Which of the following statements are true? I. The order of d^2y/dx^2 + (dy/dx)^3 = 0 is 2. II. The degree of √(d^2y/dx^2) = dy/dx + 1 is 1. III. The degree of d^2y/dx^2 + cos(dy/dx) = 0 is 1. IV. When the degree is defined, it is a positive integer.

Question 14

HardOriginal question

Which of the following statements are true?
I. The order of $\frac{d^2y}{dx^2} + \left(\frac{dy}{dx}\right)^3 = 0$ is 2.
II. The degree of $\sqrt{\frac{d^2y}{dx^2}} = \frac{dy}{dx} + 1$ is 1.
III. The degree of $\frac{d^2y}{dx^2} + \cos\left(\frac{dy}{dx}\right) = 0$ is 1.
IV. When the degree is defined, it is a positive integer.

I, II and IV onlyCorrect answerYour answerAll four: I, II, III and IVCorrect answerYour answerI and IV onlyCorrect answerYour answerI and II onlyCorrect answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

I: the highest derivative is $\frac{d^2y}{dx^2}$ . II: squaring gives $\frac{d^2y}{dx^2} = \left(\frac{dy}{dx} + 1\right)^2$ , where $\frac{d^2y}{dx^2}$ has power 1. IV: the degree is the power of a derivative in a polynomial.
III is false: $\cos\left(\frac{dy}{dx}\right)$ is not a polynomial in $\frac{dy}{dx}$ , so the degree is not defined.

Concept: Facts about order and degree
Typical timeTypical: 150 s
Your timeYours: —

The rule this testsOrder and degree

Practise this chapter →

Ten questions from Differential Equations, at your own pace.

Explanation