Mathematics
OpenStudy (anonymous):

diff eq. transform the given equation into an equivalent system of first order differential equations y'' + (y')^2 + 25y = sin(x) diff eq. transform the given equation into an equivalent system of first order differential equations y'' + (y')^2 + 25y = sin(x) @Mathematics

OpenStudy (anonymous):

anything?

OpenStudy (anonymous):

i got nothing

OpenStudy (anonymous):

feel free to throw up an airball

OpenStudy (amistre64):

nothing i can be sure about, im just learning to solve these

OpenStudy (amistre64):

y'' = -y'(x)^2 -25y(x) + sin(x) is all i got

OpenStudy (amistre64):

$\int y'' + (y')^2 + 25y\ dx= \int sin(x)dx$ $y' + \frac{1}{3y'}(y')^3 + 25xy= -cos(x)$ that doesnt look like anything useful

OpenStudy (anonymous):

kinda looks like the question again lol

OpenStudy (anonymous):

where's JamesJ

OpenStudy (amistre64):

its a mess is what it is. ive been reading these things for a week and only retain a small portion of it. james is around, he just answered a q of mine

OpenStudy (anonymous):

yea i got a test on wednesday...i need to get crackin at understanding this

OpenStudy (jamesj):

Diff eqns are honey for me; I'm surprised I didn't smell this one out 20 minutes ago.

OpenStudy (anonymous):

well then great...i got 1 more after this one :)

OpenStudy (jamesj):

So, let y1 = y and y2 = y'. Then y1' = y2 ---- (*) and y2' = y'' hence y'' + (y')^2 + 25y = sin(x) is equivalent to y2' = - y2^2 - 25y1 + sin x ---- (**) Therefore the system, combining (*) and (**) is ...

OpenStudy (jamesj):

$\left(\begin{matrix}y_1 \\ y_2\end{matrix}\right)' = \left(\begin{matrix}y_2 \\ -y_2^2 - 25y_1 + \sin x\end{matrix}\right)$

OpenStudy (jamesj):

It doesn't gain you a lot writing it in column vector form as I just have above. But most of the time when you're looking at systems they will be linear, and it is very useful to think of the system this way as a vector ODE, so I'm writing it that way here with one eye to that fact.

OpenStudy (anonymous):

can i write the answer like u have written?

OpenStudy (jamesj):

Sure. In fact, I recommend it, so you get use to this sort of notation

OpenStudy (anonymous):

wanna do another?

OpenStudy (anonymous):

i'll creat another post so i can medal u up again

OpenStudy (jamesj):

Yes ... post it on the left that's ok.