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Chapter 4: Q4.3-15E (page 172)

Find a general solution y''-3y'-11y=0

Short Answer

Expert verified

The general solution of the given equationy''-3y'-11y=0isy(t)=c1e(3+53)t+c2e(3-53)t.

Step by step solution

01

Given information.

The differential equation isy''-3y'-11y=0.

02

Finding roots of the auxiliary equation.

Then the auxiliary equation is r2-3r-11=0.

The roots of the auxiliary equation are:

r=3卤32-4脳-11脳12脳1r=3卤9+442r=3卤532

03

Final answer.

Therefore, the general solution is:

y(t)=c1e(3+53)t2+c2e(3-53)t2

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