Pure maths

上面果位人兄，呢題原本應該識做嘅，點知唔小心做錯咗！
（以下我特登用全形字打嘅部分是上面果位人兄錯咗而由本人改正過來的。）

x(dy/dx) – 4y = x^6 e^x (x > 0)
dy/dx – (4/x)y = x^5 e^x

I.F. = e^[∫– (4/x) dx]
= e^(– 4 ln x)
= e^[ln x^(– 4)]
= x^(– 4)

The equation becomes:
(d/dx)[yx^(– 4)] = x^5 e^x x^(– 4)
yx^(– 4) = ∫xe^x dx
yx^(– 4) = ∫x d(e^x)
yx^(– 4) = xe^x – ∫e^x dx
yx^(– 4) = xe^x – e^x + Ｃ＿１
y = x^5 e^x – x^4 e^x + (Ｃ＿１)ｘ^４

when x = 1, y = 1,
1 = 1e¹ – 1e¹ + (Ｃ＿１)1
Ｃ＿１= 1

∴y = x^5 e^x – x^4 e^x +ｘ^４