How to plug in one symbolic equation into another

If I have a system of differential equations:

    (1) d A(t) / dt = 2*A(t)
    (2) d B(t) / dt = 3*B(t)

And now, I also have:

    (3) C(t) = A(t) + (B(t)^2)

--> I tell Matlab to differentiate C(t):

    d C(t) / dt = A'(t) + 2*B(t)*B'(t)

     where A'(t) = d A(t) / dt, same for B'(t)

How do I tell Matlab to "plug in" for C'(t) using equations 1 and 2?

Answer 1

[Aylin]

Hello,

The subs function can be used to "plug in" values for the C'(t) equation.

In this answer, I use the Symbolic Math toolbox syntax from MATLAB R2016b. If you are using a previous version of MATLAB, you may have to adjust the syntax before using this code.

To elaborate further on your example, if A, B, and C are defined as symbolic functions of t:

syms A(t) B(t) C(t)

and eqA, eqB, eqC, and eqDC are the defined symbolic equations:

eqA  = diff(A) == 2*A
eqB  = diff(B) == 3*B

eqC  = C == A + (B*B)
eqDC = diff(eqC)

then the subs function can be used as follows to substitute eqA for dA/dt:

eqDC_subA = subs(eqDC, diff(A), eqA)

and can be used for eqB too:

eqDC_subA_subB = subs(eqDC_subA, diff(B), eqB)

Please refer to the Symbolic Math Toolbox documentation for the subs function for more information:

Documentation link for subs