Question

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

Answer 1

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’=\(\frac{dy}{dx}\)=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.