Question

Integrating Factor of the differential equation $co{s}^{2}x\frac{dy}{dx}+y=tanx$ is____

• A. $e^{secx}$
• B. $e^{tanx}$
• C. $e^{sinx}$
• D. $e^{cosx}$

Answer 1

Answer: (B)

$e^{tanx}$

Given,

$co{s}^{2}x\frac{dy}{dx}+y=tanx$

$\frac{dy}{dx}+\frac{y}{{\cos }^{2}x}=\frac{\tan x}{{\cos }^{2}x}$...............(dividing by cos^2x in both LHS and RHS)

$I.F=e^{\int P\left(x\right)dx}$

$=e^{\int \frac{1}{{\cos }^{2}x}dx}=e^{\int {\sec }^{2}xdx}$

$=e^{\tan x}$