高等数学求解(英文)!!! 5
(a)Obtainadifferentialequationdescribingthefamilyofcurvesgivenbyy^2−2y−x^...
(a) Obtain a differential equation describing the family of curves
given by
y^2− 2y − x^2+ x = c,
where c is an arbitrary constant.
(b) For the family of curves in part (a), show that the orthogonal
trajectories z = z(x) are given by
z(x) = 1 + k/(2x − 1)
where k is an arbitrary positive constant. Hint: If your answer
to part (a) is y′= f (x, y), then the orthogonal trajectories
satisfy z′= −1/f (x, z).
这算什么画图解析啊.... 展开
given by
y^2− 2y − x^2+ x = c,
where c is an arbitrary constant.
(b) For the family of curves in part (a), show that the orthogonal
trajectories z = z(x) are given by
z(x) = 1 + k/(2x − 1)
where k is an arbitrary positive constant. Hint: If your answer
to part (a) is y′= f (x, y), then the orthogonal trajectories
satisfy z′= −1/f (x, z).
这算什么画图解析啊.... 展开
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