# D Y D X − Y Cot X = C O S E C X - Mathematics

Sum

$\frac{dy}{dx} - y \cot x = cosec\ x$

#### Solution

We have,

$\frac{dy}{dx} - y \cot x = cosec\ x$

$\text{Comparing with }\frac{dy}{dx} + Py = Q,\text{ we get}$

$P = - \cot x$

$Q = cosec\ x$

Now,

$I . F . = e^{\int - \cot x\ dx}$

$= e^{- \log \left| \left( \sin x \right) \right|}$

$= e^{\log \left| \left(cosec\ x \right) \right|}$

$= cosec x$

So, the solution is given by

$y\ cosec\ x = \int cosec\ x \times cosec\ x\ dx + C$

$\Rightarrow y\ cosec\ x = \int {cosec}^2 x dx + C$

$\Rightarrow y\ cosec\ x = - \cot x + C$

Is there an error in this question or solution?

#### APPEARS IN

RD Sharma Class 12 Maths
Chapter 22 Differential Equations
Revision Exercise | Q 40 | Page 146