Solving an ODE second order

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Elia Paini
Elia Paini on 20 Apr 2021
Commented: Elia Paini on 20 Apr 2021
Hi, I have to solve an ODE second order in Matlab, like this:
a*y''(x)=b
Where x is the space coordinate, a and b are costants. The initial condition is y value at x=0. At the end I must obtain the evolution of y in function of space.
How can I model it? Should I use a certain ode solver?
Thank you!

Accepted Answer

Stephan
Stephan on 20 Apr 2021
Edited: Stephan on 20 Apr 2021
change to the initial conditions as you need:
% symbolic variables
syms a b y(x)
% Define derivatives
Dyx = diff(y,x,1)
Dyx(x) = 
D2yx = diff(y,x,2)
D2yx(x) = 
% ode
ode = a* D2yx == b
ode(x) = 
% initioal conditions
conds = [y(0)==1, Dyx(0)==0]
conds = 
% solve
sol = dsolve(ode,conds)
sol = 
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