Question about Second-order ODE.

Q. A mass-spring-damper system is to be modeled to determine behavior of the system. The damping is modeling using a non-linear damping term. The resulting differential equation is given by: x''+4*x'+2.5*x = 0

The mass is released from rest with a displacement of x(t=0) = +2. What is the velocity at t = 5?

My code is:

function dx = dx(t,x)

dx = [x(2); -2.5*x(1)-4*x(2)];

and

[t,x] = ode45(@dx,[0 5],[2 0],0.005);

x = x(end,2)

Then I got x(t=5) = -0.0423

The answer should be 0.213. How could I get this answer?

[Star Strider]

The problem could be in the absence of the ‘non-linear damping term’ because (unless I’m missing something) I see only a linear second-order differential equation.