What is the general solution of dy/dx = 1 + y^2?

Differential Equations · Question 59 of 67

Question 59

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What is the general solution of $\frac{dy}{dx} = 1 + y^2$ ?

\tan^{-1} y = x + C

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y = \tan x

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y + \frac{y^3}{3} = x + C

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\log(1 + y^2) = x + C

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CorrectNot quiteAnswer A

Correct answer: A

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 $\tan^{-1} y = x + C$ .

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.