Re: [理工] [工數]-ODE
過點(1,0.5) 且在X軸上截距為 2xy^2
取任意一點(x,y)
m= dy/dx = (y-0)/(x-2xy^2)
xdy-2xy^2dy =ydx
xdy -ydx -2xy^2dy = 0
-d(x/y) -2xdy =0
(x/y)^(-1)d(x/y)+2ydy = 0
積分
ln(x/y) +y^2 =C1
代入題目給的條件 曲線過(1,0.5)點 找C1
就解出
※ 引述《k0184990 (追隨夢想..)》之銘言：
: 【97成大電機】
: Find the curve y(x) that passes through (1,0.5) and is
: such that at each point (x,y) the intercept of the
: tangent on the x-axis is equal to 2xy^2.
: 請問這題題目是在問什麼??
: 然後該怎麼算呢??
: 謝謝各位囉:)
: 順帶一問，奇異解要怎麼判別啊??
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