The equation of the curve through the or

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Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Differential Equations

Question:

The equation of the curve through the origin satisfying the equation dy = (sec x + y tan x) dx is :

Options:

y sin x = x

y cos x = x

y tan x = x

none of these

Correct Answer:

y cos x = x

Explanation:

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

I.F. = $e^{-\int \tan x d x}=\cos x$

$y \cos x=\int \sec x \cos x d x=x+c$

$y \cos x=x+c$

At (0, $\theta$), y cos x = x Since c = 0

Hence (2) is the correct answer.