# X Cos X D Y D X + Y ( X Sin X + Cos X ) = 1 - Mathematics

Sum

x cos x(dy)/(dx)+y(x sin x + cos x)=1

#### Solution

We have,

$x \cos x\frac{dy}{dx} + y \left( x \sin x + \cos x \right) = 1$

$\Rightarrow \frac{dy}{dx} + \left( \tan x + \frac{1}{x} \right)y = \frac{1}{x \cos x}$

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

$P = \tan x + \frac{1}{x}$

$Q = \frac{1}{x \cos x}$

Now,

$I . F . = e^{\int\left( \tan x + \frac{1}{x} \right) dx} = e^{\log \left| x \sec x \right|} = x \sec x$

So, the solution is given by

$xy \sec x = \int \sec^2 x dx + C$

$\Rightarrow xy \sec x = \tan x + C$

Is there an error in this question or solution?

#### APPEARS IN

RD Sharma Class 12 Maths
Chapter 22 Differential Equations
Revision Exercise | Q 56 | Page 146