Multiplying a linear equation by its integrating factor x^2 gives d/dx(x^2y) = 3x^2. What is the general solution?

Homogeneous & Linear Differential Equations · Question 95 of 120

Question 95

EasyOriginal question

Multiplying a linear equation by its integrating factor $x^{2}$ gives $\frac{d}{dx}\left(x^{2}y\right) = 3x^{2}$ . What is the general solution?

y = x + C

Correct answerYour answer

y = x^{3} + C

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

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

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Show the answer and explanation

CorrectNot quiteAnswer D

Correct answer: D

Worth noting

$x + C$ divides $x^{3}$ by $x^{2}$ but leaves the constant undivided.

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

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