※ 引述《NTUEO (Michael Jackson)》之銘言：
: A one-parameter family of solutions for some differential eq. is
: y = 3-2ce^2x / (1-ce^2x)
: please find the differential equestion and its singilar solution
: 謝謝喔
y = 3-2ce^2x / (1-ce^2x)
1.find c=?
(1-ce^2x)(y-3)=-2ce^2x
(1)(y-3)=ce^2x(y-3-2)
y-3
c=------e^-2x
y-5
2.y'=f(x,y) =?
-4ce^2x((1-ce^2x))+2ce^2x(-2ce^2x)
y'=----------------------------------
(1-ce^2x)^2
-4(y-3)((y-5)-(y-3))+2(y-3)(-2)(y-3)
y'=--------------------------------------------
((y-5)-(y-3))^2
Ans:
y'=-(y-5)(y-3)
singilar solution, y=5 or y=3
應該是這樣吧-,-
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