Solve. (d^2 y)/(dt^2)+2 (dy)/(dt)+5y=d y=1, (dy)/(dt)=phi

ahredent89

ahredent89

Answered question

2022-08-06

Solve. d 2 y d t 2  + 2 d y d t + 5 y = d
y = 1 , d y d t = ϕ

Answer & Explanation

Mariam Hickman

Mariam Hickman

Beginner2022-08-07Added 13 answers

y'' + 2y' + 5y= y(0)=1 y'(0)=0
m 2 + 2 m + 5 = 0
m 1 , 2 = 2 ± 4 20 2 = 1 ± 2 i
y ( t ) = exp ( t ) ( c 1 cos ( 2 t ) + c 2 sin ( 2 t ) )
y ( 0 ) = 1 1 = c 1 + 0. c 2 c 1 = 1
y = exp ( t ) ( c 1 cos ( 2 t ) + c 2 sin ( 2 t ) ) + exp ( t ) ( 2 c 1 sin ( 2 t ) + 2 c 2 cos ( 2 t ) )
y'(0)=0
-c1 + 2c2=0
c2=1/2
y ( t ) = exp ( t ) ( cos ( 2 t ) + 1 / 2 sin ( 2 t ) )

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