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Homogeneous & Linear Differential Equations · Question 4 of 120

Question 4

EasyOriginal question

Which of these functions is homogeneous of degree 2?

Options for question 4

Show the answer and explanation
CorrectNot quiteAnswer D

Correct answer: D

Explanation

  1. Replace x,yx, y by λx,λy\lambda x, \lambda y; a homogeneous function gives back λn\lambda^{n} times itself.

  2. x2−3xy+y2x^{2} - 3 x y + y^{2} gives λ2\lambda^{2} times itself; each of the others fails.

Worth noting

xy+xxy + x mixes a degree-2 term with a degree-1 term.

Concept
Recognising a homogeneous function
Typical time
60 s
Your time
—
The rule this testsHomogeneous equations
Practise this chapter →

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

Practise this chapter →

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