \\
\text { where } c=\frac{1}{c_1}
\end{array}
$$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.