How to solve DE by matlab

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Christina Kao
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.

Answers (2)

halleyhit
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
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.

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