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Chapter 4: Q5RP (page 231)

Find a general solution to the given differential equation.6y''-11y'+3y=0

Short Answer

Expert verified

The general solution to the given differential equation isy=c1e32t+c2e13t.

Step by step solution

01

Write the auxiliary equation of the given differential equation 

The differential equation is6y''-11y'+3y=0.

The auxiliary equation for the above equation is6m2-11m+3=0.

02

Find the roots of the auxiliary equation

Solve the auxiliary equation,

6m2-11m+3=06m2-9m-2m+3=03m2m-3-12m-3=02m-33m-1=0

The roots of the auxiliary equation are, m1=32,鈥夆赌�&鈥夆赌�m2=13.

Thus, the general solution of the given equation isy=c1e32t+c2e13t.

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Most popular questions from this chapter

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

Find the solution to the initial value problem.

y''+y'-12y=et+e2t-1;鈥夆赌夆�夆赌夆��y(0)=1,鈥夆赌夆�夆赌�y'(0)=3

Find the solution to the initial value problem. y''+2y'+y=t2+1-et鈥夆赌夆�夆赌夆�夆赌夆�夆赌夆��y(0)=0,鈥夆赌夆�夆赌�y'(0)=2

Find a particular solution to the differential equation.

x''(t)-2x'(t)+x(t)=24t2et

The auxiliary equation for the given differential equation has complex roots. Find a general solution.y''-10y'+26y=0
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