ODE_with_Laplace - + 3 y-4 y = 2 e t-8 e 2 ( t-2) , y (0) =...

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MAT 2384-Practice Problems on Solving ODEs using Laplace Transforms- Use Laplace transforms to solve each of the following IVPs. 1. y 00 + 10 y 0 + 24 y = 144 t 2 , y (0) = 19 12 , y 0 (0) = - 5 2. y 00 + 3 y 0 + 2 y = r ( t ) , r ( t ) = ( 0 if 0 < t < 1 1 if t > 1 , y (0) = 0 , y 0 (0) = 0 3. y 00 + 3 y 0 + 2 y = r ( t ) , r ( t ) = ( t if 0 < t < 1 0 if t > 1 , y (0) = 0 , y 0 (0) = 0 4. y 00 + y = δ ( t - 2 π ) , y (0) = 10 , y 0 (0) = 0 5. y 00 + 5 y 0 - 6 y = δ ( t - 2) , y (0) = 1 , y 0 (0) = - 2 6. y 00 + 4 y 0 + 5 y = 10(1 - u ( t - 2)) - e 10 δ ( t - 10) , y (0) = 0 , y 0 (0) = 1 7. y 00
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Unformatted text preview: + 3 y-4 y = 2 e t-8 e 2 ( t-2) , y (0) = 2 , y (0) = 0 8. y 00 + 25 y = 25 t-100 ( t- ) , y (0) =-2 , y (0) = 5 9. y 00 + 2 y + 5 y = 25 t-100 ( t- ) , y (0) =-2 , y (0) = 5 10. y 00 + y =-2 sin t + 10 ( t- ) , y (0) = 0 , y (0) = 1 1...
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