How do i solve differential equation 2nd oder simbolically and numerically?

Hello everyone i am completly new to Matlab and I have a problem with an exercise in my practice book. I have this differential equation:

y(0) = 1

and i want to solve it simbolically and numerically in matlab.

so first i have to change it in first order differential equation:

But how do i continue? I´m trying for hours at this point😅

Answer 1

[Torsten]

syms t y(t) sigma(t)
eqn_diff = diff(y,t,2)+3*diff(y,t)+y(t)-2*sigma(t)==0;
ysol(t) = dsolve(eqn_diff);
var = symvar(ysol)

var = 

eqn_alg = subs(ysol,var(1),0)-1==0

eqn_alg(t) = 

C1 = solve(eqn_alg,var(2));
ysol = subs(ysol,var(2),C1)

ysol(t) = 

[Karl-JR]

first off thank you. just a small question. So if i solve it simbolically, the c in differential equation 2nd order has to be defined. Did i get that right?

[Torsten]

You specified one initial condition for a second-order ODE (y(0)=1). So one free parameter (in this case C1) can be eliminated from the two degrees of freedom (C1 and C2) for y. If you impose a second condition on y, you can get a unique solution (means: you can also eliminate C2).

[Karl-JR]

Thank you so much