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Unformatted text preview: (4) = 1 , y (4) = 8 (a) What is the longest interval in which you are sure that a solution exists? (b) Could the power series solution centered at x = 4 be used to get a good approximation for y (6 . 5)? Why or why not? 5. (15 points) Find the general solution of ( x3) 2 y 003( x3) y + 13 y = 0 on x < 3. 6. (15 points) Find the general solution of x 2 y 003 xy + 4 y = 2 x 2 ln x on x > 0. 7. (15 points) Find the recurrence relation and the ﬁrst four nonzero terms of the power series solution centered at x = 0 for the initial value problem (1x ) y 00 + 2 xy + 3 y = 0 , y (0) = 2 , y (0) = 1 ....
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 Spring '08
 Fonken
 Boundary value problem, general solution, power series solution, Dr. Schurle

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