The general solution of d y d x + y tan x = sec x is:

Question

The general solution of $\frac{d y}{d x} + y \tan x = \sec x$ is:

Smart Achievers · Accepted Answer

(1)

Ans. $y \sec x = \tan x + C$

Explanation:

Given differential equation is

$\frac{d y}{d x} + y \tan x = \sec x$

which is a linear differential equation.

Here, $P = \tan x,$ $Q = \sec x$

$∴$ $IF = e^{\int \tan x d x} = e^{\log | \sec x |} = \sec x$

The general solution is

$y \cdot \sec x = \int \sec x \cdot \sec x d x + C$

$\Rightarrow$ $y \cdot \sec x = \int \sec^{2} x d x + C$

$\Rightarrow$ $y \sec x = \tan x + C$

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