plotting an ODE with x limits and y limits.

Hello, I am trying to plot a differential equation with x-limits and y-limit that I set myself.

Not sure if this ODE would work but let's say

5y''+3y'+1=0 2<x<4 and 2<y<4

Answer 1

[Walter Roberson]

syms y(x)
Dy = diff(y);
D2y = diff(Dy);
eqn = 5*D2y + 3*Dy + 1 == 0;
y0 = y(0) == 3;     %need a boundary condition
Dy0 = Dy(0) == rand();   %need a boundary condition
F = dsolve(eqn, y0, Dy0)
fplot(F, [2 4])
ylim([2 4])

[Nadin Dimetry]

I changed the equation and it wouldn't give me any plots

clear
syms y(x)
Dy = diff(y);
D2y = diff(Dy);
D3y = diff(D2y);
D4y = diff(D3y);

eqn = -D4y-y^2-x*D2y == 0;
y0 = y(0) == 1;     %need a boundary condition
Dy0 = Dy(0) == 0;   %need a boundary condition
F = dsolve(eqn, y(0), Dy(0)
fplot(F, [2 4])
ylim([2 4])

Also, how else would you graph this without using symbolic ?

[Walter Roberson]

There does not appear to be an analytic solution to that equation (note: you would also need a few more boundary conditions to pin it down if there were a solution.)

You will need to work with one of the numeric solvers such as ode45()

Unfortunately I do not know how to translate the equations. Maybe

fun = @(y,x) [x(2);x(3);x(4);-x(1)*x(3)-y^2];
[Y, X] = ode45(fun, [0 4], [1;0;1;1]);
plot(Y, X(:,1))

after which you could put in xlim and ylim