Eulers Formula Program Help

Hello, I need a little help with my Eulers formula program that I'm creating with Matlab. This is my following program. The issue I am having is when I input the dxdy formula, for example x+y, it is giving me the incorrect answer. However, if I put that x+y in place of the dxdy in the for loop, I get the correct answer. I just don't understand why the input x+y is different then if I manually put x+y within the for loop.

x=input('Input the initial value of "x":  ');
y=input('Input the initial value of "y":  ');
dxdy=input('Input the differential equation you have: ');
value=input('Input the value of the unknown function in which you want to evaluate to. (i.e if you want y(3), type in 3) \n');
step=input('Input the step size you would like:  ');
for i=0:100
    dy=dxdy*step;
    x=x+step;
    y=y+dy;
    if x==value
        fprintf('The estimated value of the function is %3.2f \n',y)
    end
end

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Answer 1

[Walter Roberson]

When you put x+y in place of dxdy in the for loop, do you end up with

dy=x+y*step;

or do you end up with

dy=(x+y)*step;

?

Note that when you input() x+y that it evaluates the expression at the time of the input(), giving you a constant answer, whereas in either of the writings above, x and y are going to be changing because you are adding values to both of them inside the for loop.

If you want to input an expression that is to be evaluated at run time, you will need to use the 's' option of input(), and then in the loop you will need to use one of the several ways of evaluating the expression -- such as creating a function handle out of it before the loop by using str2func(), and then applying that function handle to (x,y) inside the loop. The best way to use str2func() depends on your MATLAB version; it improved somewhere around 2010b.

[Teague]

I was typing in (x+y),

As of the rest of your explanation, I believe you are dead on. I will need to look into this because I only know the basic input options.

What i can see, I want it to evaluate the expression as the x and y values are changing. I have the output working fine with what I have above. I'm kind of confused by the str2func() command. Is there a way just to change this s input you speak of without having to change anything else?

[Walter Roberson]

dxdy=input('Input the differential equation you have: ', 's');

would read in what the user typed as a character string. But then you need to find a way to evaluate that string with particular x and y values, at the appropriate time.

See http://www.mathworks.com/matlabcentral/answers/15450-convert-a-symbolic-equation-to-a-vector-equation for information about converting a string to a function handle.

When you call the function handle in the loop, make sure you provide arguments:

dy = fdydx(x,y) * step