M 427K-Vishik-Spring 2003-Test 1

M 427K-Vishik-Spring 2003-Test 1 - M 427K Midterm exam...

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Unformatted text preview: M 427K Midterm exam February 20, 2003 N.~.~ Unique # 56045 STUDENT # Please show all work clearly and circle all answers. There are 5 problems: 20 points each. Solve the initial value problem =y -1 2 3 yl x (1 +x y(O) ) = 1. ill 2. Find the general solution of the differential equation -1 yl = 2 (x + 1) 3 y + (x + 1) Show that the following equation is exact and integrate it 2 3x 2 - 6xy - (3x + 2y)yl =0 1 4. Find a fundamental set of solutions of the differential " equation 2yll + 2yl + y = 0 Find the general 5Solution of this equation. 1- L- •• ill: t l- 1,2.. . '1 ':: Ct eo.:. ~ v5. -To ~ e.. For the initial value problem 2 @ 4 yl = y 2 +x y(O)=O compute the zero, first, and second Picard's approximations to the exact solution. _ _ ...
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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 at Austin.

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