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

Differential Equations · Question 64 of 67

Question 64

HardOriginal question

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

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

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y = x + C

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

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

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Show the answer and explanation

CorrectNot quiteAnswer D

Correct answer: D

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

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.