## Contents

## 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

S = 0.6000 R = 0.0550

## 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(' ')

OUTPUTS The solution# 1 is -0.0437371 The solution# 2 is 0.0623776 The solution# 3 is 0.14636