# Thread: Simply 2nd Order ODE question

1. ## Simple 2nd Order ODE question

Find the general solution of the differential equation:

f''(x) = sin(2x-4)

Do i simply integrate both sides twice? What method of integration do i use?

2. ## Re: Simple 2nd Order ODE question

Originally Posted by remember

Find the general solution of the differential equation:

f''(x) = sin(2x-4)

Do i simply integrate both sides twice? What method of integration do i use?
Hi remember. Welcome to MHF.

y'' =
d/dx (y') = sin(2x-4)

Integrate w.r.t to x:
$\displaystyle \int\,d(y')\,=\int \sin(2x-4)\,dx$

Don't forget your constant of integration.

Write y' as dy/dx & integrate w.r.t x.

3. ## Re: Simple 2nd Order ODE question

Thanks!

Also, say for example the DE was changed to this:

$\displaystyle y'' = sin(2x-4) + cos5x$

I take it I just integrate the sin and cos parts of the equation seperately because they are added and not a product of each other?

4. ## Re: Simple 2nd Order ODE question

Originally Posted by remember
Thanks!

Also, say for example the DE was changed to this:

$\displaystyle y'' = sin(2x-4) + cos5x$

I take it I just integrate the sin and cos parts of the equation seperately because they are added and not a product of each other?
Yes.