# For the Following Differential Equation, Find a Particular Solution Satisfying the Given Condition:- Cos ( D Y D X ) = a , Y = 1 When X = 0 - Mathematics

Sum

For the following differential equation, find a particular solution satisfying the given condition:- $\cos\left( \frac{dy}{dx} \right) = a, y = 1\text{ when }x = 0$

#### Solution

We have,

$\cos \left( \frac{dy}{dx} \right) = a$

$\Rightarrow \frac{dy}{dx} = \cos^{- 1} a$

$\Rightarrow dy = \cos^{- 1} a dx$

Integrating both sides, we get

$\int dy = \int \cos^{- 1} a dx$

$\Rightarrow y = x \cos^{- 1} a + C$

Now,

When x = 0, y = 1

$\therefore 1 = 0 + C$

$\Rightarrow C = 1$

Putting the value of C in (1), we get

$y = x \cos^{- 1} a + 1$

$\Rightarrow \cos\left( \frac{y - 1}{x} \right) = a$

Is there an error in this question or solution?

#### APPEARS IN

RD Sharma Class 12 Maths
Chapter 22 Differential Equations
Revision Exercise | Q 65.2 | Page 146