4.13.1 $(x^2+y(x{)}^2)y^{\prime }(x)+xy(x)=0$
4.13.2 $(x^2+y(x{)}^2)y^{\prime }(x)=xy(x)$
4.13.3 $(x^2-y(x{)}^2)y^{\prime }(x)=2xy(x)$
4.13.4 $(x^2-y(x{)}^2)y^{\prime }(x)+x(2y(x)+x)=0$
4.13.5 $(x^2+y(x{)}^2)y^{\prime }(x)+2x(y(x)+2x)=0$
4.13.6 $(-x^2+y(x{)}^2+1)y^{\prime }(x)=x^2-y(x{)}^2+1$
4.13.7 $(a^2+x^2+y(x{)}^2)y^{\prime }(x)+2xy(x)=0$
4.13.8 $(a^2+x^2+y(x{)}^2)y^{\prime }(x)+b^2+x^2+2xy(x)=0$
4.13.9 $(x^2+y(x{)}^2+x)y^{\prime }(x)=y(x)$
4.13.10 $(3x^2-y(x{)}^2)y^{\prime }(x)=2xy(x)$
4.13.11 $(x^4+y(x{)}^2)y^{\prime }(x)=4x^{3}y(x)$
4.13.12 $y(x)(y(x)+1)y^{\prime }(x)=x(x+1)$
4.13.13 $(y(x{)}^2+2y(x)+x)y^{\prime }(x)+y(x{)}^2(y(x)+x{)}^2+y(x)(y(x)+1)=0$
4.13.14 $(x^2+y(x{)}^2+2y(x))y^{\prime }(x)+2x=0$
4.13.15 $(x^3-y(x{)}^2+2y(x))y^{\prime }(x)+3x^{2}y(x)=0$
4.13.16 $(y(x{)}^2+xy(x)+y(x)+1)y^{\prime }(x)+y(x)+1=0$
4.13.17 $(y(x)+x{)}^2{y}^{\prime }(x)=a^2$
4.13.18 $(x-y(x){)}^2{y}^{\prime }(x)=a^2$
4.13.19 $(x^2+2xy(x)-y(x{)}^2)y^{\prime }(x)+x^2-2xy(x)+y(x{)}^2=0$
4.13.20 $(x-y(x){)}^2{y}^{\prime }(x)=(-y(x)+x+1{)}^2$
4.13.21 $(y(x)+x{)}^2{y}^{\prime }(x)=(y(x)+x+2{)}^2$
4.13.22 $(y(x)+x{)}^2{y}^{\prime }(x)=x^2-2xy(x)+5y(x{)}^2$
4.13.23 $y^{\prime }(x)(a+b+y(x)+x{)}^2=2(a+y(x){)}^2$
4.13.24 $(2x^2+4xy(x)-y(x{)}^2)y^{\prime }(x)=x^2-4xy(x)-2y(x{)}^2$
4.13.25 $(y(x)+3x{)}^2{y}^{\prime }(x)=4y(x)(2y(x)+3x)$
4.13.26 $(-y(x)-3x+1{)}^2{y}^{\prime }(x)=(-4y(x)-6x+3)(1-2y(x))$
4.13.27 $y^{\prime }(x)(\cot (x)-2y(x{)}^2)=y(x{)}^3\csc (x)\sec (x)$
4.13.28 $3y(x{)}^2{y}^{\prime }(x)=ay(x{)}^3+x+1$
4.13.29 $(x^2-3y(x{)}^2)y^{\prime }(x)+2xy(x)+1=0$
4.13.30 $(2x^2+3y(x{)}^2)y^{\prime }(x)+x(y(x)+3x)=0$
4.13.31 $3(x^2-y(x{)}^2)y^{\prime }(x)-2y(x{)}^3+6x(x+1)y(x)+3e^x=0$
4.13.32 $(3x^2+2xy(x)+4y(x{)}^2)y^{\prime }(x)+2x^2+6xy(x)+y(x{)}^2=0$
4.13.33 $(2y(x)-3x+1{)}^2{y}^{\prime }(x)=(-3y(x)+2x+4{)}^2$
4.13.34 $(-3x^{2}y(x)+6y(x{)}^2+1)y^{\prime }(x)+x^2-3xy(x{)}^2=0$
4.13.35 $a+(x-6y(x){)}^2{y}^{\prime }(x)-6y(x{)}^2+2xy(x)=0$
4.13.36 $(ay(x{)}^2+x^2)y^{\prime }(x)=xy(x)$
4.13.37 $(ay(x{)}^2+x^2+xy(x))y^{\prime }(x)=a{x}^2+xy(x)+y(x{)}^2$
4.13.38 $(a{x}^2-ay(x{)}^2+2xy(x))y^{\prime }(x)-2axy(x)+x^2-y(x{)}^2=0$
4.13.39 $y^{\prime }(x)(x^2(a+2b)+2x(2b+c)y(x)+3cy(x{)}^2)+2x(a+2b)y(x)+3a{x}^2+(2b+c)y(x{)}^2=0$
4.13.40 $y^{\prime }(x)(a{x}^2+2bxy(x)+cy(x{)}^2)+2axy(x)+by(x{)}^2+k{x}^2=0$
4.13.41 $x(1-y(x{)}^2)y^{\prime }(x)=(x^2+1)y(x)$
4.13.42 $x(3x-y(x{)}^2)y^{\prime }(x)+y(x)(5x-2y(x{)}^2)=0$
4.13.43 $x(x^2+y(x{)}^2)y^{\prime }(x)=y(x)(x^4+x^2+y(x{)}^2)$
4.13.44 $x(-x^2+y(x{)}^2+1)y^{\prime }(x)+y(x)(x^2-y(x{)}^2+1)=0$
4.13.45 $x(a-x^2-y(x{)}^2)y^{\prime }(x)+y(x)(a+x^2+y(x{)}^2)=0$
4.13.46 $x(2x^2+y(x{)}^2)y^{\prime }(x)=y(x)(2x^2+3y(x{)}^2)$
4.13.47 $(x(a-x^2-y(x{)}^2)+y(x))y^{\prime }(x)-y(x)(a-x^2-y(x{)}^2)+x=0$
4.13.48 $x(a+y(x){)}^2{y}^{\prime }(x)=by(x{)}^2$
4.13.49 $x(x^2-xy(x)+y(x{)}^2)y^{\prime }(x)+y(x)(x^2+xy(x)+y(x{)}^2)=0$
4.13.50 $x(x^2-xy(x)-y(x{)}^2)y^{\prime }(x)=y(x)(x^2+xy(x)-y(x{)}^2)$