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5.4 UnitStepFunctionsandPeriodicFunc- tions

unit step functions AND periodic FUNCTIONS157 Which implies thaty(t) =t2solves the DE. (One may easily checkthat, indeedy(t) =t2does solve the DE/IVP. ExercisesIn 1-8, solve the ODE/IVP using the Laplace + 4y + 3y= 0, y(0) = 1, y (0) = + 4y + 3y=t2, y(0) = 1, y (0) = 3y + 2y= sint, y(0) = 0, y (0) = 3y + 2y=et, y(0) = 1, y (0) = 2y=t2, y(0) = 1, y (0) = 4y=e2t, y(0) = 0, y (0) = + 3ty y= 6t, y(0) = 0, y (0) = +ty 3y= 2t, y(0) = 0, y (0) = 1 (You will need integrationby parts or use technology) unit step functions and periodic Func-tionsIn this section we will see that we can use the Laplace transform tosolve a new class of problems efficiently. In particular, we will be ableto consider discontinuous forcing functions .)

5.4. UNIT STEP FUNCTIONS AND PERIODIC FUNCTIONS 157 Which implies that y(t) = t2 solves the DE. (One may easily check that, indeed y(t) = t2 does solve the DE/IVP. ¤ Exercises In 1-8, solve the ODE/IVP using the Laplace Transform

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  Unit, Step, Into, Functions, Periodic, Unitstepfunctionsandperiodicfunc tions, Unitstepfunctionsandperiodicfunc, Unit step functions and periodic functions

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