dx/(x^2-y^2)=dy/(-2xy)如何积分?

来源：学生作业帮编辑：作业帮分类：数学作业时间：2024/11/05 14:51:35

2dx/dy = (y^2-x^2)/(xy) = y/x - x/y
设x/y = p
那么dx = pdy + ydp => dx/dy = p + y dp/dy
所以2(p + y dp/dy) = 1/p - p
2dp / (1/p-3p) = dy/y
2pdp / (1-3p^2) = dy/y
积分得
-1/3 ln(1-3p^2) = lnCy
所以(Cy)^3 * (1-3x/y) = 1

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