Question

The solution of $\frac{dy}{dx} + 2y\tan x = \sin x$ is

• A. $y\sec^{3}x = \sec^{2}x + c$
• B. $y\sec^{3}x = \sec^{2}x + c$
• C. $y\sin x = \tan x + c$
• D. None of these

Answer 1

Answer: (B)

$y\sec^{3}x = \sec^{2}x + c$

Answer 2

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

$P = 2\tan x$, $Q = \sin x$

I.F.$= e^{\int_{}^{}{2\tan xdx}} = e^{2{lnsec}x} = e^{{lnsec}^{2}x} = \sec^{2}x$Multiplying given equation by I.F. and integrating, $y\sec^{2}x = \int_{}^{}{\sin x.\sec^{2}xdx} = \int_{}^{}{\sec x\tan xdx}$∴ $y\sec^{2}x = \sec x + c$