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Unformatted text preview: v = y=x  {z } memorize ) y = vx ) y = v + xv : 1 Bernoulli equations: dy dx + P ( x ) y = Q ( x ) y n ;n 6 = 0 ; 1; substitution: v = y 1 & n  {z } memorize ) y = v 1 1 & n ) y = 1 1 & n v 1 1 & n & 1 v = 1 1 & n v n 1 & n v and exact equations M ( x;y ) dx + N ( x;y ) dy = 0 ; M y = N x . Di/erential forms, exact di/erential forms. Conditions for exactness for di/erential forms. Reducible second order equations: I. F ( x;y ;y 00 ) = 0 (dependent variable is missing); substitution: p ( x ) = y ( x ) ) y 00 ( x ) = p ( x ) : II. F ( y;y ;y 00 ) = 0 (independent variable is missing; substitution: p ( y ) = y ) y 00 = dp dy dy dx = p ( y ) p ( y ) : 2...
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This note was uploaded on 01/19/2012 for the course MATH 285 taught by Professor Staff during the Spring '08 term at University of Illinois, Urbana Champaign.
 Spring '08
 Staff
 Differential Equations, Equations, Integrals, Slope

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