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Unformatted text preview: 2 + xy . Answer: y = kx 2 e x/y [6] 5. Find the general solution of the diﬀerential equation y ±y = xy 2 . Answer: y = 1x + 1c ex [6] 6. Find the general solution of the diﬀerential equation (4 x 3 +3 x 2 y +3 y 2 )+( x 3 +6 xy ) y ± = 0. Answer: x 4 + x 3 y + 3 y 2 x = K [6] 7. Show that the diﬀerential equation (3 xy +2 y 2 )+( x 2 +2 xy ) y ± = 0 is not exact, and ±nd an integrating factor which makes it exact. Write down the new exact diﬀerential equation, but do not solve it. Answer: P y ( x, y ) = 3 x + 4 y, Q x ( x, y ) = 2 x + 2 y. Hence P y ( x, y ) ± = Q x ( x, y ) . I ( x ) = x (Integrating factor) . (3 x 2 y + 2 xy 2 ) + ( x 3 + 2 x 2 y ) y ± = 0 (New exact diﬀerential equation) ....
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This note was uploaded on 02/28/2011 for the course MATH 101 taught by Professor Duke during the Spring '11 term at University of Ottawa.
 Spring '11
 duke
 Math

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