How to solve DE by matlab

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Christina Kao on 13 Jan 2017
Answered: Roger Stafford on 13 Jan 2017
Please help to solve the differential equation dy/dt = y(1-y) with t=0 out to time t=5. Do this numerical integration using 10 time steps (step size of 0.5). Also, make a plot showing the analytical solution, and the estimates obtained using the Euler.

halleyhit on 13 Jan 2017
Usually, ode45, ode23 and some other commands can solve DE. However I think in this homework, you should code yourself.

Roger Stafford on 13 Jan 2017
I can help you a little in finding the analytic solution. Temporarily consider that y is the independent variable and t is the dependent variable, which would give you the equation:
dt/dy = 1/(y*(1-y))
Integrating with respect to y while making use of partial fractions would lead to:
log(abs(y/(1-y))) = t + C
where C is an arbitrary constant of integration. You would need some initial condition to find its value. The final step would then be to solve this equation for y in terms of t.