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Chapter 4: Q4.3-9E (page 172)

Find a general solution.y''-8y'+7y=0

Short Answer

Expert verified

The general solution of the given equation y''-8y'+7y=0isy(t)=c1et+c2e7t.

Step by step solution

01

Differentiate the value of y.

Given differential equation is y''-8y'+7y=0

Let role="math" localid="1654066682579" y=ert

Therefore,

y'(t)=rerty''(t)=r2ert

02

Finding the roots of the auxiliary equation.

Then the auxiliary equation is r2-8r+7=0.

Now find the roots of the auxiliary equation.

role="math" localid="1654066897417" r2-8r+7=0r2-r-7r+7=0r(r-1)-7(r-7)=0(r-1)(r-7)=0

r=1,r=7

03

Final answer.

Therefore, the general solution isy(t)=c1et+c2e7t

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Most popular questions from this chapter

Decide whether the method of undetermined coefficients together with superposition can be applied to find a particular solution of the given equation. Do not solve the equation.y''-6y'-4y=4sin3t-t2e3t+1t

Decide whether or not the method of undetermined coefficients can be applied to find a particular solution of the given equation. ty''-y'+2y=sin3t

Find a particular solution to the differential equation.

y''-y'+9y=3sin3t

Decide whether the method of undetermined coefficients together with superposition can be applied to find a particular solution of the given equation. Do not solve the equation.y''-2y'+3y=cosht+sin3t

Using the mass-spring analogy, predict the behavior as t→∞of the solution to the given initial value problem. Then confirm your prediction by actually solving the problem.

(a). y''+16y=0;y(0)=2,y'(0)=0(b). y''+100y'+y=0;y(0)=1,y'(0)=0(c). y''-6y'+8y=0;y(0)=1,y'(0)=0(d). y''+2y'-3y=0;y(0)=-2,y'(0)=0(e). y''-y'-6y=0;y(0)=1,y'(0)=1
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