What is the general solution of dy/dx = 2xy?

Differential Equations · Question 54 of 67

Question 54

MediumOriginal question

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

y = Ce^{2x}

Correct answerYour answer

y = Ce^{x^2}

Correct answerYour answer

y = x^2 + C

Correct answerYour answer

y = Ce^{-x^2}

Correct answerYour answer

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CorrectNot quiteAnswer B

Correct answer: B

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 $y = Ce^{x^2}$ .

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.