Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 12

# D Y D X + Y Tan X = X N Cos X , N ≠ − 1 - Mathematics

Sum

(dy)/(dx)+ y tan x = x^n cos x, n ne− 1

#### Solution

We have,

(dy)/(dx)+ y tan x = x^n cos x

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

$P = \tan x$

$Q = x^n \cos x$

Now,

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

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

$= \sec x$

So, the solution is given by

$y \times I . F . = \int Q \times I . F . dx + C$

$\Rightarrow y \sec x = \int x^n \cos x \sec x\ dx + C$

$\Rightarrow y \sec x = \int x^n dx + C$

$\Rightarrow y \sec x = \frac{x^{n + 1}}{n + 1} + C$

Is there an error in this question or solution?

#### APPEARS IN

RD Sharma Class 12 Maths
Chapter 22 Differential Equations
Revision Exercise | Q 61 | Page 146