revf4 - Then ﬁnd a minimum value for the radius of...

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EXAM FOUR SAMPLE 1. Use convolution to express a particular solution to x 00 + x = sec ( t ) as an integral–then evaluate. 2. Solve using Laplace transforms: y 00 + 25 y = 10 δ ( t - 2); y (0) = y 0 (0) = 0 3. A mass of 4 grams on a spring with constant k = 100 is released from rest at time t = 0, 2 cm above equilibrium. Then at time t = 3, the mass is given an upward impulse of power 120. Write the differential equation for the position x ( t ) of the mass at time t and use Laplace transforms to solve for x ( t ). 4. Use the Taylor Series Method to find the first 4 terms of a series solution for y 0 = y 2 - xy with y (0) = 2. 5. Find the singular points of ( x 2 - 9) 2 y 00 +( x 2 - 3 x ) y 0 +( x +3) y = 0 and classify
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Unformatted text preview: Then ﬁnd a minimum value for the radius of convergence of a power series solution about x = 1. 6. Find the indicial equation of 6 x 3 y 000 + 13 x 2 y 00 + ( x 2 + 2 x ) y + xy = 0 and give the form of the general solution. 7. Find the ﬁrst four terms of a power series for R e x 1-x dx . 8. Find the recurrence relation and the ﬁrst 5 nonzero terms in a power series solution of y 00 = 2 xy with y (0) = 6 and y (0) = 3. 9. Solve the Cauchy-Euler di±erential equation x 2 y 00-5 xy + 8 y = 2 x 3 with y (1) = 3 and y (1) = 5....
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