Solving an integro-differential equation

Saruultugs Batzorig

2019 10 24

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Hello, I'm trying to solve the following differential equation that also has an integral.

I am trying to solve for L (output) with initial conditions of h0=0 and h'=0. The h is with respect to time. r, U and B are constants. The integral part of the equation is equated to A for Matlab coding. So far I have:

syms B h(t) L r U h0 Y 
A = @(t,U,B) integral(@(t) exp((-U*t/B)*0.1843)*h, 0, t);
Eqn = diff(h) == (L/((-1.8775)*U*r*B))+(-0.1654)*U*h/B-...
    ((0.0466*U^2)/(B^2))*A(t,U,B);
hsol = dsolve(Eqn, h(0)==h0);                                 
Lsol = solve(hsol,L);                                         
Lsol = simplify(Lsol, 'Steps',500);                            
Lfcn = matlabFunction(Lsol);     

Eqn normally works if I have A as constant. However, when I have it as the definite integral, Matlab wants me to have h as an input argument. How can I have Lfcn as having only r, U, B, h0, t as inpute arguments? Thank you.