What is the general solution of dy/dx = x^2/y^2?

Differential Equations · Question 51 of 67

Question 51

EasyOriginal question

What is the general solution of $\frac{dy}{dx} = \frac{x^2}{y^2}$ ?

y^3 + x^3 = C

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y^2 - x^2 = C

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y^3 - x^3 = C

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y = x + C

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CorrectNot quiteAnswer C

Correct answer: C

Separate the variables, with every $y$ on the side of $dy$ and every $x$ on the side of $dx$ .
Integrating both sides and collecting the constants gives $y^3 - x^3 = C$ .

Worth noting

Check an answer by differentiating it: it must give back the equation.

Ten questions from Differential Equations, at your own pace.

Ten questions from Differential Equations, at your own pace.