# Which of the following functions is a solution for the differential equation xy’-y=0?

Category: QuestionsWhich of the following functions is a solution for the differential equation xy’-y=0?
Editor">Editor Staff asked 11 months ago

Which of the following functions is a solution for the differential equation xy’-y=0?

(a) y=4x

(b) y=x^2

(c) y=-4x

(d) y=2x

The question was posed to me in homework.

My question is taken from General and Particular Solutions of Differential Equation topic in section Differential Equations of Mathematics – Class 12
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Editor">Editor Staff answered 11 months ago

The correct choice is (d) y=2x

To explain I would say: Consider the function y=2x

Differentiating w.r.t x, we get

y’=
dy
dx
=2

Substituting in the equation xy’-y, we get

xy’-y=x(2)-2x=2x-2x=0

Therefore, the function y=2x is a solution for the differential equation xy’-y=0.