解dy/dx+1/3y=1/3*(1-2x)y^4高数第六版习题,我感觉答案错了,

Question

解dy/dx+1/3y=1/3*(1-2x)y^4
高数第六版习题,我感觉答案错了,

Answer 1

dy/dx=-1/3y+1/3(1-2x)y^4
dy/dx=-1/3y+1/3y^4-2/3xy^4
dy=(-1/3y+1/3y^4-2/3xy^4)dx
两边同时积分得:
y=-1/3xy+1/3xy-1/3x^2y^4+t(t=0,1,2,3.)