The Laplace Transform HW

Solving Differential Equations:

1. Solve the following differential equations using the Laplace Transform method:

a) & ; ( ) sin( ), ( )y y x x t t y+ = = =4 3 2 0 1

b) && & & ; ( ) ( ), ( ) , & ( )y y y x x x t u t y y+ + = − = = =4 20 2 0 0 0 1

c) && & ; ( ) ( ), ( ) , & ( )y y y x x t u t y y+ + = = = = −7 12 6 0 0 0 2

d) && & ( ), ( ) , & ( )y y y x t y y+ + = = = −9 20 0 1 0 2 , x(t) = 2u(t)