Question

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

Answer 1

.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^