解方程 (x^2-1)*(dy/dx)*siny+2*x*cosy=2*x-2*x^3

原式两边同除以x^2-1得siny*y'+(2*x*cosy)/(x^2-1)=-2x设u=cosy原式可化为：-u'+(2*x*u)/(x^2-1)=-2x即u'-(2*x*u)/(x^2-1)=2x用常数变易法求解一阶线形微分方程得u=(ln(x^2-1)+C)(x^2-1)即cosy=(ln(x^2-1)+C)(x^2-1)...