4.12.1 $x(2y(x)+x)y^{\prime }(x)+(2x-y(x))y(x)=0$
4.12.2 $x(x-2y(x))y^{\prime }(x)+(2x-y(x))y(x)=0$
4.12.3 $x(-2y(x)+x+1)y^{\prime }(x)+y(x)(y(x)-2x+1)=0$
4.12.4 $x(-2y(x)-x+1)y^{\prime }(x)+y(x)(y(x)+2x+1)=0$
4.12.5 $2x(2x^2+y(x))y^{\prime }(x)+y(x)(12x^2+y(x))=0$
4.12.6 $-3x^2+2(x+1)y(x)y^{\prime }(x)+y(x{)}^2+2x=0$
4.12.7 $x(3y(x)+2x)y^{\prime }(x)=y(x{)}^2$
4.12.8 $x(3y(x)+2x)y^{\prime }(x)+3(y(x)+x{)}^2=0$
4.12.9 $(x^2+6xy(x)+3)y^{\prime }(x)+3y(x{)}^2+2xy(x)+2x=0$
4.12.10 $x^3+3x(2y(x)+x)y^{\prime }(x)+3y(x)(y(x)+2x)=0$
4.12.11 $axy(x)y^{\prime }(x)=x^2+y(x{)}^2$
4.12.12 $axy(x)y^{\prime }(x)+x^2-y(x{)}^2=0$
4.12.13 $x{y}^{\prime }(x)(a+by(x))=cy(x)$
4.12.14 $x(x-ay(x))y^{\prime }(x)=y(x)(y(x)-ax)$
4.12.15 $y^{\prime }(x)(x(Ax+By(x))+\text{a0}+\text{a1}x+\text{a2}y(x))=y(x)(Ax+By(x))+\text{b0}+\text{b1}x+\text{b2}y(x)$
4.12.16 $y^{\prime }(x)(x(\text{a1}+\text{b2}x+\text{c2}y(x))+\text{a1}+\text{b1}x+\text{c1}y(x))=y(x)(\text{a2}+\text{b2}x+\text{c2}y(x))+\text{a3}+\text{b3}x+\text{c2}y(x)$
4.12.17 $x{y}^{\prime }(x)(ay(x)+x^n)+y(x{)}^2(b+cy(x))=0$
4.12.18 $(1-x^{2}y(x))y^{\prime }(x)-xy(x{)}^2+1=0$
4.12.19 $(1-x^{2}y(x))y^{\prime }(x)+xy(x{)}^2-1=0$
4.12.20 $x(1-xy(x))y^{\prime }(x)+y(x)(xy(x)+1)=0$
4.12.21 $x(xy(x)+2)y^{\prime }(x)=2x^3-xy(x{)}^2-2y(x)+3$
4.12.22 $x(2-xy(x))y^{\prime }(x)-x(xy(x)+1)y(x{)}^2+2y(x)=0$
4.12.23 $x(3-xy(x))y^{\prime }(x)=y(x)(xy(x)-1)$
4.12.24 $x^2(1-y(x))y^{\prime }(x)+(1-x)y(x)=0$
4.12.25 $x^2(1-y(x))y^{\prime }(x)+(x+1)y(x{)}^2=0$
4.12.26 $(x^2+1)y(x)y^{\prime }(x)+x(1-y(x{)}^2)=0$
4.12.27 $(1-x^2)y(x)y^{\prime }(x)+2x^2+xy(x{)}^2=0$
4.12.28 $2x^{2}y(x)y^{\prime }(x)=x^2(2x+1)-y(x{)}^2$
4.12.29 $x(1-2xy(x))y^{\prime }(x)+y(x)(2xy(x)+1)=0$
4.12.30 $x(2xy(x)+1)y^{\prime }(x)+y(x)(3xy(x)+2)=0$
4.12.31 $y(x)(-x^{2}y(x{)}^2+2xy(x)+1)+x(2xy(x)+1)y^{\prime }(x)=0$
4.12.32 $x^2(x-2y(x))y^{\prime }(x)=2x^3-4xy(x{)}^2+y(x{)}^3$
4.12.33 $2x(x+1)y(x)y^{\prime }(x)=y(x{)}^2+1$
4.12.34 $3x^{2}y(x)y^{\prime }(x)+2xy(x{)}^2+1=0$
4.12.35 $x^2(4x-3y(x))y^{\prime }(x)=y(x)(6x^2-3xy(x)+2y(x{)}^2)$
4.12.36 $(1-x^{3}y(x))y^{\prime }(x)=x^{2}y(x{)}^2$
4.12.37 $a+2x^{3}y(x)y^{\prime }(x)+3x^{2}y(x{)}^2=0$
4.12.38 $x(3-2x^{2}y(x))y^{\prime }(x)=3x^{2}y(x{)}^2-3y(x)+4x$
4.12.39 $x(2x^{2}y(x)+3)y^{\prime }(x)+y(x)(3x^{2}y(x)+4)=0$
4.12.40 $3x^4+8x^{3}y(x)y^{\prime }(x)-6x^{2}y(x{)}^2-y(x{)}^4=0$
4.12.41 $xy(x)(a+b{x}^2)y^{\prime }(x)=A+By(x{)}^2$
4.12.42 $3x^{4}y(x)y^{\prime }(x)=1-2x^{3}y(x{)}^2$
4.12.43 $x^{7}y(x)y^{\prime }(x)=5x^{3}y(x)+2(x^2+1)$
4.12.44 $\sqrt{x^2+1}y(x)y^{\prime }(x)+x\sqrt{y(x{)}^2+1}=0$
4.12.45 $\sqrt{x^2+1}(y(x)+1)y^{\prime }(x)=y(x{)}^3$
4.12.46 $y^{\prime }(x)(\text{g0}(x)+\text{g1}(x)y(x))=\text{f0}(x)+\text{f1}(x)y(x)+\text{f2}(x)y(x{)}^2+\text{f3}(x)y(x{)}^3$
4.12.47 $y(x{)}^2{y}^{\prime }(x)+x(2-y(x))=0$
4.12.48 $y(x{)}^2{y}^{\prime }(x)=x(y(x{)}^2+1)$
4.12.49 $(y(x{)}^2+x)y^{\prime }(x)+y(x)=a+bx$
4.12.50 $(x-y(x{)}^2)y^{\prime }(x)=x^2-y(x)$