solving non linear differential equations

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

Answer 1

[Torsten]

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)

[berrabah imad eddine]

Thank you for your help, but are you sure for you answer, could you explain more the method of your work, please.

[Torsten]

Take a look at how ODE integrators are invoked:

help ode45

[berrabah imad eddine]

Would you change this algorithm to Runge Kutta algorithm, pleas?!

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)

[Torsten]

ODE45 is a Runge-Kutta integrator ...