Question

what is the code to solve and graph the following function in matlab

dv/dt=80.5(1-e^(.4t))

Answer 1

>>syms v(t)                              %We just defined a symbolic function

>>ode = diff(v,t) == 80.5*(1-exp(4*t))    %we made the differential equation of v interms of t and

                                                                           stored it in ode

>>vSol=dsolve(ode)                           %we used dsolve to solve the equation ode and stored the

                                                                 function in vSol

Output

C1 + (161*t)/2 - (161*exp(4*t))/8

NOTE: we didnt give it any initial conditions so it put in a constant C1.

If you want to add an initial condition then add the following line before using dsolve

>>cond1 = v(0) == 'some number here'                   %cond1 is the name of the condition

then instead of last line use :

>>vSol = dsolve(ode,cond1)

Graphing

Here iam going to assume the constant C1 to be 0.

>> t=linspace(0,30,300);     %this basically gives t values from 0-30 divided into 300 equal parts

>> v=(161*t)/2 - (161*exp(4*t))/8;

>>plot(t,v);