ansmidrev1 - μ = y-4 The general solution is F x,y = x 2...

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MAP 2302 Fall 2010 Review for Midterm 1 (Key). (1) Separable equation, the general solution is y - 1 3 y 3 = x + ln | x | + C. (2) Separable and linear equation, the solution of IVP is x ( t ) = 1 - e 3 t 2 2 . (3) Linear equation, the general solution is u ( t ) = e - t ( C + t ) . (4) Linear (or separable) equation, the solution of IVP is y ( x ) = e x - 1 . (5) Exact equation, the solution of IVP is F ( x,y ) = xy 2 + e x = e. (6) Exact equation, the general solution is F ( x,y ) = x 2 y 3 + 2 xy + x 3 = C. (7) The integrating factor is
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Unformatted text preview: μ = y-4 . The general solution is F ( x,y ) = x 2 y-3-y-1 = C or y = 0 . (8) Linear equation, the general solution is x ( y ) = C y + y 2 3 . (9) Separable equation, the general solution is r ( θ ) =-ln( C + 1 3 e-3 θ ) . (10) Homogeneous equation, the solution of IVP is y ( x ) = x tan(ln( | x | )) = x tan(ln( x )) . Additional problems: see the back of the book. 1...
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