What is the general solution of xdy/dx - 2y = x^3?

Homogeneous & Linear Differential Equations · Question 103 of 120

Question 103

MediumOriginal question

What is the general solution of $x\frac{dy}{dx} - 2y = x^{3}$ ?

y = x^{3} + Cx^{2}

Correct answerYour answer

y = x^{3} + C

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y = \frac{x^{3}}{3} + Cx^{2}

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y = x^{3} + \frac{C}{x^{2}}

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Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

Divide by $x$ : $\frac{dy}{dx} - \frac{2}{x}y = x^{2}$ , with factor $\frac{1}{x^{2}}$ .
$\frac{y}{x^{2}} = \int 1\,dx = x + C$ , so $y = x^{3} + Cx^{2}$ .

Worth noting

$x^{3} + C$ forgets to multiply the constant by $x^{2}$ .

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

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