MATLAB: Solving non linear differential equations

differential equationsmathematicsMATLAB

I am working at a mathematical problem and I wanted to solve it numerically through MATLAB. The equation has the form:

epsilon*y'(t) =t*y(t)(y(t)-a)(y(t)-b)+c

where a<0 and b>0 and c>0

a = -0.2;
b = 0.1;
c = 0.1;
epsilon = 1.0;
fun = @(t,y)(t*y*(y-a)*(y-b)+c)/epsilon;
tspan = [0 3.5];
y0 = 0;
[T,Y] = ode45(fun,tspan,y0);
plot(T,Y)

I have no idea what you want to do, or what ‘x’ and ‘y’ are.

This will get you closer to an actual result:

tspan = [0 5];
y0 = [100; 0];
Q = 30; 
b = 0.2;
[t,y] = ode45(@(t,y) [y(1); Q-b*y(1)*y(2)], tspan, y0); 
figure
plot (t,y,'-o')

ode = @(t,y) y.^2-y.*0.1*cos(2.*t)-0.2*cos(2.*t);
t=[0 8];
y0 = -1;
[t,y] = ode45(ode,t,y0);
plot(t,y)