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Chapter 4: Q4.3-10E (page 172)

Find a general solution y''+4y'+8y=0

Short Answer

Expert verified

The general solution of the given equation y''+4y'+8y=0isy(t)=e-2t(c1cos(2t)+c2sin(2t)).

Step by step solution

01

Differentiate the value of y.

Given differential equation is y''+4y'+8y=0.

Let role="math" localid="1654067583036" y=ert

Therefore, we have:

y'(t)=rert

y''(t)=r2ert

02

Finding the roots.

Then the auxiliary equation is r2+4r+8=0

The roots of the auxiliary equation are:

r=-4卤42-4脳1脳82脳1r=-4卤16-322r=-4卤4i2r=-2卤2i

03

Final answer.

Therefore, the general solution is:

y(t)=e-2脳t(c1cos(2t)+c2sin(2t))y(t)=e-2t(c1cos(2t)+c2sin(2t))

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Most popular questions from this chapter

Find a general solution. y''+2y'+5y=0

Find the solution to the initial value problem.

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Find a general solution to the differential equation.

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