Which of these is the standard form of a differential equation that is linear in $x$ ?

\frac{dx}{dy} + P_{1}x = Q_{1}

, with

P_{1}

Q_{1}

functions of

x

Correct answerYour answer

\frac{dx}{dy} + P_{1}x = Q_{1}

, with

P_{1}

Q_{1}

functions of

y

Correct answerYour answer

\frac{dy}{dx} + P_{1}x = Q_{1}

, with

P_{1}

Q_{1}

functions of

y

Correct answerYour answer

\frac{dx}{dy} + P_{1}x^{2} = Q_{1}

, with

P_{1}

Q_{1}

functions of

y

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer B

Correct answer: B

With $x$ as the unknown, $y$ is the independent variable, so the derivative is $\frac{dx}{dy}$ .
$x$ appears only to the first power, and $P_{1}$ , $Q_{1}$ may depend on $y$ alone.

Worth noting

$P_{1}$ and $Q_{1}$ cannot contain $x$ , the unknown; they are functions of $y$ .

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

Which of these is the standard form of a differential equation that is linear in xxx?