一阶微分方程dy/dx=xcos(x^2)/y

Question

一阶微分方程dy/dx=xcos(x^2)/y

Answer 1

一阶微分方程dy/dx=[xcos(x²)]/y分离变量得 ydy=xcos(x²)dx取积分得∫ydy=∫xcos(x²)dx=(1/2)∫cos(x²)d(x²)故得(1/2)y²=(1/2)sin(x²)+C/2即通解为y²=sin(x²)+C....