How to solve a parametric differential equation in MATLAB

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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

Accepted Answer

Ameer Hamza
Ameer Hamza on 3 May 2020
Edited: Ameer Hamza on 3 May 2020
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

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