What our customers say...
Thousands of users are using our software to conquer their algebra homework. Here are some of their experiences:
Thank you very much for your help!!!!! The program works just as was stated. This program is a priceless tool and I feel that every student should own a copy. The price is incredible. Again, I appreciate all of your help.
Linda Hodges, SC
Graduating high-school, I was one of the best math students in my class. Entering into college was humbling because suddenly I was barely average. So, my parents helped me pick out Algebrator and, within weeks, I was back again. Your program is not only great for beginners, like my younger brothers in high-school, but it helped me, as a new college student!
Keith Erich Johnston, KS
It's good news for any school, teacher or student when such a fantastic software is specifically designed for Algebra. Great job!
Bim Oyadare, FL
The most valuable algebra tutor I have ever come across. It caters not only the basic learners but also the students who are doing advanced algebra. The step-by-step solution to the problems accompanied by explanation of each step makes this software priceless mathematical tool.
Ann Wills, KY
I am a parent of an 8th grader:The software itself works amazingly well - just enter an algebraic equation and it will show you step by step how to solve and offer clear, brief explanations, invaluable for checking homework or reviewing a poorly understood concept. The practice test with printable answer key is a great self check with a seemingly endless supply of non-repeating questions. Just keep taking the tests until you get them all right = an A+ in math.
Gary Sterns, CA
I have tried everything. We use it every day for her schooling. Great program!
C.B., Oklahoma
HOW TO SOLVE A 2ND ORDER DIFFERENTIAL EQUATIONS
free solving equations with fractional coefficients help ,
sat prep formulas square root ,
ti-89 convert number base 6 to number base 3 ,
factorization fraction quadratic equations equation,
algebraic equation with fractional exponent ,
simultaneous linear equation in two variable for class ten,
multiplication division rational expressions problem solvers ,
ti 83 plus factoring complex number ,
quadratic formula square root method ,
free answers for comparing linear combination methods for solving systems of equation in a chart ,
Algebra, what are the difference between evaluation and simplification of an expression ,
partial differential equation solution first order linear ,
Algebra help with factoring sums of cubes ,
charts and graph on the comparison of substitution and linear combination ,
substitution method is easier than the addition method when one of the equations is very simple and can readily be solved for one of the variables ,
why use factoring to solve quadratic equations ,
java code convert mixed fraction to decimal ,
math equations percent algebra formulas,
square root revision for calculator common entrance ,
addition and subtraction of fractions worksheets lcd ,
online algebra calculator square root,
algebra square root solver ,
algebra square cube roots interactive lessons ,
simplifying radicals absolute value ,
Algebra expressions, what is the difference between evaluation and simplification of an expression? ,
algebra linear equations graphing worksheet ,
calculating a 3rd order polynomial with one variable,
java examples to find the number & sum of integers divisible by 7 ,
cube root calculator TI-83 plus how to do ,
addition and subtraction formulas solved problems,
solve quadratic equation for the specified variable,
maple solve nonlinear multivariable two equations problems examples ,
solving solving binomial equations india,
free Algebra calculator for Rational Expression
Thank you for visiting our site! You landed on this page because you entered a search term similar to this: how to solve a 2nd order differential equations. We have an extensive database of resources on how to solve a 2nd order differential equations. Below is one of them. If you need further help, please take a look at our software "Algebrator", a software program that can solve any algebra problem you enter!
MA2051 - Ordinary Differential Equations
Matlab - Solve a second-order equation numerically
Start by reading the instructions in wrk4 (or wheun or weuler); just type help wrk4 and focus on the last part of the help. Here is how it goes. To solve
,
define 
and rewrite the second-order
equation as a system of two first-order equations:
In vector notation, this system has the form 
,
where
Now use an editor to create a M-file named frcdsprg.m for this
vector system 
:
% frcdsprg.m - new version % x'' + 2x' + x = sin( 0.9 t ) written as the system % x' = v, v' = -x - 2v + sin( 0.9 t) % y(1) is x, y(2) is v. function yprime = frcdsprg( t, y ) yprime(1) = y(2); % x' = v in terms of y's yprime(2) = -y(1) - 2*y(2) + sin( 0.9*t ); % v' = -x ... in terms of y's
The following sequence of commands will solve this system
with initial conditions x(0) = 1, v(0) = 2
for 
.
y0 = [1; 2]; [t, y] = wrk4( 'frcdsprg', 0, 30, y0, 0.2 );The plot that appears is the graph of the approximate solution curve x(t) for
.
Type [t,y] (without a semicolon). Three columns of numbers will fly by; the first column is t, the second column is y(1) = x(t), and the third column is y(2) = v(t). In the above instructions, notice that you are solving both of the first-order equations at the same time. The initial data is specified in y0 = [1;2], and the time step by 0.2.
The following commands will plot x(t) and v(t) again st t and annotate the plot:
plot(t,y(:,1),'-'); % plots x(t) with lines
hold on; % holds the old plot
plot(t,y(:,2),'.'); % plots v(t) with dots
title(' x" + 2 x'' + x = sin(0.9 t) '); % adds a title ('' prints as ')
xlabel(' time ');
ylabel(' position and velocity '); % label the axes
text(15,1.0,' ... velocity '); % put text at (15,1.0)
text(15,1.5,' --- position '); % put text at (15,1.5)
Note that y(:,1) refers to the first column of y (which is
x(t)) and y(:,2) refers to the second column of y (which
is 
). To make a new plot, type hold off.
The following commands will plot v(t) against x(t) (instead of t), producing a phase plane plot of this nonautonomous system:
plot(y(:,1),y(:,2),'.'); % plots x and v
title(' Phase Plane: x" + 2 x'' + x = sin(0.9 t) '); % adds a title
xlabel(' position ');
ylabel(' velocity '); % label the axes
To control the axis limits, type axis( [ -0.75 1 -1 1.5] ); the graph will show ``x'' values from -0.75 to 1 and ``y'' values from - 1 to 1.5. Type help axis for more information.
Alternatively, to get a phase plane plot directly for an autonomous system, type pplane and enter your equations into the text box that appears.
Next: Index
© 1996 . All rights Reserved. File November 21, 1996.
How can Algebrator Help YOU?
- It solves any problem from your textbook
- It gives you all the steps, not just solutions - just like a teacher!
- Algebrator is your personal 24/7 math tutor that costs less than one hour of live tutoring
- When you don't understand a step, it gives you an explanation
- You get your homework done in minutes, and you learn algebra
Algebrator can solve problems in all the following areas:
- simplification of algebraic expressions (operations with polynomials (simplifying, degree, synthetic division...), exponential expressions, fractions and roots (radicals), absolute values)
- factoring and expanding expressions
- finding LCM and GCF
- operations with complex numbers (simplifying, rationalizing complex denominators...)
- solving linear, quadratic and many other equations and inequalities (including basic logarithmic and exponential equations)
- solving a system of two and three linear equations (including Cramer's rule)
- graphing curves (lines, parabolas, hyperbolas, circles, ellipses, equation and inequality solutions)
- graphing general functions
- operations with functions (composition, inverse, range, domain...)
- simplifying logarithms
- basic geometry and trigonometry (similarity, calculating trig functions, right triangle...)
- arithmetic and other pre-algebra topics (ratios, proportions, measurements...)
- NEW! Linear Algebra (operations with matrices, inverse matrix, determinants...)
Instant Bonus: Receive thousands of problems pre-entered
by Algebrator's users if you buy the software now!
