How can I graph differential equations without initial conditions?

I have a system of four differential equations that I was trying to graph. This part of a mathematical model and as such I do not have initial conditions. i.e I called y(0)=y_(0). My equations also has 6 parameters of unknown value. I was trying to graph it to only show the general trend of the curve.

Answer 1

[John D'Errico]

If all you have is a symbolic solution of a system, and you are unwilling/unable to substitute specific numerical values, then no, you cannot plot anything.

The implication being, IF you do want to plot something, then you need to provide values for those unspecified constants.

[Walter Roberson]

... Even if that might mean plotting over a range of values to get an idea of how the parameter affects the results

[John D'Errico]

For example, suppose I gave you the simple function (which just happens to be the solution to a differential equation if you want to be picky):

y = a + b*x + c*x^2 + d*x^3 + e*x^4

Can one plot it as is, just to get a feel for the "general trend of the curve"? Of course not. That simple function has all sorts of simple behaviors, ranging from a constant, to a straight line, to a parabola, etc. Some of the potential shapes can have one or more inflection points in them, some not. The function may go to plus or minus infinity as a limit in either direction. While mathematical analysis can allow you to predict what will happen, a plot cannot be created.

Without knowing anything about the specific values of those unknown constants, the equation is not plottable.

The differential equation was

f'''''(y) = 0

:)

[Steven Lord]

A simpler variant of your question, John, is which direction does this parabola open: up or down? [I'm not going to tell you what a is yet.]

x = -10:10;
y = a*x.^2;
plot(x, y)

Trick question: when I ran this code a was 0, so this code plotted a straight line. :)

[Walter Roberson]

Ah, but topologically all mononomials are the same! ;-)