- Thread starter
- #1

- Mar 10, 2012

- 835

a) 4

b) 3

c) 5

d) Maximum value does not exist.

I am quite lost on this one. After some thought I am convinced that the maximum value should exist, though I do not have a good argument to support this claim.

- Thread starter caffeinemachine
- Start date

- Thread starter
- #1

- Mar 10, 2012

- 835

a) 4

b) 3

c) 5

d) Maximum value does not exist.

I am quite lost on this one. After some thought I am convinced that the maximum value should exist, though I do not have a good argument to support this claim.

- Admin
- #2

- Mar 5, 2012

- 9,308

So it seems it is none of the above, but the answer $3$ is close.

For reference, I have re-encoded the differential equation a bit to solve it with Octave's [M]lsode[/M].

Let $y=f(x)$, $u=y'$, and $Y=(u,y)$ then:

$f(x)+f''(x)=-x|\sin x|f'(x) \\

y + u' = -x|\sin x|u \\

\begin{cases}u'=-y-x|\sin x|u\\ y'=u\end{cases}\\

(u', y') = (-y-x|\sin x|u,\, u) =: g(u,y;x)\\

Y' = g(Y;x)

$