# notes 2-1 - y ( t ). NOTE: The integral in Step 3 is the...

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SECTION 2.1 FIRST ORDER LINEAR EQUATIONS Find the general solution of e 3 t y 0 + 3 e 3 t y = e 5 t and use it to determine how solutions behave as t → ∞ . Find the general solution of y 0 + 3 y = e 2 t and use it to determine how solutions behave as t → ∞ . Find the general solution of y 0 + 2 x y = x 5 .

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This works in general, as long as we can do the integrals, and in some form even when we can’t. To solve y 0 + p ( t ) y = g ( t ) , (NOTE THE COEFFICIENT OF y 0 !!) 1. ﬁnd I ( t ) = R p ( t ) dt , then 2. form exp( I ( t )) = e I ( t ) , then 3. solve e I ( t ) y = R e I ( t ) g ( t ) dt for
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Unformatted text preview: y ( t ). NOTE: The integral in Step 3 is the only one that needs a constant of integration. EXAMPLES. Find the general solution of ty + 2 y = cos t . Find the solution of the initial value problem y + (1 / 4) y = 3 + 2 cos 2 t , y (0) = 0 and describe its behavior for large t . Find the value of t for which the solution rst intersects the line y = 12. HOMEWORK: SECTION 2.1...
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## This note was uploaded on 05/19/2010 for the course M 427K taught by Professor Fonken during the Spring '08 term at University of Texas at Austin.

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notes 2-1 - y ( t ). NOTE: The integral in Step 3 is the...

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