dx/(x^2-y^2)=dy/(-2xy)如何积分?

来源：学生作业帮助网编辑：作业帮时间：2024/05/03 05:58:58

dx/(x^2-y^2)=dy/(-2xy)如何积分?
dx/(x^2-y^2)=dy/(-2xy)如何积分?

dx/(x^2-y^2)=dy/(-2xy)如何积分?
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

dx/(x^2-y^2=dy/(-2xy)
两边积分
∫(1/(x^2-y^2))dx=∫dy/(-2xy)
-1/2y*ln((y+x)/(y-x))=-1/2y*lnx
(y+x)/(y-x)=x
y=(x^2+x)/(x-1)

(x^2)dy+（y^2)dx=dx-dy 微分方程 dy/dx=(-2x)/y 解方程y^2+x^2*(dy/dx)=x*y*(dy/dx) dy/dx=x/2y dy/dx=x+y dy/dx,y=(1+x+x^2)e^x dy/dx=2y/x+3x/2y x^y-y^x=2,求dy/dx 求dy/dx=(x-y+5)/(x+y-2) （-2x-y+9)dy=(-y+x+3)dx y=2x^2+x求dy/dx 微分方程 dy/dx=(e^y+3x)/x^2 dy/dx=(e^x+x)(1+y^2)通解 x=sin(y/x)+e^2 求dy/dx y=e^x/x^2+sin2x 求dy/dx dy/ dx +2y=x*e^x的通解, y=[sin(x^4)]^2,则dy/dx=?,dy^2/dx^2=?,dy/d(x^2)=? 1.dy/dx=(y-x)/(y+x)2.x^2*dy/dx=xy-y^2 x^2+y^2=e^y求dy/dx