Solving an ODE second order

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!

Answer 1

[Stephan]

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 = 

[Elia Paini]

Thank you! What should I add if I want to integrate in an x interval?

[Stephan]

Do you mean that you want to treat it as a boundary value problem in a way x(0)=... and x(5)=...?

[Elia Paini]

Exactly

[Stephan]

Change the conds:

% 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, y(5)==0]

conds = 

% solve
sol = dsolve(ode,conds)

sol = 

[Elia Paini]

Thank you!!