What is the general solution of dy/dx + ytan x = sec x?

Homogeneous & Linear Differential Equations · Question 114 of 120

Question 114

HardOriginal question

What is the general solution of $\frac{dy}{dx} + y\tan x = \sec x$ ?

y = \sin x + C\sec x

Correct answerYour answer

y = \tan x + C\cos x

Correct answerYour answer

y = \cos x + C\sin x

Correct answerYour answer

y = \sin x + C\cos x

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer D

Correct answer: D

The factor is $e^{\int \tan x\,dx} = \sec x$ : $\frac{d}{dx}(y\sec x) = \sec^{2}x$ .
$y\sec x = \tan x + C$ , so $y = \sin x + C\cos x$ .

Worth noting

$\tan x + C\cos x$ divides only the constant by $\sec x$ , not $\tan x$ .

Ten questions from Homogeneous & Linear Differential Equations, at your own pace.

Ten questions from Homogeneous & Linear Differential Equations, at your own pace.