Which equation has its variables separable?

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

Correct answerYour answer

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

Correct answerYour answer

\frac{dy}{dx} = \sin(xy)

Correct answerYour answer

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

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer B

Correct answer: B

Separable means $\frac{dy}{dx} = f(x)g(y)$ : a product of a function of $x$ alone and a function of $y$ alone.
$x^2y$ is such a product, so $\frac{dy}{y} = x^2\,dx$ . A sum such as $x + y$ cannot be split this way.

Worth noting

$x + y$ is a sum, not a product; that equation is linear, a Section B1 method.

Ten questions from Differential Equations, at your own pace.

Ten questions from Differential Equations, at your own pace.

Explanation