求方程yx^2-∫(0到y)根号(1+t^2)dt=0所确定的隐函数y=y(x)的微分dy

问题描述:

求方程yx^2-∫(0到y)根号(1+t^2)dt=0所确定的隐函数y=y(x)的微分dy

对方程求导,得y'x^2+2xy-y'sqrt(1+y^2)=0,整理,得dy/dx=2xy/(sqrt(1+y^2)-x^2) 即dy=[2xy/(sqrt(1+y^2)-x^2)]dx sqrt是指平方根