大學考試卷求解答

1.dx/dy = 8x^3*y^2c + ∫dx/x^3 =∫ 8y^2*dyc = 1/(2x^2) + (8y^3)/3 2.f(t)=t^3*e^2t 拉普拉斯轉換L{g(t)*e^at} = F(s-a)L{g(t)} = L{t^3} = 3!/s^4F(s-a) = 6/(s-2)^4
=> L{f(t)} = 6/(s-2)^4
3.f(t)=(10cost)^2 基本週期 = 100 * (1 + cos 2t ) / 2= 50 + 50 * cos 2t
=> 2t = 2π=> t = π=> 週期 = π

2015-07-17 04:30:40 補充：
第2題符號打錯修改:

L{f(t)}= L{g(t)*e^at} = G(s-a)

L{g(t)} = L{t^3} = 3!/s^4

G(s-a) = 6/(s-2)^4

L{f(t)} = 6/(s-2)^4

第2題是否抄錯題目?
似乎是 f = t^3 e^2t 比較可能

2015-07-14 21:12:16 補充：
1.
dx / x^3 = 8y^2 dy
- (1/2)x^(-2) + c1 = (8/3)y^3 + c2
3x^(-2) + 16y^3 = c

2015-07-14 21:13:37 補充：
3.
f
= 100 ( 1 + cos 2t )/2
= 50 + 50 cos 2t
週期為 π