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Question: Variation of Parameters Problem

Question:Variation of Parameters Problem

cojx16 5 Maple
linearalgebra homework differential-equations vectorcalculus
November 21 2019
1

I have a problem for school that I need help with. 

Solve: by variation of parameters.

x3y’’’ – x2y’’ − 2xy’ + 6y = x2

Use any software, e.g. Maple, as an aid in computing roots of the auxiliary equation and the Wronskian-based determinants W, W1, W2, W3

I was able to hand calculate the roots as [m1 = 3, m2 = 2, m3 = -1]
 

NULL

with(VectorCalculus); Wronskian([x^3, x^2, 1/x], x, 'determinant')

Matrix(%id = 18446744078324919462), -12*x

 (1)

with(VectorCalculus); Wronskian([0, x^2, 1/x], x, 'determinant')

Matrix(%id = 18446744078349556782), 0

 (2)

with(VectorCalculus); Wronskian([x^3, 0, 1/x], x, 'determinant')

Matrix(%id = 18446744078266878782), 0

 (3)

with(VectorCalculus); Wronskian([x^3, x^2, 0], x, 'determinant')

Matrix(%id = 18446744078331625094), 0

 (4)

m3 := Matrix(3, 3, [0, x^2, 1/x, 0, 2*x, 1/x^2, x^2, 2, 2/x^3])

Matrix(%id = 18446744078385724822)

 (5)

Determinant(m3, method = multivar)

Determinant(Matrix(%id = 18446744078385724822), method = multivar)``

 (6)

roots(x^3-x^2-2*x+6, alpha, beta)

[]

 (7)

``

solve(x^3-x^2-2*x+6 = 0, x)

-(1/3)*(71+9*58^(1/2))^(1/3)-(7/3)/(71+9*58^(1/2))^(1/3)+1/3, (1/6)*(71+9*58^(1/2))^(1/3)+(7/6)/(71+9*58^(1/2))^(1/3)+1/3+((1/2)*I)*3^(1/2)*(-(1/3)*(71+9*58^(1/2))^(1/3)+(7/3)/(71+9*58^(1/2))^(1/3)), (1/6)*(71+9*58^(1/2))^(1/3)+(7/6)/(71+9*58^(1/2))^(1/3)+1/3-((1/2)*I)*3^(1/2)*(-(1/3)*(71+9*58^(1/2))^(1/3)+(7/3)/(71+9*58^(1/2))^(1/3))

 (8)

m3 := Matrix(3, 3, [0, x^2, 1/x, 0, 2*x, 1/x^2, 1/x, 2, 2/x^3])

Matrix(%id = 18446744078348970214)

 (9)

Determinant(m3, method = multivar)

Determinant(Matrix(%id = 18446744078348970214), method = multivar)

 (10)

``

m3 := Matrix(3, 3, [0, x^2, 1/x, 0, 2*x, 1/x^2, 1/x, 2, 2/x^3])

``

``


 

Download project_27.mw

 

 

 
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