Find the particular solution of the differential equation satisfying the given conditions:
$\frac{dy}{dx} = y \tan x$ , given that y = 1 when x= 0.

Solution

$\frac{dy}{dx} = y \tan x \Rightarrow \frac{dy}{y} = \tan x dx$

On integration, we get

$\int \frac{dy}{y} = \int \tan x dx \Rightarrow \log y = \log (\sec x) + \log C . . . . . . . . (i) \Rightarrow \log y = \log (C \sec x) \Rightarrow y = C \sec x$

Now, it is given that y = 1 when x = 0

$\Rightarrow 1 = C x \sec 0 \Rightarrow 1 = C x 1 ∴ C = 1$

substituting C = 1 in equation (i), we get

y = sec x as the required particular solution.

For Daily Free Study Material Join wiredfaculty

Differential Equations

Find the particular solution of the differential equation satisfying the given conditions:
$\frac{dy}{dx} = y \tan x$ , given that y = 1 when x= 0.

Some More Questions From Differential Equations Chapter

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Phone Number

Email Address

Loaction

For Daily Free Study Material Join wiredfaculty

Differential Equations

Find the particular solution of the differential equation satisfying the given conditions:dydx = y tan x, given that y = 1 when x= 0.

Some More Questions From Differential Equations Chapter

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Find the particular solution of the differential equation satisfying the given conditions:
$\frac{dy}{dx} = y \tan x$ , given that y = 1 when x= 0.