Differential Equation Matlab Resolve

Hello everyone, I can not resolve / implement the follow differential equation. Is there anyone who can help me??

y''(t)+p(t)y'+q(t)y=0

q=1/(1+t)^2;

p=1+q;

y(0)=1; y'(0)=0; y''(0)=0; ------>    y'(4*pi)=??

Answer 1

[Andrei Bobrov]

Your odefun - funnn:

function dy = funnn(t,y)

      q = 1./(1+t).^2;

      dy = [ y(2);
             -((q + 1).*y(2) + q.*y(1))];
end

solve:

sol = ode45 (@funnn, [0 20], [1 0]);
out = deval(sol,4*pi,2);

Answer 2

[MiguelMauricio]

Try using dsolve

syms y(t) t
q=1/(1+t)^2;
p=1+q;
Dy=diff(y);D2y=diff(y,2);
solution=dsolve(D2y+p*Dy+q*y==0,Dy(0)==0,y(0)==1,t)

In any case, your last initial condition (y''(0) must be wrong since the equation would not hold. For t=0 you would have 0 + 2*0 + 1*1=0