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Chapter 6: Q12E (page 337)

find a differential operator that annihilates the given function.

3x2-6x+1

Short Answer

Expert verified

D3is the differential operator that annihilates the given function.

Step by step solution

01

Differentiate the function continuously

Let the function bef(x)=3x2-6x+1

Then

f'(x)=6x-6f''(x)=6f'''(x)=0

HenceD3[f]=0

ThenD3 is the differential operator that annihilates the given function.

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Most popular questions from this chapter

Determine whether the given functions are linearly dependent or linearly independent on the interval(0,鈭�) .

(a){e2x,x2e2x,e-x}

(b){exsin2x,xexsin2x,ex,xex}

(c) {2e2x-ex,e2x+1,e2x-3,ex+1}

Use the annihilator method to determine the form of a particular solution for the given equation.

(a)y''+6y'+5y=e-x+x2-1

(b)y'''+2y''-19y'-20y=xe-x

(c)y(4)+6y''+9y=x2-sin3x

(d)y'''-y''+2y=xsinx

Solve the given initial value problem

y'''+7y''+14y'+8y=0y(0)=1y'(0)=鈭�3y''(0)=13

find a general solution to the given equation.

y'''-3y''+3y'-y=ex

Find a general solution toy(4)+2y(3)+4y''+3y'+2y=0 by using Newton鈥檚 method to approximate numerically the roots of the auxiliary equation. [Hint: To find complex roots, use the Newton recursion formulazn+1=zn鈭�f(zn)f'(zn)and start with a complex initial guess z0.]
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