Differentiate the following. How do i solve y''(x) = -y ?

[CosmicC]

Is y''(x) same as d²y/dx².
As it's y''(x) so how do we find out y(x) and if it can be taken as a double derivative, i was having doubts in this.
Double differentiation of y is equal to -y...
e^ something maybe ? and sign should change ?

 

[BvU]

Is y''(x) same as d²y/dx².

Yes

As it's y''(x) so how do we find out y(x) and if it can be taken as a double derivative, i was having doubts in this.

experience

Double differentiation of y is equal to -y...
e^ something maybe ? and sign should change ?

Good idea. Try $e^{kx}$ differentiate twice and solve !

 

[CosmicC]

Yes
experience

Good idea. Try $e^{kx}$ differentiate twice and solve !

Thanks a lot for replying. Can you please ellaborate?

 

[BvU]

Take the derivative: $y = e^{kx}\rightarrow {dy\over dx} =$ ?
Do that once more to get $y''$
that has to be equal to $-y = - e^{kx} \quad$ -- an equation that you should be able to solve for $k$

 

[CosmicC]

Take the derivative: $y = e^{kx}\rightarrow {dy\over dx} =$ ?
Do that once more to get $y''$
that has to be equal to $-y = - e^{kx} \quad$ -- an equation that you should be able to solve for $k$

Thanks i'll try and post the answer or difficulty i have.