# Of the differential equation y y 4sec x 4 10 pts set

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, of the differential equation y y 4sec( x ). ______________________________________________________________________ 4. (10 pts.) Set up the correct linear combination of undetermined coefficient functions you would use to find a particular integral, y p , of the O.D.E. y 4 y 5 y x 2 e 2 x sin( x ) e 2 x . [ Warning: (a) If you skip a critical initial step, you will get no credit!! (b) Do not waste time attempting to find the numerical values of the coefficients!! ]

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TEST2/MAP2302 Page 3 of 4 ______________________________________________________________________ 5. (10 pts.) The factored auxiliary equation of a certain homogeneous linear O.D.E. with real constant coefficients is as follows: m(m - 2 π ) 2 (m - (5i)) 3 (m - (-5i)) 3 = 0 (a) (5 pts.) Write down the general solution to the differential equation. [ WARNING: Be very careful. This will be graded Right or Wrong!! ] (b) (5 pt.) What is the order of the differential equation? ______________________________________________________________________ 6. (15 pts.) (a) Obtain the differential equation satisfied by the family of curves defined by the equation (*) below. (b) Next, write down the differential equation that the orthogonal trajectories to the family of curves defined by (*) satisfy. (c) Finally, solve the differential equation of part (b) to obtain the equation(s) defining the orthogonal trajectories. [These, after all, are another family of curves.] (*) . x 2 2 y 1 ce 2 y
TEST2/MAP2302 Page 4 of 4 ______________________________________________________________________ 7. (10 pts.) It turns out that the nonzero function f( x ) = exp( x) is a solution to the homogeneous linear O.D.E.
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