Question

求一道高等数学微分方程题，图上第三题，求详细过程，不会的人勿扰，谢谢

Answer 1

三、解：∵dy/dx=(x-y^2)/(2y(x+y^2))
==>2y(x+y^2)dy-(x-y^2)dx=0
==>(2xydy+y^2dx)+2y^3dy-xdx=0
==>d(xy^2)+2y^3dy-xdx=0
==>∫d(xy^2)+2∫y^3dy-∫xdx=0 (积分)
==>xy^2+y^4/2-x^2/2=C/2 (C是任意常数)
==>2xy^2+y^4-x^2=C
∴此方程的通解是2xy^2+y^4-x^2=C
∵y(1)=0
∴代入通解，得C=-1
故所求此方程的特解是2xy^2+y^4-x^2+1=0。

Answer 2