设y=y(x)是由y^2(x-y)=x^2所确定的隐函数,求∫(1/y^2)dx

题目

设y=y(x)是由y^2(x-y)=x^2所确定的隐函数,求∫(1/y^2)dx

答案

.y/x=t y=tx
y=xt
dy/dx=t+t'x
dy=(t+t'x)dx
y^2(x-y)=x^2
t^2(x-tx)=1
x=1/[t^2(1-t)]
y=1/[t(1-t)]
1/y^2=t^2(1-t)^2
积分：∫(1/y^2)dx=∫(1/y^