Mathematic Methods HW Solutions 45

Mathematic Methods HW Solutions 45 - Chapter 8 45 12.13 y =...

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Unformatted text preview: Chapter 8 45 12.13 y = braceleftBigg x- 2 sin x, x < / 4 2- x- 2 cos x, x > / 4 12.15 y = x sinh x- cosh x ln cosh x 12.16 y =- x ln x- x- x (ln x ) 2 / 2 12.17 y =- 1 4 sin 2 x 12.18 y = x 2 / 2 + x 4 / 6 13.1 y =- 1 3 x- 2 + Cx linear 1st order 13.2 (ln y ) 2- (ln x ) 2 = C separable 13.3 y = A + Be- x sin( x + ) 3rd order linear 13.4 r = ( A + Bt ) e 3 t 2nd order linear, a = b 13.5 x 2 + y 2- y sin 2 x = C exact 13.6 y = Ae- x sin( x + ) 2nd order linear, complex a,b,c +2 e x + 3 xe- x sin x 13.7 3 x 2 y 3 + 1 = Ax 3 Bernoulli, or integrating factor 1 /x 4 13.8 y = x ( A + B ln x ) + 1 2 x (ln x ) 2 Cauchy 13.9 y ( e 3 x + Ce- 2 x ) + 5 = 0 Bernoulli 13.10 u- ln u + ln v + v- 1 = C separable 13.11 y = 2 x ln x + Cx linear 1st order, or homogeneous 13.12 y = A ln x + B + x 2 y missing, or Cauchy 13.13 y = Ae- 2 x sin( x + ) + e 3 x 2nd order linear, complex a,b 13.14 y = Ae- 2 x sin( x + ) 2nd order linear, complex a,b,c + xe- 2 x sin x 13.15 y = ( A + Bx )...
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This note was uploaded on 02/29/2012 for the course MHF 2312 taught by Professor Dr.chet during the Fall '11 term at UNF.

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