How to solve a parametric differential equation in MATLAB

Hello all,

I have a differential equation which is as follows:

I want to solve the above differential equation and find y(t) in terms of a and b.

I also have the following initial condition:

t=294 y=0

Answer 1

[Ameer Hamza]

You can use dsolve() if you have symbolic toolbox

syms y(t) a b

eq = diff(y) == a*exp(b/t)*(1-y);
ic = y(294) == 0;

sol = dsolve(eq, ic)

Result:

sol =
1 - exp(294*a*exp(b/294) - a*b*ei(b/294))*exp(a*b*ei(b/t) - a*t*exp(b/t))

Note that the output is given in term of an integral function ei(): https://www.mathworks.com/help/releases/R2020a/symbolic/ei.html

[Faezeh Manesh]

Thank you so much!

[Ameer Hamza]

I am glad to be of help.