推 G41271 :這叫因變數轉換法 04/30 01:27
推 jacky7987 :我沒學過這方法耶QQ 04/30 06:25
※ 引述《ak127911400 (秀蓮)》之銘言：
: Find the general soultion y{X} of the following differnetial euations
: y"+4xy'+4x^2y =0
: 有請神人感謝
1.
-∫[(4x)/2] dx -(x^2)
令y = e *v = e *v
-(x^2) -(x^2)
y'= -2xe *v + e *v'
-(x^2) -(x^2) -(x^2) -(x^2) -(x^2)
y''= -2 e *v + 4(x^2)e *v -2xe *v'-2xe *v' + e *v''
代入ODE
-(x^2) -(x^2)
---> e v'' -2e v = 0
---> v'' -2v = 0
2.
求v_h:
-(√2)x (√2)x
v_h= ae +be
3.
-(x^2) -(x^2) -(√2)x (√2)x
y= e *v = e [ae +be ] , where a and b are constants.
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