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Unformatted text preview: of t , sines, cosines, and exponentials. If we start with L [ y ] = g ( t ), then nd a D-operator K that kills (annihilates!) g ( t ), write down the general solution of KL [ y ] = 0, strike out the solutions of L [ y ] = 0, and determine the remaining coecients by plugging the result into L [ y ] = g ( t ). This works because we can nd a constant-coecient K and because the algebra of constant-coecient operators like K and L is just like polynomials. EXAMPLE. Find the solution of the initial value problem y 00-3 y + 2 y = 8 te 3 t + 20 cos t + 3 t 2 e 2 t , y (0) = 0 , y (0) = 0 HOMEWORK: SECTION 4.3...
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