1+（dy/dx）^2=y^2怎么解

题目

1+（dy/dx）^2=y^2怎么解
求y

答案

(dy/dx)=sqrt(y^2-1) which implies:dy/sqrt(y^2-1)=dx integrate both sides:integrate (1/sqrt(y^2-1))dy = x which leads to:ln|y+sqrt(y^2-1)|=x Please pay attention to the +/- after each steps.I didnt consider this issue here.