所屬科目：研究所、轉學考(插大)◆工程數學
$(a) (x^3 - y)dx + (y^3 - x)dy = 0 \quad (10\%)$
$(b) y'' + 3y' + 2y = 2e^{-x} \quad (15\%)$
$(a) L\{\cos 2t\} = ? \quad (10\%)$
$(b) L\{e^{3t} \cos 2t\} = ? \quad (5\%)$
$(c) L\{3^t \sin 2t\} = ? \quad (5\%)$
$(d) L\{e^{3t} t \sin 2t\} = ? \quad (5\%)$
(a) Formulate the system as an Ordinary Differential Equation. (5%)
(b) Specify the initial conditions. (10%)
(c) Find the solution of this system. (10%)
(a) Find the surface elevations at point A(2,2). (5%)
(b) Determine the magnitude of the slope at point A. (10%)
(c) Determine the unit normal vector to the land surface at point A. (10%)
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