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Unformatted text preview: =8 y (b) (20 points) Suppose y is a solution for the initial value problem 2 y 00 =8 y, y (0) =2 , y (0) =4 √ 3 Find t withπ ≤ t < π so that y ( t ) = 4 Hint: One way to ﬁnd t is by examining the graph of y. Hint: cos( a + b ) = cos( a ) cos( b )sin( a ) sin( b ) . 2. (a) (20 points) Find the general solution for: y 002 y + y = 0 (b) (20 points) Find the general solution for: y 002 y + y = e t 3. (40 points) Without using the shortcut formula from the book, ﬁnd a solution for: ty 00(1 + t ) y + y = t 2 e 2 t Hint: 1 + t and e t are each solutions for ty 00(1 + t ) y + y = 0 Hint: R te t dt = te te t Extra Scratch Paper: Extra Scratch Paper:...
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 Spring '07
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 Math, Differential Equations, Equations, Boundary value problem, extra scratch paper

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