which differential equation solver should I use?

I have a differential equation of the form following:

dy(t)/dt = ay(t) + bx(t) + cx(t)/dt

y(t) is the output I am looking for, when x(t) is a given input (discrete samples from collected data). a, b, c are constants.

I followed ode45 instructions for differential equation of time dependent variables. To test out the code, I set x(t) = sin(t). Accordingly I set x(t)/dt = cos(t). this probably is not the way I will test out the real data since they are noisy discrete samples. I need to figure out how to find calculate x(t)/dt for those but that's another question.

I got a straight linear line with positive slope for output y(t). I was expected oscillating function like modified sin(t) and cos(t). I tried on wolfram alpha and that displayed oscillating (damping) graph for y(t), so I think I did not solve this equation correctly on MATLAB. I am pretty sure I implemented ode45 correctly, so I am wondering I may be using a wrong differential equation solver.

Could you give me any feedback? Thanks.

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t = linspace(0,pi*20,pi*20/0.01);

Pa = sin(t)';

dPa = cos(t)';

f = 4 * -2.6021e-07 * ones(size(Pa,1),1);

g = 4 * 2.6021e-07 * Pa + .6 * dPa;

Tspan = [0 pi*20];

IC = 5 * ones(size(Pa,1),1);

t = t';

Tspan = Tspan';

[T Pic] = ode45(@(t,Pic) f1(t,Pic,t,f,t,g),Tspan, IC');

plot(t,Pa,'b') % input

hold on;

plot(T,Pic(:,45)) % one possible output

%

and function f1 is defined as following:

function dydt = f1(t,y,ft,f,gt,g)

dydt = f.*y + g;

end

[Torsten]

Show us the MATLAB code you are using.

Best wishes

Torsten.

[Torsten]

You have to supply g at the times indicated by the variable "t" in dydt. Thus your function routine must look like

function dydt = f1(t,y,ft,f,gt,g)

f = 4*(-2.6021e-07);
Pa = sin(t);
dPa = cos(t);
g = 4*2.6021e-07*Pa + .6*dPa;

dydt=f*y+g;

end

And you only have to supply one value as initial condition for y, not a vector of length 5*size(Pa).

Best wishes

Torsten.

[February]

Thank you, Torsten. I finally figured out.