For the differential equation, 2xy´´+ (1+ x) y´ + 3y = 0 , find two linearly independent
solutions of y(x) about x = 0 in the form of power series.
Find general solutions of y1(t) and y2(t) :
A mass m = 1 is attached to spring with constant k = 4 , and there is no friction, as
shown in Fig. 1. The mass is released from rest with y(0) = 3 . At the instant t = 2π
the mass is struck with a hammer, providing an impulse F(t) = 8×δ(t − 2π ) .
Determine the motion of the mass, y(t) .
The faces of a thin square copper plate (Fig. 2, where a = 2 and b = 1) are perfectly
insulated. The upper side is kept at 20oC and the other sides are kept at 0oC . Find
the steady-state temperature u(x, y) in the plate. (Solve the Laplace equation,
∇2u = 0 .)
可觀看題目詳解,並提供模擬測驗!(免費會員無法觀看研究所試題解答)