第九次習題 Exercise 5.7-40

1. 學號：U10011024 姓名：王冠倫
Exercise 5.7-40
dy 1 1
=− √ √ 2 , (x0, y0) = (4, )
dx 2 x(1 + x) 3
√ 1
令u = 1 + x，則du = 1 x− 2 dx
2
1 1 1
− √ √ = − du = u−1+C = √ +C
2 x(1 + x)2 u2 1+ x
1
代入(x0, y0) = (4, 3 )
1
f (4) = + C, C = 0
3
於是
1
y= √
1+ x
1