M 427K-Vishik-Spring 2003-Test 2

# M 427K-Vishik-Spring 2003-Test 2 - ~\l.ll.r.•"-~Q l ~...

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M 427K Midterm exam March 27 , 2003 NAM~~~~~~~~~~~~ Unique # 56045 STUDENT # _ Please show all work clearly and circle all answers. There are 5 problems: 20 points each. Find a fundamental set of solution of the differential equation (6) (4) II W · y +3y +3y ,0 . Using variation of parameters find the g~neral solution of rJ the ODE yl' - 16 y = g(x), + y = 0 where g(x) is an arbitrary contunuous function on~ . Let y (x) , y (x), y (x) be three solutions of the homogeneous 1 2 3 linear ODE + (sin x) y = 0 , Assume W(y , Y , Y i x) ~ 1 as x ~ - 00 123 Compute the Wronskian W(y , Y i x) . .., 1 3 [Hint: dont try to solve the Q 4. Find the power series expansion in x Cauchy problem ~ yll -x y = 0 i y(O) = 0, y/(O) = 1. of solution to the general solution of the Euler equation x 2 yll -x yl + y = 0 , x > 0 .

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## This note was uploaded on 01/27/2012 for the course MATH 427 k taught by Professor Goddard during the Fall '10 term at University of Texas.

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M 427K-Vishik-Spring 2003-Test 2 - ~\l.ll.r.•"-~Q l ~...

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