Project Help Notebook by Keith Stroyan

Help NoteBook Copyright 1998 by Academic Press, Inc. - All rights reserved.
Modify this Notebook to prepare your project report.

Project 18: Repeated Exponents

by A. Student and B. Pupil

with technical help from Da LabMonitor and Help Notebook

My Project Introduction

Write this last.  Begin with the basic question and state your main finding clearly, but with few technical details.  You might even modify the title of this section to make it more interesting.

The Homogeneous Case:  dx = r x dt

This is a paper and pencil project.  Type up your solution in Mathematica and compare it with the Mathematica solutions below.

Hint 19.1

Hint 19.1 is a paper and pencil problem, but here is a Mathematica solution:

\(Clear[t, r, x, X0]; 
r[t_] = t; 

    solution = DSolve[{x[0] == X0, \(x'\)[t] == r[t]\ x[t]}, {x[t]}, t]; 

    x[t_] = x[t] /. solution[\([1]\)]\)\(	x[0]\)

Hint 19.2

Hint 19.2 is a paper and pencil problem, but here is a Mathematica solution:

\(Clear[t, r, x, X0]; 
r[t_] = Sin[t]; 

    solution = DSolve[{x[0] == X0, \(x'\)[t] == r[t]\ x[t]}, {x[t]}, t]; 

    x[t_] = x[t] /. solution[\([1]\)]\)\(	x[0]\)

Hint 19.3

Hint 19.3 is a paper and pencil problem, but here is a Mathematica solution:

Clear[t, r, x, X0];
r[t_] = (1/Cos)[t]^2;
X0 = 3;
solution=DSolve[{x[0] == X0,x'[t]==r[t] x[t]},{x[t]},t];x[t_] = 
        x[t] /. solution[[1]]x[t_] = Simplify[x[t]]x[0]

The Inhomogeneous Case:  dx - r x = f

Solve 19.4 and 5 by hand, type up your solution and compare with the following:

Hint 19.4&5

Clear[t, r, x, f, X0];
r[t_] = t;
f[t_] = t;

solution=DSolve[{x[0] == X0,x'[t]==r[t] x[t] + f[t]},{x[t]},t];x[t_] = 
        x[t] /. solution[[1]]x[0]