Solve the boundary value problem with the of this theorem.

problem:

ky a y

(0)(0

theorem: the unique solution to y+px}y° + q#}y = g(x}

satisfying the initial conditions y(o0, y(to) = 0 is given by

y1(t) y (ar)y2() 42(t) g )d (t)dt y() w(t)

where y1 and y2 are linearly independent solutions of y+p(x}y° + q[x)y = 0

and w is their wronskian.

(x3 + 6x2 + 2x - 6) • (x - 1)

step-by-step explanation:

polynomial long division :

3.2     polynomial long division

dividing :   x4+5x3-4x2-8x+6

                              ("dividend")

by         :     x-1     ("divisor")

dividend     x4   +   5x3   -   4x2   -   8x   +   6

- divisor   * x3     x4   -   x3            

remainder         6x3   -   4x2   -   8x   +   6

- divisor   * 6x2         6x3   -   6x2        

remainder             2x2   -   8x   +   6

- divisor   * 2x1             2x2   -   2x    

remainder               -   6x   +   6

- divisor   * -6x0               -   6x   +   6

remainder                     0

quotient :   x3+6x2+2x-6   remainder:   0

the monthly balance will be $75,000

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so

step-by-step explanation:

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