Problem with ordinary differential equation

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Fatemeh
Fatemeh 2023-4-22
评论： Fatemeh 2023-4-23
Hello, can anyone clarify me why I'm getting a line chart with the following code and how can I fix that? My initial conditions are y(C0)=t0, and y'(C0)=0. Thanks
syms y(x) x Y
N=5;
r=0.05;
m=0.01;
p=1;
s=1;
t=0.1;
a=0.25;
b=0.25;
C0=1;
C=5;
t0= (((1-a)/a)*N^(a+b))/(r-m);
Dy = diff(y);
D2y = diff(y,2);
ode = y-((((1-a)/a)*N^(a+b))-x*m*Dy+0.5*D2y*(x^2)*(s^2))/(r-m);
[VF,Subs] = odeToVectorField(ode);
odefcn = matlabFunction(VF, 'Vars',{x,Y});
tspan = [C0 80];
ic = [t0 0];
[x1,y1] = ode45(odefcn, tspan, ic);
figure
plot(x1,y1(:,1), 'DisplayName','(x_1,y_1_1)')
grid

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Star Strider
Star Strider 2023-4-22
Ran in:
The initial condition of 0 for keeps it 0 througuout the integration.
syms y(x) x Y
N=5;
r=0.05;
m=0.01;
p=1;
s=1;
t=0.1;
a=0.25;
b=0.25;
C0=1;
C=5;
t0= (((1-a)/a)*N^(a+b))/(r-m)
t0 = 167.7051
Dy = diff(y);
D2y = diff(y,2);
ode = y-((((1-a)/a)*N^(a+b))-x*m*Dy+0.5*D2y*(x^2)*(s^2))/(r-m);
[VF,Subs] = odeToVectorField(ode)
VF = 
Subs = 
odefcn = matlabFunction(VF, 'Vars',{x,Y})
odefcn = function_handle with value:
@(x,Y)[Y(2);(1.0./x.^2.*(sqrt(5.0).*-3.0e+2+x.*Y(2)+Y(1).*4.0))./5.0e+1]
tspan = [C0 80];
ic = [t0 0];
[x1,y1] = ode45(odefcn, tspan, ic);
figure
plot(x1,y1(:,1), 'DisplayName','(x_1,y_1_1)')
grid
.
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Star Strider
Star Strider 2023-4-23
@Fatemeh — As always, my pleasure!
@Torsten — Thank you!
(I just now saw this.)

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