ODE45 for a second order differential equation

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Remston Martis
Remston Martis 2018-4-21
编辑： Ebraheem Menda 2021-6-30
I have a second order differential equation : y''=(2*y)+(8*x)*(9-x); Boundary Conditions y(0)=0 , y(9)=0 Need to solve the diff eq using ode45.
I've tried watching a bunch of tutorials but I just cannot seem to figure out how the function is written as a column vector [y';y'']. I don't understand it at all and that might make this query vague too.
Hope someone can help with the code or the explanation on how to solve the above.
Thank you

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采纳的回答

Torsten
Torsten 2018-4-23
[x,y] = ode45(@fun,[0 9],[0 -28]);
function dy = fun(x,y)
dy = zeros(2,1);
dy(1) = y(2);
dy(2) = 2*y(1)+8*x*(9-x);
But for a boundary value problem like yours, you will have to use "bvp4c" instead of "ode45".
Best wishes
Torsten.
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Torsten
Torsten 2018-4-23
编辑：Torsten 2018-4-23
There seems to be a duplicate of ode45 on your desktop - rename or remove it.

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更多回答（2 个）

Stephan
Stephan 2018-4-22
编辑：Stephan 2018-4-22

Hi,

transform a n-th order ode into a system of n 1st order ode's to solve it.

Matlab documentation example: https://de.mathworks.com/help/matlab/math/solve-nonstiff-odes.html

More examples here: https://www.google.de/url?sa=t&source=web&rct=j&url=http://www.math.poly.edu/courses/ma2132/Notes/MA2132EquationsToSystems.pdf&ved=2ahUKEwiQ_tCRq83aAhWMMewKHQ7CC1IQFjALegQIBxAB&usg=AOvVaw07Im9F42d9LrfvRIzL35Pd

If you read this i guess you can quickly solve your problem.

  2 个评论
Remston Martis
Remston Martis 2018-4-23
编辑：Remston Martis 2018-4-23

I keep getting these errors: Attempt to execute SCRIPT ode45 as a

function: C:\Users\remst\Desktop\ode45.m

Error in ode45 (line 3) [x,y] = ode45(@fun,[0 9],[0 -28]);

My function declarations are:

function fun=fun(x,y)
fun=zeroes(2,1);
fun(1)=y(2);
fun(2)=(2*y(1))+8*x*(9-x);

Calling the function :

[x,y] = ode45(@fun,[0 9],[0 -28]);

Where am I going wrong? I've tried 10000s of ways

Ebraheem Menda
Ebraheem Menda 2021-6-30
编辑：Ebraheem Menda 2021-6-30
In this case you have declared the name of the function and its output both with the same name 'fun'. That is the problem it seems.

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NARSIRAM GURJAR
NARSIRAM GURJAR 2019-9-16
C:\Users\remst\Desktop\ode45.m
save this file with different name

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