What is the general solution of xdy/dx = x + 2y?

Homogeneous & Linear Differential Equations · Question 41 of 120

Question 41

MediumOriginal question

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

y = Cx^{2} + x

Correct answerYour answer

y = Cx^{2} - x

Correct answerYour answer

y = Cx - x

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y = Cx^{2}

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Show the answer and explanation

CorrectNot quiteAnswer B

Correct answer: B

$y = vx$ : $v + x\frac{dv}{dx} = 1 + 2v$ , so $\frac{dv}{1 + v} = \frac{dx}{x}$ .
$\log\lvert 1 + v \rvert = \log\lvert x \rvert + c$ , so $1 + \frac{y}{x} = Cx$ : $y = Cx^{2} - x$ .

Worth noting

$y = Cx^{2} + x$ moves the 1 across without changing its sign.

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

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