What is its general solution?

Question 104

MediumOriginal question

Consider the linear differential equation $\frac{dy}{dx} + 2xy = 2x$ .

y = 1 + Ce^{x^{2}}

Correct answerYour answer

y = 1 + Ce^{-x^{2}}

Correct answerYour answer

y = x^{2} + Ce^{-x^{2}}

Correct answerYour answer

y = Ce^{-x^{2}}

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer B

Correct answer: B

$\frac{d}{dx}\left(ye^{x^{2}}\right) = 2xe^{x^{2}}$ , so $ye^{x^{2}} = e^{x^{2}} + C$ .
$y = 1 + Ce^{-x^{2}}$ .

Worth noting

$Ce^{-x^{2}}$ solves the equation with the right side 0, dropping the 1 that $2x$ adds.

Ten questions from Homogeneous & Linear Differential Equations, at your own pace.

Ten questions from Homogeneous & Linear Differential Equations, at your own pace.