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March 20, 2018 Compiled on March 20, 2018 at 7:59pm

This report gives the result of running a number of partial differential equations on Mathematica and Maple.

The following systems were used at this time.

- Mathematica 11.3 (64 bit). Windows 7.
- Maple 2017.3 (64 bit). Windows 7. (With updated Physics Version 2018, March 9)

The PC used is an Intel i7-3930k running at 3.20 GHz with 16 GB memory.

Number of problems is [ 52 ]. Mathematica solved 32 or %61.54. Maple solved 48 or %92.31

problem number 1

Solve for

Raw commands

Result Solved

Raw commands

Result Solved

problem number 2

Solve for

With initial conditions

Raw commands

Result Solved

Raw commands

Result Solved

problem number 3

Solve for

Raw commands

Result Solved, solution in implicit form

Raw commands

Result Solved

problem number 4

Solve for

With

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Result Solved

Raw commands

Result Solved

problem number 5

Solve for

Raw commands

Result Solved

Raw commands

Result Solved

problem number 6

Solve for

With

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Result Solved

Raw commands

Result Solved

problem number 7

This is problem 2.3.3, part (a) from Richard Haberman applied partial differential equations, 5th edition.

Consider the heat equation

Subject to boundary conditions and with the temperature initially

Raw commands

Result Solved

Raw commands

Result Solved

problem number 8

This is problem 2.3.3, part (b) from Richard Haberman applied partial differential equations, 5th edition.

Consider the heat equation

Subject to boundary conditions and with the temperature initially

Raw commands

Result Solved

Raw commands

Result Solved

problem number 9

This is problem 2.3.3, part (c) from Richard Haberman applied partial differential equations, 5th edition.

Consider the heat equation

Subject to boundary conditions and with the temperature initially

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Result Solved

Raw commands

Result Solved

problem number 10

This is problem 2.3.3, part (d) from Richard Haberman applied partial differential equations, 5th edition.

Consider the heat equation

Subject to boundary conditions and with the temperature initially

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Result Solved

Raw commands

Result Solved

problem number 11

This is problem 2.3.7, from Richard Haberman applied partial differential equations, 5th edition.

Consider the heat equation

Subject to boundary conditions with the temperature initially

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Result Solved

Raw commands

Result Solved

problem number 12

This is problem 2.3.8, from Richard Haberman applied partial differential equations, 5th edition.

Consider the heat equation

This corresponds to a one-dimentional rod either with heat loss through the lateral sides with outside temperature zero degrees () or with insulated sides with a heat sink propertional to the temperature.

Suppose the boundary conditions are , solve with the temperature initially if

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Result Did not solve

Raw commands

Result Solved

problem number 13

This is problem 2.4.1 part(a) from Richard Haberman applied partial differential equations, 5th edition.

Consider the heat equation

The boundary conditions are with the temperature initially

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Result Solved

Raw commands

Result Solved

problem number 14

This is problem 2.4.1 part(b) from Richard Haberman applied partial differential equations, 5th edition.

Solve the heat equation

The boundary conditions are with the temperature initially

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Result Solved

Raw commands

Result Solved

problem number 15

This is problem 2.4.1 part(c) from Richard Haberman applied partial differential equations, 5th edition.

Solve the heat equation

The boundary conditions are with the temperature initially

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Result Solved

Raw commands

Result Solved

problem number 16

This is problem 2.4.1 part(d) from Richard Haberman applied partial differential equations, 5th edition.

Solve the heat equation

The boundary conditions are with the temperature initially

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Result Solved

Raw commands

Result Solved

problem number 17

This is problem 2.4.2 from Richard Haberman applied partial differential equations, 5th edition.

Solve the heat equation

The boundary conditions are with the temperature initially

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Result Solved

Raw commands

Result Solved

problem number 18

This is problem at page 76 from David J Logan text book.

Solve the heat equation

The boundary conditions are and initial conditions

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Result Solved

Raw commands

Result Solved

problem number 19

Solve the heat equation

For and . The boundary conditions are

And initial conditions

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Result Did not solve

Raw commands

Result Solved

problem number 20

Solve the heat equation

For and . The boundary conditions is and And initial condition

Raw commands

Result Solved

Raw commands

Result Solved

problem number 21

Solve the heat equation

For and . The boundary conditions is and And initial condition

Raw commands

Result Solved

Raw commands

Result Solved

problem number 22

Solve the heat equation

For and . The boundary conditions are

And initial condition

Raw commands

Result Did not solve

Raw commands

Result Solved

problem number 23

Solve the heat equation

For and . The boundary conditions are

Initial condition is

Raw commands

Result Solved

Raw commands

Result Solved

problem number 24

Solve the heat equation

For and . The boundary conditions are zero at both ends. Initial condition is

Raw commands

Result Did not solve

Raw commands

Result Solved

problem number 25

This is problem 8.2.1 par(d) from Richard Haberman applied partial differential equations 5th edition.

Solve the heat equation

For and . The boundary conditions are

Initial condition is

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Result Did not solve

Raw commands

Result Solved

problem number 26

Solve the heat equation

For and . The boundary conditions are

Initial condition is

Raw commands

Result Did not solve

Raw commands

Result Solved

problem number 27

added Feb 10, 2018.

