Dear experts,

I am sorry to bother you again with different questions. I am attempting to get a solution with various methods so that I can grasp my problem as clear as possible. 

I am attempting maximizing this problem, so I am looking for functional solution of c(t). However, as you can see, in the optimization problem there is one bothering expression, which is a integral of c(h) from 0 to t. 

I looved optimal control theory book, but still I could not find a protocol example. 

int([int(e^(-rh)*[log(c(h)) + w - p*c(h)], h = 0 .. t)]*b*[int(c(h), h = 0 .. t)]*e^(-b*int(c(h), h = 0 .. t)), t = 0 .. infinity) 

How shall I approach this problem with Euler Lagrange in Maple? Thank you

ode := D(c)(t) = (ln(c(t)) + w - p*c(t))*(c(t)(t + 1/int(c(h), h = 0 .. t)) + int(c(h), h = 0 .. t))/(p - 1/c(t))

I have such differential equation derived from Euler-Lagrange condition of calculus of variation problem. 

I tried to solve it, but it says there are two c(t) and c(h). c(t) is what I want to get.

Thank you

Hi, 

I was attempting to solve an ODE, but it does not turn out anything. It is a bit complicated ODE. dsolve turns nothing, and I tried little different specification for an end point or initial point, but it calculates like forever giving nothing. What shall I do?

ode := 0 = diff(y(x), x) + ((r + 2*x)*(p - y(x)^(-s)))/(-(b*y(x) - x^2)*s*y(x)^(-s - 1))

parameters(0 < r, 0 < p, b < 1 and 0 < b, 0 < s)