# How to use ode45 on a second-order ODE, but without a function file (just one script)?

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EB 8 Oct 2019
댓글: Star Strider 9 Oct 2019
I am given the following second-order ODE and I want to use ode45 and by not creating a function file. I am given the equation above, a timespan t, and initial y and dy values.
I first set up my dydt into a matrix [y1' y2']"
dydt = [y(2); eps*((y(1)^2) - 1)*y(2) - y(1)]
func= dydt(t,y)
and tried to evaluate such ode45(@func, t, [y0, dy0]), but it gives me an error
I also tried setting it up as just one function:
f = @(y1,y2) eps*((y1^2) - 1)*y2 - y1;
Here, it gives me the error that I am using the same function, which was previously used as a variable:
ode45(@f, t, [y0, dy0])

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### 채택된 답변

Star Strider 8 Oct 2019
You are almost there!
Try this:
dydt = @(t,y) [y(2); eps*((y(1)^2) - 1)*y(2) - y(1)];
ic = [1 1]*eps;
tspan = [0 10];
[T,Y] = ode45(dydt, tspan, ic);
figure
plot(T,Y)
grid
That worked when I tried it. Change the initial conditions vector ‘ic’ to match your initial conditions, and ‘tspan’ to get the result you want.

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Star Strider 8 Oct 2019
My pleasure!
Of course!
The MATLAB ODE solvers calculate values for the independent variable (usually time, so ‘T’ here) and dependent variable vector or matrix (here ‘Y’).
Are they just the y and y' values with the tspan I have it set calculating for?
Yes! The ‘y'’ value is the first column of ‘Y’, and ‘y’ is the second column, corresponding to the rows of your ‘dydt’ function.
EB 9 Oct 2019
I see, that makes sense. Thanks again!!
Star Strider 9 Oct 2019
As always, my pleasure!

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