Could anyone tell me what f(x) is in this equation:

f''(x) = -sin(f(x))

Question

Could anyone tell me what f(x) is in this equation:

f''(x) = -sin(f(x))

amistre64 · Answer

its an arugment for sin?

anonymous · Answer

Yes, it is.

amistre64 · Answer

its not an ordinary diffyQ

anonymous · Answer

I know.
I had a masterclass today about these kind of equations, and the university teacher wrote  this one the board, and it has been bugging me ever since.

amistre64 · Answer

y'' = -sin(y)  might make it look better

amistre64 · Answer

y'' + sin(y) = 0

amistre64 · Answer

y' = cos(y)/y'

2y' = cos(y)

y' = cos(y)/2

but im sure we cant do that for some reason

amistre64 · Answer

y = sin(y)/2y'

y' = sin(y)/2y

cos(y)/2 = sin(y)/2y

cos(y) = sin(y)/y
y = tan(y)  maybe?

amistre64 · Answer

or can we separable it?

amistre64 · Answer

d^2y/dx^2 = -sin(y)

d^2y/dx^2 csc(y)= - dx

dy/dx ln(csc(y)+cot(y)) = -x + C

something along those lines?

amistre64 · Answer

oh yeah, that AINT pretty

amistre64 · Answer

http://www.wolframalpha.com/input/?i=y%27%27%3D-sin%28y%29

anonymous · Answer

Not pretty is an eufimism for that function...
Although I DO think there is a better function to describe my question, because that teacher practically did it out of his head.

amistre64 · Answer

they got saws at the hospital for stuff like that :)

amistre64 · Answer

at any rate, good luck with it :)

anonymous · Answer

I just sent him an e-mail, hoping he will provide me with the answer anytime soon.
Do you want me to send you the answer when he does?

amistre64 · Answer

im already trying to forget i ever saw this to begin with ;)

amistre64 · Answer

sure, post the results when you get them, itd be nice to see what im missing out on

anonymous · Answer

Okay, will do :)