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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