2 years, 94 days

## How to find integration of max of two fu...

Maple

Suppose we have a parametric function g(x)=max{h(x,p),f(x,p)}. How can I find the exact form of g(x) by conditioning on x and also how I can find the integration of g(x) over an interval [a,b]?

For example, g(x)= max{ x-p, x^2+px} and [a,b]=[0,10].

## How to rearrange a polynomial based on a...

Maple 2019

I have a parametric polynomial which is defined based on the multiplication of different variables and I want to rearrange the polynomial based on specific variables. For example, suppose the polynomial is defined as follows:

a:= (1+x+y)(2x-yx+z)(y^2-zy)

and I want to have a based on first, and second orders of x, or even other variables. Thanks

## Solving an optimal control problem...

Maple 2019

Hello all

I wanna solve an optimal control problem and I have searched the Internet but I could not find any tutorial or video course on how to solve it with the Pontryagin maximum principle method. It is my first time that I want to use MAPLE for solving an optimal control problem and I would be thankful if someone can help me.

$$\max \int_{0}^{1} x_{2} [u(t)-u(t)^2] dt$$

$$\dot{x}_{0} = -(1-u(t)) x_{0}(t)+2 x_{1}(t)$$

$$\dot{x}_{1}(t) = (1-u_{t}) x_{0}(t) +2 x_{2}(t) -[3-u(t)]x_{1}(t)$$

$$\dot{x}_{2}(t) = (1-u(t))x_{1}(t) -2 x_{2}(t)$$

$$0 \le u_{t} \le \frac{1+t^2}{1+t}$$

Thanks

## How to find integral of the output of a ...

Maple 2019

I am using Maple to solve a system of ODEs numerically. Right now, I want to find the integration of the output of the system of ODEs. How it is possible to do this?

F := dsolve(ODESys union ICs, {y0(t), y1(t), y2(t), y3(t)}, type = numeric)

Y0 := t -> rhs(op(2, F(t)))

Now, I want to find int(Y0,t=0..1).

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