Rewrite the following differential equation as an equivalent system of first-order differential equations. Use the variables x1=x, x2=x′,x3=x′′,etc. (so that your equations will have the form x′2=x3, etc.: denote subscripts by appending the subscript to the variable name: x1= x1) Equation to rewrite: x(4) + 17x" - 17' + 17x = -9 cos(2t)

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Step-by-step explanation:

Your equation is . Solve for the fourth derivative to get

Now apply said change of variables: let . Then, substituting on out first equation, we obtain the system:

In general, if you have an nth order ordinary differential equation, you can apply the same idea to obtain a system of differential equations with n unknowns. Therefore, solving systems of differential equations is equivalent to solving higher-order differential equations.

(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

where is the figure