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

Differential Equations · Question 53 of 67

Question 53

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

e^y = e^{-x} + C

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e^{x + y} = C

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e^y = e^x + C

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y = e^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 $e^y = e^x + C$ .

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.