I need help solving a equation with the Runge-Kutta-Fehlberg adaptive step size method using ode45.

I need help solving the last two problems. I attached my code for the first one and what I have of the second and third. In my command window, it is saying function_handle with my last two equations, and it will not run it to get the final answers. I need help fixing my code for the last two problems, and it must be solved using ode45.

% Problem 1

xspan = linspace(0.1,10);

for n = 1:10;

for x = 0.1:10;

roc = @(x,y) (-1^(n+1))./(x^n.*factorial(n));

[x, y] = ode45(roc, xspan, 0, odeopts);

end

end

fprintf('Problem 2 answer is %0.3f.\n', sum(y))

% Problem 2

xspan = linspace(0,4*pi);

for n = 0:4*pi;

roc = @(x, y) (cos(x/2)+sin(2*x)).^2

[x, y] = ode45(roc, xspan, 0, odeopts);

end

fprintf('Problem 3 answer is %0.3f.\n')

% Problem 3

xspan = linspace(0,pi);

for x = 0:pi;

roc = @(x,y) (cos(y)).^2 + (sin(x)).^2

[x, y] = ode45(roc, xspan, 0, odeopts);

end

fprintf('Problem 4 answer is %0.3f.\x')

Answer 1

[James Tursa]

For Problem 2 and Problem 3, you should not be looping over any variables. You simply have a derivative function that you pass to ode45 along with some other inputs. ode45 will do the looping over the variables internally. E.g.,

% Problem 2
xspan = linspace(0,4*pi);
roc = @(x, y) (cos(x/2)+sin(2*x)).^2;
[x, y] = ode45(roc, xspan, 0, odeopts);

and

% Problem 3
xspan = linspace(0,pi);
roc = @(x,y) (cos(y)).^2 + (sin(x)).^2;
[x, y] = ode45(roc, xspan, 0, odeopts);

You might want to save the results of Problems 2 and 3 under different variable names so they don't overwirte.

For Problem 1, the way I read the problem statement you actually have 10 different ode's to solve. That is, you have g1, g2, ..., g10 variables, each with their own ode involving a sum of terms. So you would need 10 different solutions. Can you clarify this?