KdV ODE third-order
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It is necessary to find a solution that satisfies the boundary conditions:
u′′′+u′+λu=f.
initial conditions:
u′′(0)=
u′(0)+
u(0),
u′(0)+u(0),u′′(1)=
u(1),
u(1), u′(1)=
u(1),
u(1),How to define u and fin matlab?
where λ>0, 
;
, 
, 
and 
- given numbers.
;, , and - given numbers.
≤ 
where C is a positive constant independent of 𝑢 and f
clear;
syms y(x) y0 lambda u
Dy = diff(y);
D2y = diff(y,2);
D2y_2 = diff(y,2);
D3y = diff(y,3);
ode = D3y + lambda*u == y(x);
ySol(x) = dsolve(ode);
