# Question:How to integrate this ode and how to substitue this boundary value

## Question:How to integrate this ode and how to substitue this boundary value

Maple

The example below is an attempt to solve a boundary value problem (BVP) without manually replacing terms in expressions and some questions where there might be room for improvement. (Only the first integration step is shown to keep it short)

My objective is to have clean Maple input with minimal manual interventions or low-level manipulations (such as using op and similar commands).

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 (1)

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 (2)
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...not a clue for me

Since I know the result: Multiplying by  to make integration work.  Q1: Are there other ways to integrate a single step without a priori knowledge?

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 (3)

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 (4)

Boundary condition for

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 (5)

(4) evaluated at the boundary

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 (6)

Q2: How to simplify expression (6) with (5) using Maple commands to get this expression for the integration constant

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 (7)

Some attempts

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 (8)

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 (9)

Doing it manually

 (10)

or

 (11)

 (12)

Q3: Are there ways to prevent commands evaluating to which might suggest incorrectly a new independent variable?

Q4: In (6), why is s = L sometimes in brackets {} ?