# Plot 3rd differential equation

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RazvanA on 16 Jan 2022
Commented: Star Strider on 16 Jan 2022
Hello everyone, I could use a little help with plotting a 3rd differential equation usind "eqn" and "dsolve" syntax.
Here is my equation:
y''' - 3y' + 2y = x^2*e^x

Star Strider on 16 Jan 2022
The documentation section on dsolve and Solve Differential Equation describes it better than I can!
(It will be necessary to determine if the left-hand-side are in terms of or .)
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Star Strider on 16 Jan 2022
Thank you. That’s what I thought, since the Newton ‘prime’ notation implies derivatives of time.
It would also be nice to know if ‘x’ is a function of time (or anything else) or is simply a value. If it is a funciton of time, integrating the differential equation symbolically may not be possible (at least in a closed form, since the RHS would have to be integrated separately, then substituted back into the integrated LHS). That would slightly complicate things.
With what I currently know about this, it can just be plugged into the demonstration code I cited to in my original Answer to produce —
syms x y(t) t y0 D1y0 D2y0
sympref('AbbreviateOutput',false);
D1y = diff(y);
D2y = diff(D1y);
D3y = diff(D2y);
Eqn = D3y - 3*D1y + 2*y == x^2*exp(x)
ics = [y(0) == y0, D1y(0) == D1y0, D2y(0) == D2y0]; % Initial Conditions
Sy = dsolve(Eqn, ics);
Sy = simplify(Sy, 500)
Use the fplot function to do the actual plotting.
I leave the rest to you.
.

Friedel Hartmann on 16 Jan 2022
syms x y(x)
D1y = diff(y,1)
D3y = diff(y,3)
dsolve(D3y - 3*D1y + 2*y == x^2 * exp(x),x)