# 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 http://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

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### 18 Responses to How do I solve a nonlinear equation in MATLAB?

1. nice blog…..

2. chris

Nice …. and thnx….

3. chris

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

thnx.
chris

4. Vahid

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

5. siamak

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

6. siamak

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

7. somayeh

please help me to solve this nonlinear oderinery differntial equation
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

8. somayeh

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

• Nnc

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 ??

Nice blog!

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

11. ``` ```

12. Den

Thanks man!! That really helped my work.

13. roshan

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?