RE: Octave code for y'''=0 ODE

[Allen.Windhorn]

> -----Original Message-----
> From: address@hidden
> [mailto:address@hidden On
> Behalf Of deepus
> 
> Find the particular solution of
> 
> y'''=0
> ​​
> given that:
> 
> y(0)=3, y'(1)=4, y''(2)=6
> 
> How can I write the Octave code for solve the above equation?
> Please help me...

Your instructor is trying to give you a problem you can't solve
by plugging numbers into formulas in Octave.  (Actually, Octave
can't "solve" any problem, only YOU can solve the problem, using
Octave as a tool.)   So you should respect his wishes and try to
think about how derivatives work in differential equations.

You know the value of y''', it is given.  Because it is ZERO,
and it is the time rate of change (the derivative) of y", then
y" can never change (it has a ZERO rate of change).  You know the
value of y" at one time (6), so you know it at all times (6).

You now know how fast y' is changing with time, and that is y",
which is CONSTANT, the rate of change, which is the slope, of
y' as a function of time.  So if you know the value of y' at
some time, which you do, then you know the value of y' at all
times, because it is just a line, and you know one point on the
line and the slope, so using elementary geometry or a little
algebra, you know the equation of the line that defines y'.

NOW you know enough to apply Octave's differential equation
solver, because you know the starting value of y and you know
the formula for the derivative of y, but why bother, you can
easily complete the solution without using Octave, it's just
the integral of the derivative of y (which is y'), which you
know from elementary calculus.

If it were a really complicated equation for y''' then it would
be a "boundary value" problem and you would have to use iteration
or optimization, which is probably beyond the scope of your class
for now at least.

Regards,
Allen