How to solve differential equations which has more time dependent arguments ?

I have equation gdot=-k*g+xdot, where xdot=-k*x+sin(t). how can I solve gdot using ode45 ?

[Torsten]

Insert the expression from the second equation for xdot in the first equation and solve both equations simultaneously.

I think you can use dsolve instead of ode45 since the system most probably has an analytical solution.

[J. Alex Lee]

if you use ode45, you don't need to insert the expression for xdot into the first equation...did you read documentation for ode45, and did you try to write an odefun yourself?

[Torsten]

If you use the mass matrix option, you don't need to insert the expression for xdot into the first equation.

If you don't use the mass matrix option, you must.

[J. Alex Lee]

@Torsten, interesting about the mass matrix method...but without it, I am just saying there wouldn't be a need to duplicate the expression from a coding perspective, right?

[Torsten]

Of course, you can write

function dy = fun(t,y)

k = ...;

dy = zeros(2,1)

dy(1) = -k*y(1) + sin(t); % equation for x

dy(2) = -k*y(2) + dy(1) % equation for g

end

Thus you don't need to repeat the formula for dy(1) in dy(2), if this is what you meant to ask.

[J. Alex Lee]

haha yes exactly...but now the answer is given away :)

and g should likely be Y(2) as far as we know from pritesh's nomenclature

[Torsten]

Yes, you are right with the g. I always associate it with the gravity constant ...