which one of the following functions is a solution to:

(4d^2y/dx^2 ) - y = 0

a) y = sin 2x
b) y = e^(x/2)
c) y = xlogx
d) y = x^2 +1
e) y = 2/(x+1)

Is there an easier way of finding the solution without testing each option out?

Question

which one of the following functions is a solution to:

(4d^2y/dx^2 ) - y = 0

a) y = sin 2x
b) y = e^(x/2)
c) y = xlogx
d) y = x^2 +1
e) y = 2/(x+1)

Is there an easier way of finding the solution without testing each option out?

anonymous · Answer

the answer is b

Most of the times in solving Differential Equations solutions are first guessed upon and then verified. At times there are unique solutions. At times a linear combination of two solutions is a solution. So, in general I would advise to check each option out if the DE is not easily solvable.

anonymous · Answer

i see ok i was just checking if there was a method thanks for your help:)