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math 310 a7 Sol

# math 310 a7 Sol - MATH 310-3 Differential Equations...

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MATH 310-3 Fall 2011 Diﬀerential Equations Homework Set 7 Some Solutions The following solutions are not necessarily complete, but should highlight the main points for most questions. If you have any further questions regarding the problems and solutions, feel free to discuss them on WebCT. Solutions marked by * are taken from the publisher’s solutions for the textbook by Boyce and DiPrima, 9th edition (Wiley). Section 3.2: * Section 3.2 # 5 : * Section 3.2 # 6 : Section 3.2 # 18 : * Section 3.2 # 20 : The calculation here is W ( u,v ) = W ( f + 3 g,f - g ) = ( f + 3 g )( f - g ) 0 - ( f + 3 g ) 0 ( f - g ) = ( f + 3 g )( f 0 - g 0 ) - ( f 0 + 3 g 0 )( f - g ) = ( ff 0 - fg 0 + 3 gf 0 - 3 gg 0 ) - ( ff 0 + 3 fg 0 - f 0 g - 3 gg 0 ) = - 4 fg 0 + 4 f 0 g = - 4( fg 0 - f 0 g ) = - 4 W ( f,g ) .

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* Section 3.2 # 23 : Section 3.2 # 26 : * Section 3.2 # 31 : In standard form, Bessel’s equation is y 00 + 1 x y 0 + x 2 - ν 2 x 2 y = 0 . * Section 3.2 # 33 : * Section 3.2 # 35 : * Section 3.2 # 36 : Section 3.2 # 38 :
Section 3.4: * Section 3.4 # 6 : Section 3.4 # 9 : Section 3.4 # 14 : * Section 3.4 # 18 :

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Section 4.1:
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math 310 a7 Sol - MATH 310-3 Differential Equations...

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