HOW DO I DO THAT IN MATLAB SERIES?

In this series, I am answering questions that students have asked me about MATLAB. Most of the questions relate to a mathematical procedure.

Contents

TOPIC

How do I solve an ordinary differential equation

SUMMARY

Language : Matlab 2010a; Authors : Autar Kaw and Sri Harsha Garapati; Mfile available at Last Revised : January 23, 2012; Abstract: This program shows you how to solve an ordinary differential equation in MATLAB

clc
clear all

INTRODUCTION

disp('ABSTRACT')
disp('   This program shows you how to solve an ordinary differential equation')

disp(' ')
disp('AUTHOR')
disp('   Autar Kaw and Sri Harsha Garapati of http://autarkaw.wordpress.com')
disp(' ')
disp('MFILE SOURCE')
disp('   http://numericalmethods.eng.usf.edu/blog/calc_operations_ode_blog.m')
disp(' ')
disp('LAST REVISED')
disp('   January 23, 2012')
disp(' ')

ABSTRACT
   This program shows you how to solve an ordinary differential equation
 
AUTHOR
   Autar Kaw and Sri Harsha Garapati of http://autarkaw.wordpress.com
 
MFILE SOURCE
   http://numericalmethods.eng.usf.edu/blog/calc_operations_ode_blog.m
 
LAST REVISED
   January 23, 2012
 

INPUTS

% enter differential equation as string
eqn3='3*Dy+6*y=exp(-x)';
% initial condition
inco='y(0)=6';

DISPLAYING INPUTS

disp('  ')
disp('INPUTS')
% printing the the input ordinary differential equation with initial
% condition
fprintf('  equation to solve: %s\n  with: %s\n\n',eqn3,inco)

  
INPUTS
  equation to solve: 3*Dy+6*y=exp(-x)
  with: y(0)=6

THE CODE

% "dsolve" is the command to solve the ordinary differential equation
% enter all as strings!!!
soln =dsolve(eqn3,inco,'x');
% convert the solution to a string to print in the outputs section
solnd=char(vpa(soln,4));

DISPLAYING OUTPUTS AND PLOTS

disp('  ')
disp('OUTPUTS')
% printing the outputs
fprintf('  The solution is: y=%s\n\n',solnd)

  
OUTPUTS
  The solution is: y=0.3333/exp(1.0*x) + 5.667/exp(2.0*x)

Published with MATLAB® 7.10