Solve the heat equation

For and . The boundary conditions are

Initial condition is

Raw commands

Result Solved

Raw commands

Result Solved

problem number 28

added Feb 10, 2018.

Solve the heat equation

For and . The boundary conditions are

Initial condition is

Raw commands

Result Solved

Raw commands

Result Solved

problem number 29

added March 8, 2018.

Solve the heat equation

For and . The boundary conditions are

Initial condition is .

Raw commands

Result Solved

Raw commands

Result Did not solve

problem number 30

added March 18, 2018.

This is problem 8.2.1, part(f) from Richard Haberman applied partial differential equations 5th edition.

Solve the heat equation

For and . The boundary conditions are

Initial condition is .

Raw commands

Result Did not solve

Raw commands

Result Solved

problem number 31

added March 18, 2018.

Solve the heat equation

For and . The boundary conditions are

Initial condition is .

Raw commands

Result Did not solve

Raw commands

Result Solved

problem number 32

This is problem 2.5.5 part (c) from Richard Haberman applied partial differential equations, 5th edition

Solve Laplace equation

Inside quarter circle of radius 1 with and , with following boundary conditions

Raw commands

Result Did not solve

Raw commands

Result Did not solve

problem number 33

Solve Laplace equation

Inside semi-circle of radius 1 with and , with following boundary conditions

Raw commands

Result Did not solve

Raw commands

Result Gave a solution, but extra terms in solution is not correct. Therefore counted as not solved

problem number 34

This is problem 2.5.1 part (a) from Richard Haberman applied partial differential equations, 5th edition

Solve Laplace equation

inside a rectangle , with following boundary conditions

Raw commands

Result Solved

Raw commands

Result Solved

problem number 35

This is problem 2.5.1 part (b) from Richard Haberman applied partial differential equations, 5th edition

Solve Laplace equation

inside a rectangle , with following boundary conditions

Raw commands

Result Solved

Raw commands

Result Solved

problem number 36

This is problem 2.5.1 part (c) from Richard Haberman applied partial differential equations, 5th edition

Solve Laplace equation

inside a rectangle , with following boundary conditions

Raw commands

Result Did not solve

Raw commands

Result Solved

problem number 37

This is problem 2.5.1 part (d) from Richard Haberman applied partial differential equations, 5th edition

Solve Laplace equation

inside a rectangle , with following boundary conditions

Raw commands

Result Did not solve

Raw commands

Result Solved

problem number 38

This is problem 2.5.1 part (e) from Richard Haberman applied partial differential equations, 5th edition

Solve Laplace equation

inside a rectangle , with following boundary conditions

Raw commands

Result Did not solve

Raw commands

Result Solved

problem number 39

Solve Laplace equation

inside a rectangle , with following boundary conditions

Raw commands

Result Solved

Raw commands

Result Solved

problem number 40

This is problem 2.5.8 part (b) from Richard Haberman applied partial differential equations, 5th edition

Solve Laplace equation

Inside circular annulus subject to the following boundary conditions

Raw commands

Result Did not solve

Raw commands

Result Did not solve

problem number 41

Solve Laplace equation

With boundary conditions

Raw commands

Result Solved

Raw commands

Result Solved

problem number 42

Solve Laplace equation

With boundary conditions

Raw commands

Result Did not solve

Raw commands

Result Solved

problem number 43

This is problem at page 115, David J Logan textbook, applied PDE textbook.

Falling cable lying on a table that is suddenly removed.

With boundary condition

And initial conditions

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Result Solved

Raw commands

Result Solved

problem number 44

This is problem at page 28, David J Logan textbook, applied PDE textbook.

With boundary condition

Raw commands

Result Did not solve

Raw commands

Result Solved

problem number 45

This is problem at page 130, David J Logan textbook, applied PDE textbook.

With boundary conditions

With initial conditions

Raw commands

Result Did not solve

Raw commands

Result Solved

problem number 46

This is problem at page 149, David J Logan textbook, applied PDE textbook.

With boundary conditions

With initial conditions

Raw commands

Result Did not solve

Raw commands

Result Solved

problem number 47

This is problem at page 213, David J Logan textbook, applied PDE textbook.

With boundary conditions

With initial conditions

Raw commands

Result Did not solve

Raw commands

Result Solved

problem number 48

Solve

With boundary conditions

With initial conditions

Raw commands

Result Solved

Raw commands

Result Solved

problem number 49

Solve

With boundary conditions

With initial conditions

Raw commands

Result Did not solve

Raw commands

Result Solved, But should not be included.

problem number 50

Added March 9, 2018.

Solve

With boundary conditions

With initial conditions

Raw commands

Result Solved but sum should not include

Raw commands

Result Solved, but sum should not include

problem number 51

From page 30, David J Logan textbook, applied PDE textbook.

Solve

With boundary conditions

Raw commands

Result Solved

Raw commands

Result Solved

problem number 52

Added January 20, 2018.

Solve

With boundary conditions

And initial conditions

Raw commands

Result Solved

Raw commands

Result Solved