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
NCERT Solutions for Subject Clas 12 Math Select the correct answer from above options 
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1 Answers
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.