Question

Solving a differential with initial values, question below

Answer 1

:)

Answer 2

\[u'' + 4u + 5u = 0\]
\[u(0)=1\]
\[u'(0)=0\]

Answer 3

Aux equation is:
\[\lambda ^{2} + 4\lambda + 5 = 0\]

Answer 4

\[\lambda = 2 \pm i\]

Answer 5

I think I get B = 1

Answer 6

\[e^{0}((A*0)+(B*1)) = B\]

Answer 7

\[u(t)=e^{−2t}(Acos(t)+Bsin(t))\]
\[u(0)=e^{−2(0)}(Acos(0)+Bsin(0))\]

Answer 8

\[u(0)=e^{−2(0)}(Acos(0)+Bsin(0))=0\]

Answer 9

ok I'm following now I need to find \[u'(t)\]