Which of the following functions is the solution of the differential equation \frac{dy}{dx}+2y=0?

Category: QuestionsWhich of the following functions is the solution of the differential equation \frac{dy}{dx}+2y=0?
Editor">Editor Staff asked 11 months ago

Which of the following functions is the solution of the differential equation \frac{dy}{dx}
+2y=0?
 
(a) y=-2e^-x
 
(b) y=2e^x
 
(c) y=e^-2x
 
(d) y=e^2x
 
I got this question during an internship interview.
 
The above asked question is from General and Particular Solutions of Differential Equation topic in division 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

Right choice is (c) y=e^-2x
 
Easy explanation: Consider the function y=e^-2x
 
Differentiating both sides w.r.t x, we get
 
dy
dx
=−2
e
−2x
 
 
dy
dx
=-2y
 

dy
dx
+2y=0.