Solve the following differential equation:
$\cos^{2} x \frac{dy}{dx} + y = tanx$

Solution

$\cos^{2} x \frac{dy}{dx} + y = \tan x \frac{dy}{dx} + \sec^{2} x . y = \tan x . \sec^{2} x$

It is a linear differential equation of the first order.

comparing it with $\frac{dy}{dx} + py = Q,$ we get:

P = sec²x and Q = tanx.sec²x

$Integration factor = e^{\int P dx} = e^{\int \sec^{2} x dx} = e^{\tan x} The solutoin of the given linear differential equation is given as : y e^{\tan x} = \int \tan x . \sec^{2} x . e^{\tan x} dx + C Let \tan x = t \Rightarrow \sec^{2} x dx = dt y e^{t} = \int t . e^{t} . dt + C y e^{t} = t . e^{t} - \int 1 . e^{t} . dt + C y e^{t} = t . e^{t} - e^{t} + C y e^{t} = e^{t} (t - 1) + C y e^{\tan x} = e^{\tan x} \tan x - 1 + C y = \tan x - 1 + C e^{- \tan x}$

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Differential Equations

Solve the following differential equation:
$\cos^{2} x \frac{dy}{dx} + y = tanx$

Some More Questions From Differential Equations Chapter

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

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For Daily Free Study Material Join wiredfaculty

Differential Equations

Solve the following differential equation:cos2 x dydx + y = tanx

Some More Questions From Differential Equations Chapter

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Solve the following differential equation:
$\cos^{2} x \frac{dy}{dx} + y = tanx$