# Homework1 - Homework 1 AMATH 383 Autumn 2009 Due Friday...

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Homework 1 AMATH 383, Autumn 2009 Due: Friday, October 16, after class 1. (each 1 point) For the following equations determine the order and if it is non-linear or linear: (a) y 5 y 2 + y = 0 , (b) y ′′ y + y + 2 y = 0 (c) 6 y y y ′′ = 1 (d) y ( x ) = (2 + x ) y ( x ) (e) d 4 x dt 4 + 2 t dx dt = exp ( x ) (f) d dx p y ′′ ( x ) + xy ( x ) y ( x ) P = 1 2. (4+4+7 points) Give the general solutions to the following equations: (a) y ′′ = 3 y , (b) 6 y y y ′′ = 1 (c) y = 6 y 4 y 2 2 3. (2+2 points) The following gives equivalent solutions to ODEs which written with di±erent integration constants. Give a relation between the constants. (a) For y = y (1 y ) equivalent solutions are y ( x ) = C exp ( x ) 1 + C exp( x ) = 1 1 + ˆ C exp( x ) = exp( x + ˜ C ) exp( x + ˜ C ) 1 (b) For y ′′ + ω 2 y = 0 equivalent solutions are y ( x ) = C 1 exp ( ω i x ) + C 2 exp ( ω i x ) = ˆ C 1 cos ( ω x

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Homework1 - Homework 1 AMATH 383 Autumn 2009 Due Friday...

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