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Chapter 4: Q15RP (page 231)

Question: Find a general solution to the given differential equation.3y'''+10y''+9y'+2y=0

Short Answer

Expert verified

The general solution to the given differential equation is:

y=c1e-t+c2e-2t+c3e-13t

Step by step solution

01

Write the auxiliary equation of the given differential equation

The differential equation is3y'''+10y''+9y'+2y=0.

The auxiliary equation for the above equation3m3+10m2+9m+2=0.

02

Find the roots of the auxiliary equation.

Solve the auxiliary equation,

3m3+10m2+9m+2=03m3+m2+9m2+3m+6m+2=0m23m+1+3m3m+1+23m+1=03m+1m2+3m+2=03m+1m2+2m+m+2=03m+1mm+2+1m+2=0m+1m+23m+1=0

The roots of the auxiliary equation are m1=-1,鈥�m2=-2,鈥�m3=-13.

Thus, the general solution of the given equation isy=c1e-t+c2e-2t+c3e-13t.

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Most popular questions from this chapter

Decide whether or not the method of undetermined coefficients can be applied to find a particular solution of the given equation.2y''(x)-6y'(x)+y(x)=sinxe4x

Find a particular solution to the given higher-order equation.

y'''-2y''-y'+2y=2t2+4t-9

Find the solution to the initial value problem.

y''+9y=27;鈥夆赌夆赌夆赌夆赌�y(0)=4,鈥夆赌夆赌夆赌�y'(0)=6

Find a particular solution to the differential equation.

y''+2y'+2y=4te-tcost

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