Which of these differential equations is linear in $y$ ?

\frac{dy}{dx} + y^{2} = x

Correct answerYour answer

y\frac{dy}{dx} + x = 0

Correct answerYour answer

\frac{dy}{dx} = \sin y

Correct answerYour answer

\frac{dy}{dx} + xy = \sin x

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer D

Correct answer: D

Linear in $y$ means the form $\frac{dy}{dx} + Py = Q$ with $P$ , $Q$ functions of $x$ only.
Only $\frac{dy}{dx} + xy = \sin x$ fits, with $P = x$ and $Q = \sin x$ .

Worth noting

$y\frac{dy}{dx}$ multiplies $y$ by its derivative, which a linear equation never does.

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

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

Which of these differential equations is linear in yyy?