Which of these differential equations is NOT of the variables separable type?

\frac{dy}{dx} = xy

Correct answerYour answer

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

Correct answerYour answer

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

Correct answerYour answer

\frac{dy}{dx} = e^{x}e^{y}

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer B

Correct answer: B

Separable means $\frac{dy}{dx} = g(x)h(y)$ , a product of a function of $x$ and a function of $y$ .
$xy$ , $\frac{x}{y}$ and $e^{x}e^{y}$ are such products; $x + y$ is a sum and cannot be split this way.

Worth noting

$e^{x}e^{y} = e^{x + y}$ looks like a sum in the power, but it is a product of two functions.

Ten questions from Differential Equations, at your own pace.

Explanation