(a) Use a CAS as an aid in finding the roots of the auxiliary equation for 12y...

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(a) Use a CAS as an aid in finding the roots of the auxiliary equation for

12y(4) + 64y''' + 59y'' - 23y' - 12y = 0.

Give the general solution of the equation.

(b) Solve the DE in part (a) subject to the initial conditions y(0) = -1, y'(0) = 2, y''(0) = 5, y'''(0) = 0.

Use a CAS as an aid in solving the resulting systems of four equations in four unknowns.

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