Could you tell me if i did this problem correctly? I don't have the answer to this problem. But here's my work:
Use Laplace transforms to solve the initial value problem
y'' +5y' + 4y = delta 1 (t) ,y(o)=0 , y'(0)= 0
p^2 Y - py(0)-y'(0)+5(pY-y(0))+4Y = e^-p
Y(p^2 + 5p +4) = e^-p
Y= (e^-p)/(p^2 + 5p +4)
1/ [(p+4)(p+1)] = A/ (p+4) + B/(p+1)
A=-1/3, B=1/3
(-1/3)(e^-p)/(p+4) + (1/3)(e^-p)/(p+1)
-1/3 U1(t)e^(-4(t-1)) + 1/3U1(t)e^(-(t-1))
thanks
Use Laplace transforms to solve the initial value problem
y'' +5y' + 4y = delta 1 (t) ,y(o)=0 , y'(0)= 0
p^2 Y - py(0)-y'(0)+5(pY-y(0))+4Y = e^-p
Y(p^2 + 5p +4) = e^-p
Y= (e^-p)/(p^2 + 5p +4)
1/ [(p+4)(p+1)] = A/ (p+4) + B/(p+1)
A=-1/3, B=1/3
(-1/3)(e^-p)/(p+4) + (1/3)(e^-p)/(p+1)
-1/3 U1(t)e^(-4(t-1)) + 1/3U1(t)e^(-(t-1))
thanks