# Second-order linear ODE

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#1
Show that the following are solutions [(a),(b)] to the differential equation:

(a)
(b)

I am not actually sure where to start here, I am very confused. I am not given a definition of in terms of . First steps?
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6 years ago
#2
(Original post by halpme)
Show that the following are solutions [(a),(b)] to the differential equation:

(a)
(b)

I am not actually sure where to start here, I am very confused. I am not given a definition of in terms of . First steps?
differentiate each expression twice and substitute into the ODE
it should balance with w=4 in the first and w =25 in the second
0
6 years ago
#3
These are solutions to the equation for simple harmonic motion I do believe. So you can read a little more into it using that.
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#4
(Original post by TeeEm)
differentiate each expression twice and substitute into the ODE
it should balance with w=4 in the first and w =25 in the second
Did you forget to square root your solutions?
0
6 years ago
#5
(Original post by halpme)
Did you forget to square root your solutions?
He did yes
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6 years ago
#6
(Original post by halpme)
Did you forget to square root your solutions?
sorry, you can say that
I meant w2 = ...
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6 years ago
#7
(Original post by halpme)
Show that the following are solutions [(a),(b)] to the differential equation:

(a)
(b)

I am not actually sure where to start here, I am very confused. I am not given a definition of in terms of . First steps?
As mentioned in post 3 regarding S.H.M, if you are some what knowledgeable in physics you'd be able to see that the modulus of the exponent in both y expression is equal to in this case.

Hence from inspection, for part a)

and for b)

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