Solve the following differential equations.
(1) (x2 + 4xy)dx + (2x2 + y)dy = 0 .
(2) y''− 2y'− 3y = 0 , y(0) = 0 , y'(0) = 8 .
(3) y''− 4y'+ 4y = sin x .
Find the answers for the following Laplace operations
(1) AA.
(2) det A.
(3) A−1 .
f(t) is a periodic function and in one period it can be expressed by
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