Question

Rewrite the second order DE as 'n system first order equations and solve the problem using one step of the Runge-Kutta method, using h=0.1
x''+4x'=3sin(t)-1; x(0)=1; x'(0)=-1

Answer 1

Define u as u=x', the first derivative of x.
That is one equation.
Next equation is u' + 4u =3 sin(t) =1.

Runge-Kutta is numerical method. Look up actual formula.