# Question:Help With Maple Codes for one dimensional rod with a constant thermal properties (Newbie Here)

## Question:Help With Maple Codes for one dimensional rod with a constant thermal properties (Newbie Here)

Maple 2019

Hi everyone, I need someone’s expertise with the Maple Soft Application, I am currently into my 4th day of my Maple Soft experience and also returning to School after many years. Can someone help me with the following codes to solve step by step Differential Equation 1 below;

1. Boundary Condition 1
2. Boundary Condition 2
3. General Solution
4. The integration Part of the Equation
5. Solving the Differential Equation

Equation 1.

Determine the equilibrium temperature for a one dimensional rod with a constant thermal properties with the following source and boundary conditions.

1. Q = 0, U(0) = 10, u(L) = 20
2. Q/K0 = x, u(0) = 0, u(L) = 10

I understand how to obtain the solution to the equation above,

(a) Equilibrium satisfies

U’’(x) = 0,

Whose general solution is u = c1 + c2x.

The boundary condition u(0) = 0 implies c1 = 0 and u(L) = T implies c2 = T/L so that u = T x/L.

(f) In equilibrium, u satisfies

U’’(x) = −Q/K0 = −x^2,

Whose general solution (by integrating twice) is

u = −x ^4 /12 + c1 + c2x.

The boundary condition u(0) = T yields c1 = T, while u’(L) = 0 yields c2 = L^3/3.

Thus u = −x ^4 /12 + L^3x/3 + T.

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