What is the general solution of d^2y/dx^2 = 0?

Differential Equations · Question 18 of 67

Question 18

EasyOriginal question

What is the general solution of $\frac{d^2y}{dx^2} = 0$ ?

y = ax + b

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y = c

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y = ax

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y = 0

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Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

Integrating once, $\frac{dy}{dx} = a$ ; integrating again, $y = ax + b$ .
A second-order equation needs two arbitrary constants, $a$ and $b$ : every straight line.

Worth noting

$y = ax$ has one constant, too few for a second-order equation; it is only a particular family.

Ten questions from Differential Equations, at your own pace.

Ten questions from Differential Equations, at your own pace.