For Problems 41-44, use the Laplace transform to solve the given system of differential equations subject to the given initial conditions. d x 1 d t = 2 x 1 + 4 x 2 + 16 sin 2 t d x 2 d t = − 2 x 1 − 2 x 2 + 16 cos 2 t x 1 ( 0 ) = 0 x 2 ( 0 ) = 1
For Problems 41-44, use the Laplace transform to solve the given system of differential equations subject to the given initial conditions. d x 1 d t = 2 x 1 + 4 x 2 + 16 sin 2 t d x 2 d t = − 2 x 1 − 2 x 2 + 16 cos 2 t x 1 ( 0 ) = 0 x 2 ( 0 ) = 1
Solution Summary: The author explains how to solve a given system of differential equations, using the convolution theorem, properties of the Laplace transform, and the table (1).
For Problems 41-44, use the Laplace transform to solve the given system of differential equations subject to the given initial conditions.
d
x
1
d
t
=
2
x
1
+
4
x
2
+
16
sin
2
t
d
x
2
d
t
=
−
2
x
1
−
2
x
2
+
16
cos
2
t
x
1
(
0
)
=
0
x
2
(
0
)
=
1
With integration, one of the major concepts of calculus. Differentiation is the derivative or rate of change of a function with respect to the independent variable.
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