東南電機系大學部二技 工程數學作業（4）
To find the solutions of the following problems and D.E.s.
01) Show the W then tell about they are linearly
dependent or linearly independent ?
ronskian of cos
c
2x, sin2 x, cos2xh
.x
02) Are function pair,
c
eλ1x,eλ2xh
, linearly dependent or linearly independent ? 03) x y′ +2y=x204) y′ + ⋅y cotx=6csc2 05) ′ −
− = ∧ =
y x
x y y
2
1 2 1, ( ) 10
= .
06)
c
x y dx y− 2h
+b g
1+x d y 0.07) y′ + =y
b g
x y 2. 08) x y′ + =y y2. 09) ′ = +y x y y
x 2 2
2 .
10) y dx2 + +
b
1 x y d yg
=0 [ Hint: trying dxd y ]11) Try to set u= y2 in 06), we could have first-order D.E. and solve it.
