dy/dx+siny+xosy+x=0主要是如何做变换dy/dx+siny+xcosy+x=0

Question

dy/dx+siny+xosy+x=0
主要是如何做变换
dy/dx+siny+xcosy+x=0

Answer 1

y'(x)+sin(y)+xcos(y)+x=0为了消去三角函数,令t=tan(y/2),这时y=2arctan(t),sin(y)=2t/(1+t^2),cos(y)=(1-t^2)/(1+t^2)化简后有t'(x)+t+x=0exp(x)(t'+t)+exp(x)*x=0两边积分有exp(x)*t+exp(x)*x-exp(x)=_C1t=_C1*exp...