# How do I solve a nonlinear equation in MATLAB?

Many students ask me how do I do this or that in MATLAB.  So I thought why not have a small series of my next few blogs do that.  In this blog, I show you how to solve a nonlinear equation.

The MATLAB program link is here.

The HTML version of the MATLAB program is here.

%% 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.

%% TOPIC
% How do I solve a nonlinear equation?

%% SUMMARY

% Language : Matlab 2008a;
% Authors : Autar Kaw;
% Mfile available at
% http://numericalmethods.eng.usf.edu/blog/integration.m;
% Last Revised : March 28, 2009;
% Abstract: This program shows you how to solve a nonlinear equation.
clc
clear all

%% INTRODUCTION

disp(‘ABSTRACT’)
disp(‘   This program shows you how to solve’)
disp(‘   a nonlinear equation’)
disp(‘ ‘)
disp(‘AUTHOR’)
disp(‘   Autar K Kaw of https://autarkaw.wordpress.com&#8217;)
disp(‘ ‘)
disp(‘MFILE SOURCE’)
disp(‘   http://numericalmethods.eng.usf.edu/blog/nonlinearequation.m&#8217;)
disp(‘ ‘)
disp(‘LAST REVISED’)
disp(‘   April 11, 2009’)
disp(‘ ‘)

%% INPUTS
% Solve the nonlinear equation x^3-15*x^2+47*x-33=0
% Define x as a symbol
syms x
% Assigning the fleft hand side o the equation f(x)=0
f=x^3-15*x^2+47*x-33;
%% DISPLAYING INPUTS

disp(‘INPUTS’)
func=[‘  The equation to be solved is ‘ char(f), ‘=0’];
disp(func)
disp(‘  ‘)

%% THE CODE

% Finding the solution of the nonlinear equation
soln=solve(f,x);
solnvalue=double(soln);

%% DISPLAYING OUTPUTS

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

This post is brought to you by Holistic Numerical Methods: Numerical Methods for the STEM undergraduate at http://numericalmethods.eng.usf.edu, the textbook on Numerical Methods with Applications available from the lulu storefront, and the YouTube video lectures available at http://numericalmethods.eng.usf.edu/videos

## Author: Autar Kaw

Autar Kaw (http://autarkaw.com) is a Professor of Mechanical Engineering at the University of South Florida. He has been at USF since 1987, the same year in which he received his Ph. D. in Engineering Mechanics from Clemson University. He is a recipient of the 2012 U.S. Professor of the Year Award. With major funding from NSF, he is the principal and managing contributor in developing the multiple award-winning online open courseware for an undergraduate course in Numerical Methods. The OpenCourseWare (nm.MathForCollege.com) annually receives 1,000,000+ page views, 1,000,000+ views of the YouTube audiovisual lectures, and 150,000+ page views at the NumericalMethodsGuy blog. His current research interests include engineering education research methods, adaptive learning, open courseware, massive open online courses, flipped classrooms, and learning strategies. He has written four textbooks and 80 refereed technical papers, and his opinion editorials have appeared in the St. Petersburg Times and Tampa Tribune.

## 19 thoughts on “How do I solve a nonlinear equation in MATLAB?”

1. chris says:

Nice …. and thnx….

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2. chris says:

Can u please tell me how i can solve a nonlinear equation with a set of constraints in matlab….

thnx.
chris

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3. Vahid says:

Hi
Can you help me to solve this equation?

h (d2h/dx2)=4.822h-1.5h3-3.322
Boundary conditions:
X=0 h=0.73
X=-2 dh/dx=0

Regards,
Vahid

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4. siamak says:

i need help with solving nonlinear system of three equations that repeated over 30000000
nodes see the number of nodes a lot and due to saving the function problem i cant use the fsolve please help me

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5. siamak says:

i need to solve system of three equations over a 30000000 node my problem is how to save them to use in fsolve you know the node number

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6. somayeh says:

ydot1 = 20*y(1)*((y(2)-30.6176)/30.6176)-0.03*y(1);
ydot2 = -0.07*y(2)-(28.7776)*((1.4873)^t)*(y(2)^2)/y(1)^0.38-10*y(2)^2*(y(2)-30.6176)^2/30.6176;
and initial conditions are y1(0)=1706115.9
y2(0)=30.75819596
thanx alot

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7. somayeh says:

i used ode45 for solving it but the answer was NaN!!!!!

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1. Nnc says:

I have a similar problem, I want to solve a non linear 2nd order system of 3 equations & when i use ode45 the answer is NAN :s. Have you solved yours ??

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Nice blog!

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9. <a href=" to get detail knowledge about mathlab and soln with their quastions

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10. Den says:

Thanks man!! That really helped my work.

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11. roshan says:

i want to solve this four equations;
x(3) – ((log(x(1)/ 65792043000 )) -( 0.07+(0.5*(x(2)^2))))/x(2);
x(4) – x(3) + x(2);
8507000337- x(1)*normcdf(x(3)) + 65792043000*exp(-0.07)*normcdf(x(4));
(8507000337* 0.347089018056744) – x(1)*x(2)*normcdf(x(3))];
can u solve?