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Homogeneous & Linear Differential Equations · Question 101 of 120

With y = 3 when x = 0, what is y when x = 1?

Question 101

MediumOriginal question

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

With $y = 3$ when $x = 0$ , what is $y$ when $x = 1$ ?

\frac{2}{e}

Correct answerYour answer

\frac{3}{e}

Correct answerYour answer

\frac{2}{e} + 1

Correct answerYour answer

1 + 2 e

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer C

Correct answer: C

$y = 1 + 2e^{-x^{2}}$ .
At $x = 1$ : $1 + \frac{2}{e}$ .

Worth noting

$1 + 2e$ drops the minus sign in the exponent $-x^{2}$ .

Concept: A particular solution of a homogeneous equation
Typical timeTypical: 120 s
Your timeYours: —

The rule this testsSolving linear equations

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