Solution of $\cos x\frac{dy}{dx}+y\sin x

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Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Differential Equations

Question:

Solution of $\cos x\frac{dy}{dx}+y\sin x = 1$ is:

Options:

y sec x tan x = c

y sec x = tan x + c

y tan x = sec x + c

y tan x = sec x tan x + c

Correct Answer:

y sec x = tan x + c

Explanation:

$\frac{dy}{dx}+y\tan x=\sec x;I.F.=e^{\int\tan xdx}=e^{\log \sec x}=\sec x$

$y\sec x=\int\sec^2 xdx$ ⇒ y sec x = tan x + c