∵4xdx-3ydy=3x^2ydy-2xy^2dx
==>2d(x^2)-(3/2)d(y^2)=(3/2)x^2d(y^2)-y^2d(x^2)
==>y^2d(x^2)+2d(x^2)=(3/2)x^2d(y^2)+(3/2)d(y^2)
==>(y^2+2)d(x^2)=(3/2)(x^2+1)d(y^2)
==>d(x^2)/(x^2+1)=(3/2)d(y^2)/(y^2+2)
==>d(x^2+1)/(x^2+1)=(3/2)d(y^2+2)/(y^2+2)
==>ln(x^2+1)=(3/2)ln(y^2+2)+ln│C│ (C是常数)
==>x^2+1=C(y^2+2)^(3/2)
==>(x^2+1)/(y^2+2)^(3/2)=C
∴原方程的通解是(x^2+1)/(y^2+2)^(3/2)=C.
说明：你的这个答案肯定是错的.方程的答案是否正确,你可以代入原方程检验.