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Example 2:



Obtain the solution x(t), t>=0, of the differential equation



d^2x(t)/dt^2+5*dx(t)/dt+6=f(t)



where f(t) is the pulse function



         | 3 (0<= t <6)

 f(t) =  |

         | 0 (t >= 6)



Initial conditions x(0)=0 and x'(0)=2



First rewriting f(t) to Heaviside functions



f(t) = 3*(u(t) - u(t-6))



Now the equation can be solved with SolvD



SolveD( d(x(t),t,2)+5*d(x(t),t)+6=3*(u(t)-u(t-6)),{x(t),0,2})



Result



x(t)=(13/25-3*t/5-13*e^(-5t)/25)*u(t)+(93/25-3*t/5-3*e^(-5*t+30)/25)*u(t-6)