Find the particular solution of the differential equation $\frac{dy}{dx} + 2 y \tan x = \sin x$ , given that y = 0 when $x = \frac{π}{3}$

Solution

$\frac{dy}{dx} + (2 \tan x) y = \sin x \frac{dy}{dx} + py = Q P = 2 \tan x and Q = \sin x I . F = e^{\int Pdx} = e^{2 \int \tan x dx} = e^{2 In \sec x} = e^{In \sec^{2} x} = \sec^{2} x soln . y (I . F) = \int Q (I . F) dx y . \sec^{2} x = \int \sin x . \sec^{2} x dx y \sec^{2} x = \int \tan x \sec x dx y \sec^{2} x = \sec x + C Given y = 0 x = \frac{π}{3} \sec \frac{π}{3} + C = 0 C = - \sec \frac{π}{3} = - 2 ∴ y \sec^{2} x = \sec x - 2 y \sec^{2} x - \sec x + 2 = 0$

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Differential Equations

Find the particular solution of the differential equation $\frac{dy}{dx} + 2 y \tan x = \sin x$ , given that y = 0 when $x = \frac{π}{3}$

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Differential Equations

Find the particular solution of the differential equation dydx + 2 y tan x = sin x, given that y = 0 when x = π3

Some More Questions From Differential Equations Chapter

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Find the particular solution of the differential equation $\frac{dy}{dx} + 2 y \tan x = \sin x$ , given that y = 0 when $x = \frac{π}{3}$