How do i write this differential equation in matlab?

global R C u
R = 10e3;
C = 3.3e-6;
tau = R*C; 
u = @(t)  10*(t>tau); 

The initial value is uC(0)=0

I want to write the diff equation in a function and use ode45 to solve it. Can someone please help me? i've tried everything but i dont understand how to write it into a function and how to solve it. Would be really appreciated!

Answer 1

[Star Strider]

There are several options, including using the numerical solvers.

This approach uses the Symbolic Math Toolbox —

syms C R uc(t) u 
eqn = R*C*diff(uc)+uc == u;
uc(t) = dsolve(eqn, uc(0)==0)

uc(t) = 

uc = subs(uc,{C,R,u},{1E-9,1E+3,sin(2*pi*t)})

uc(t) = 

figure
fplot(uc, [0 10])
grid

.

[Augustine Nashwan Aziz Al-Zebary]

Thank you for the fast response!

Is there a more simple way to solve this without using any toolboxes?. I want to solve this using pure programming from scratch

[Augustine Nashwan Aziz Al-Zebary]

I also want to solve it using ode45

[Star Strider]

That is relatively straightforward —

syms C R uc(t) u Y 
eqn = R*C*diff(uc)+uc;
[VF,Sbs] = odeToVectorField(eqn)

VF = 

Sbs = 

fcn = matlabFunction(VF,'Vars',{t,Y,C,R})

fcn = function_handle with value:
    @(t,Y,C,R)[-Y(1)./(C.*R)]

Then, write your function to add ‘u(t)’ to it using the value of ‘t’ provided by ode45 (or whatever solver you decide to use). Either use a direct function call, or interp1 if ‘u(t)’ is a vector that neds to be interpolated to a particular time in each step.

EDIT — (12 May 2021 at 21:08)

to add ‘u(t)’ is straightforward —

fcn = @(t,Y,C,R) [-Y(1)./(C.*R)] + u(t);

Provide whatever ‘u(t)’ is, and it will work.

[Augustine Nashwan Aziz Al-Zebary]

I got it working, big thanks for the help!

[Star Strider]

As always, my pleasure!