d^2y/dx^2 = 6x, with y = 1 and dy/dx = 2 when x = 0. What is y?

Differential Equations · Question 28 of 67

Question 28

MediumOriginal question

$\frac{d^2y}{dx^2} = 6x$ , with $y = 1$ and $\frac{dy}{dx} = 2$ when $x = 0$ . What is $y$ ?

y = x^3 + x + 2

Correct answerYour answer

y = 3x^2 + 2x + 1

Correct answerYour answer

y = x^3 + 2x + 1

Correct answerYour answer

y = x^3 + 1

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer C

Correct answer: C

Integrate once: $\frac{dy}{dx} = 3x^2 + A$ ; $\frac{dy}{dx} = 2$ at $x = 0$ gives $A = 2$ .
Integrate again: $y = x^3 + 2x + B$ ; $y = 1$ at $x = 0$ gives $B = 1$ .

Worth noting

$y = x^3 + 1$ uses only the condition on $y$ ; an order-2 equation needs both constants fixed.

Ten questions from Differential Equations, at your own pace.

Ten questions from Differential Equations, at your own pace.