Question

微积分 y'=-4ty/(1+t^2)+1/((1+t^2)^3) 如果t无限大,y=?

Answer 1

y'=-4ty/(1+t^2)+1/((1+t^2)^3)

=> y ' + [4t/(1+t^2)] * y = 1/(1+t^3)^3 一阶线性方程

=> y = .= 1/(1+t^2)^2 * [ arctant + C ]

lim [ ( arctant + C) /(1+t^2)^2 ,t->∞] = 0