O
ODE
p.1
1 Which of the following sets of functions, each defined on x R are linear
dependent?
(a) sin x , cos x (5%)
2
93
(b) cos x , sin 2 x , cos 2 x (5%)
(c) 1, x, x 2 (5%)
< >
93
100 93
O
ODE
p.2
2 Let the scalar functions x1 (t ) and x2
O
ODE
p.1
1 Find the general solution of the following ODE
x 2 y" xy ' y 0 .
(8%)100 (7%)100 (5%)101
O
ODE
p.2
2 The differential equation x y" xy ' y ln( x) has the solution with the
2
form: y c1 x c2 g1 ( x ) p1 g 2 ( x ) . Find p1 , g1 ( x )