How to solve an ODE with a function symbolically?

So I have this ODE to solve (26) with a set of conditions (27). I evaluated the conditions prior to going forward to solve the ODE. I want to solve it symbolically for each mk because I will use the results later on. I wrote a function file for dmk/dt, and then in a loop I want to solve for each mk and save the function. However I am not sure if I am able to save all the functions in a matrix. Moreover, when I input the initial conditions while using ode45, I get an error. This is the code in the loop:

    [t,m]=ode45('mp',[0,10],m0val(x));

where m0val(x) contains the values for the initial conditions.

[Karan Gill]

You could start with the existing doc on solving ODEs symbolically:

• https://www.mathworks.com/help/symbolic/solve-a-single-differential-equation.html
• Fall back to numeric solution: https://www.mathworks.com/help/symbolic/examples/solve-a-second-order-differential-equation-numerically.html

[Edgard El Cham]

Thank you, I think that's what I was looking for.

[Karan Gill]

Great! I copied my comment to an Answer. If this was what you wanted, could you accept the Answer?

Answer 1

[Karan Gill]

You could start with the existing doc on solving ODEs symbolically:

• https://www.mathworks.com/help/symbolic/solve-a-single-differential-equation.html
• Fall back to numeric solution: https://www.mathworks.com/help/symbolic/examples/solve-a-second-order-differential-equation-numerically.html