# HW5s - 2 2 1 3 2 3 4 2 1 3 1 2 3 2 2 2 − = = ⇓ = −...

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P14.6-1: on Page 667 of the textbook Solve the following differential equations using Laplace transform (a) () () () t t i dt t di cos = + with initial condition: ( ) . 1 0 = i (b) () () () 0 2 3 2 2 = + + t v dt t dv dt t v d with initial condition: ( ) () . 1 0 0 = = = v dt t dv t Solution: (a) Taking Laplace transform to the equation, we have () () () () () () () () 1 2 1 1 2 1 1 2 1 1 1 1 1 1 1 0 2 2 2 2 2 2 + + + + + = + + + + = + = + + = + s s s s s s s s s I s s s I s sI s s s I i s sI Using inverse Laplace transform, we have () () () () () ( ) t u t t t u e t i t sin cos 2 1 2 1 + + = (b)
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Unformatted text preview: ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 2 2 1 3 2 3 4 2 1 3 1 2 3 2 2 2 + − + + = + + + = ⇓ = + − + − − ⇓ = + − + − − = s s s s s s V s V s sV s s V s s V v s sV dt t dv sv s V s t Using inverse Laplace transform, we have ( ) ( ) ( ) t u e e t v t t 2 2 3 − − − = ....
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HW5s - 2 2 1 3 2 3 4 2 1 3 1 2 3 2 2 2 − = = ⇓ = −...

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