SOLUTION: Solve the initial-value problem d^(2)y/dt^(2)+4dy/dt+4y=0,y(1)=0,y′(1)=1. y(t)=

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Question 1184644: Solve the initial-value problem d^(2)y/dt^(2)+4dy/dt+4y=0,y(1)=0,y′(1)=1.
y(t)=

Answer by robertb(5830)   (Show Source): You can put this solution on YOUR website!

The characteristic equation of the D.E. is , which gives the double root .
===> The general solution to the D.E. is .

==> ===> ===> .

Also, ===> A + B = 0, or B = -A.

Combining this with the preceding equation, we get

. ===> ===> .

after combining factors and simplifying,


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