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Chapter 4: Q4.3-11E (page 172)

Find a general solution z"+10z'+25z=0

Short Answer

Expert verified

The general solution of the given equationz"+10z'+25z=0isy(t)=(c1+c2t)e鈭�5t.

Step by step solution

01

Given information.

Given differential equation isz"+10z'+25z=0.

02

Finding roots of the auxiliary equation.

Then the auxiliary equation is r2+10r+25=0

Solve the auxiliary equation to obtain the roots.

(r+5)2=0r+5=0r=-5

03

Final answer.

Therefore, the general solution isy(t)=(c1+c2t)e-5t

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Most popular questions from this chapter

Find the solution to the initial value problem.

y''=6t;鈥夆赌夆赌夆赌夆赌�y(0)=3,鈥夆赌夆赌夆赌�y'(0)=-1

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

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y''+ety'+y=7+3t
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