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Chapter 4: Q6RP (page 231)

Find a general solution to the given differential equation.y''+8y'-14y=0

Short Answer

Expert verified

Thus, the general solution of the given differential equation is:

y=c1e-4-30t+c2e-4+30t

Step by step solution

01

Write the auxiliary equation of the given differential equation

The differential equation isy''+8y'-14y=0.

The auxiliary equation for the above equation ism2+8m-14=0.

02

Find the roots of the auxiliary equation. 

Solve the auxiliary equation,

m2+8m-14=0m=-8±64--562m=-8±1202m=-4±30

The roots of the auxiliary equation arem1=-4+30,  &  m2=-4-30.

Thus, the general solution of the given equation isy=c1e-4-30t+c2e-4+30t.

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Most popular questions from this chapter

Vibrating Spring with Damping. Using the model for a vibrating spring with damping discussed in Example3

(a)Find the equation of motion for the vibrating spring with damping ifm=10kg,b=60kg/sec,k=250kg/sec2,y(0)=0.3m,andy'(0)=-0.1m/sec.

(b)After how many seconds will the mass in part(a) first cross the equilibrium point?

(c)Find the frequency of oscillation for the spring system of part (a).

(d)Compare the results of problems32 and33determine what effect the damping has on the frequency of oscillation. What other effects does it have on the solution?

Find a particular solution to the differential equation.

θ''(t)-θ(t)=tsint

In Problems 35, use the method of undetermined coefficients to find a particular solution to the given higher-order equation.y'''+y''-2y=tet

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.

2y''+3y'-4y=2t+sin2t+3

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''+y'+ty=et+7
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