multiple choice question but please show working, thks a lot .
The general solution of the differential equation dy/dx = x (e^-2y) is
(a) y= 1/2 ln (1/4x^2)+c
(b) y= In(x)+c
(c) y = 1/2 ln (1/4x^2+c)
(d) y = 1/2 ln (x^2+c)
about differential equation
2012-03-25 1:37 pm
回答 (1)
2012-03-25 4:28 pm
✔ 最佳答案
dy/dx = x[e^(-2y)]dy/[e^(-2y)] = x dx
I dy/[e^(-2y)] = I x dx
Ie^(2y) dy = x^2/2 + C
e^(2y)/2 = x^2/2 + C
e^(2y) = x^2 + C
2y = ln (x^2 + C)
y = (1/2) ln (x ^2 + C)
Ans. is (d).
Note : 2C is also an unknown constant, so C or 2C makes no difference, so simply put it as C.
2012-03-25 08:30:18 補充：
Remark : I means the integration sign ∫.
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