NonlinearEquations

SUMMARY
INTRODUCTION
INPUTS
DISPLAYING INPUTS
THE CODE
DISPLAYING OUTPUTS

SUMMARY

Language : Matlab 2018b; Authors : Autar Kaw and Luis Serrano; Mfile available at http://nm.mathforcollege.com/blog/NonlinearEquations_withSetUp.m; Last Revised : January 22, 2020; Abstract: This program shows you how to solve a nonlinear equation that needs to set up as opposed that is just given to you.

clc
clear all

INTRODUCTION

disp('ABSTRACT')
disp('   This program shows you how to solve')
disp('   a nonlinear equation that needs to be setup')
disp(' ')
disp('AUTHORS')
disp('   Autar Kaw and Luis Serrano')
disp(' ')
disp('MFILE SOURCE')
disp('   http://nm.mathforcollege.com/blog/NonlinearEquations_withSetUp.m')
disp(' ')
disp('LAST REVISED')
disp('   January 22, 2020')
disp(' ')

ABSTRACT
   This program shows you how to solve
   a nonlinear equation that needs to be setup
 
AUTHORS
   Autar Kaw and Luis Serrano
 
MFILE SOURCE
   http://nm.mathforcollege.com/blog/NonlinearEquations_withSetUp.m
 
LAST REVISED
   January 22, 2020

INPUTS

Solve the nonlinear equation where you need to set up the equation For example to find the depth 'x' to which a ball is floating in water is based on the following cubic equation 4*R^3*S=3*x^2*(R-x/3) R= radius of ball S= specific gravity of ball So how do we set this up if S and R are input values

S=0.6
R=0.055

DISPLAYING INPUTS

disp('INPUTS')
func=['  The equation to be solved is 4*R^3*S=3*x^2*(R-x/3)'];
disp(func)
disp('  ')

INPUTS
  The equation to be solved is 4*R^3*S=3*x^2*(R-x/3)

THE CODE

Define x as a symbol

syms x
% Setting up the equation
C1=4*R^3*S
C2=3*x^2*(R-x/3)
f=C1==C2
% Finding the solution of the nonlinear equation
soln=vpasolve(f,x);
solnvalue=double(soln);

C1 =

   3.9930e-04

 
C2 =
 
-3*x^2*(x/3 - 11/200)
 
 
f =
 
7365784908632225/18446744073709551616 == -3*x^2*(x/3 - 11/200)

DISPLAYING OUTPUTS

disp('OUTPUTS')
for i=1:1:length(solnvalue)
fprintf('\nThe solution# %g is %g',i,solnvalue(i))
end
disp('  ')