[微積] Orthogonal trajectories
題目:
Find the orthogonal trajectories of {y^2 = kx^3 , k∈R} which passes through
the point (1,2)
我的想法是先對原式微分得到 2y dy/dx = 3k x^2
=>dy/dx=3kx^2/2y
再根據垂直的定義得到正交的軌跡有dy/dx=-2y/3kx^2 再去變數分離積分得到答案
可是解答給的是:
dy/dx=-2x/3y =>-x^2+c=3/2 y^2 => 3/2 y^2=-x^2+7
我的想法好像完全錯了...到底是為甚麼呢?卡了好久orz...謝謝解惑> <"
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