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# B 3 pts next write down the differential equation

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(b) (3 pts.) Next, write down the differential equation that the orthogonal trajectories to the family of curves defined by (*) satisfy. (c) (3 pts.) Finally, solve the differential equation of part (b) to obtain the equation(s) defining the orthogonal trajectories. (*) y e cx

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MAP2302/FinalExam Page 5 of 6 ______________________________________________________________________ 6. (10 pts.) The equation has a regular singular point at x 0 = 0. Substitution of into the ODE and a half a page of algebra yields Using this information, (a) write the form of the two linearly independent solutions to the ODE given by Theorem 6.3 without obtaining the numerical values of the coefficients of the series involved, and then (b) do obtain the the numerical values of the coefficients c 1 , ... , c 5 to the first solution, y 1 ( x ), given by Theorem 6.3 when c 0 = 1. [ Keep the parts separate. ] ______________________________________________________________________ 7. (10 pts.) Solve the following second order initial-value problem using only the Laplace transform machine.
MAP2302/FinalExam Page 6 of 6 ______________________________________________________________________ 8. (10 pts.) (a) Given
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b 3 pts Next write down the differential equation that the...

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