4.15.1 $x(2y(x{)}^3+y(x)+x)y^{\prime }(x)=(x-y(x))y(x)$
4.15.2 $(-7xy(x{)}^3-y(x)+5x)y^{\prime }(x)-y(x{)}^4+5y(x)=0$
4.15.3 $y(x)(1-2x^{3}y(x))+x(1-2xy(x{)}^3)y^{\prime }(x)=0$
4.15.4 $x(-2xy(x{)}^3-xy(x{)}^2+2)y^{\prime }(x)+2y(x)+1=0$
4.15.5 $(-10x^{2}y(x{)}^3+3y(x{)}^2+2)y^{\prime }(x)=x(5y(x{)}^4+1)$
4.15.6 $x{y}^{\prime }(x)(a+bxy(x{)}^3)+y(x)(a+c{x}^{3}y(x))=0$
4.15.7 $y(x)(1-2x^{3}y(x{)}^2)+x(1-2x^{2}y(x{)}^3)y^{\prime }(x)=0$
4.15.8 $x(1-xy(x))(1-x^{2}y(x{)}^2)y^{\prime }(x)+y(x)(xy(x)+1)(x^{2}y(x{)}^2+1)=0$
4.15.9 $(x^2-y(x{)}^4)y^{\prime }(x)=xy(x)$
4.15.10 $(x^3-y(x{)}^4)y^{\prime }(x)=3x^{2}y(x)$
4.15.11 $(a^2{x}^2+{(x^2+y(x{)}^2)}^2)y^{\prime }(x)=a^{2}xy(x)$
4.15.12 $2(x-y(x{)}^4)y^{\prime }(x)=y(x)$
4.15.13 $(-2y(x{)}^4-xy(x{)}^3+4x)y^{\prime }(x)=y(x)(y(x{)}^3+2)$
4.15.14 $y(x)y^{\prime }(x)((ax+by(x){)}^3+a{x}^3)+x((ax+by(x){)}^3+by(x{)}^3)=0$
4.15.15 $(2x^{2}y(x{)}^3+xy(x{)}^4+2y(x)+x)y^{\prime }(x)+y(x)(y(x{)}^4+1)=0$
4.15.16 $2x(x^3+y(x{)}^4)y^{\prime }(x)=y(x)(x^3+2y(x{)}^4)$
4.15.17 $x(1-x^{2}y(x{)}^4)y^{\prime }(x)+y(x)=0$
4.15.18 $(x^2-y(x{)}^5)y^{\prime }(x)=2xy(x)$
4.15.19 $x(x^3+y(x{)}^5)y^{\prime }(x)=y(x)(x^3-y(x{)}^5)$
4.15.20 $y(x{)}^3(3x^{5}y(x{)}^5-1)+x^3(5x^{3}y(x{)}^7+1)y^{\prime }(x)=0$
4.15.21 $y^{\prime }(x)(\text{f1}(x,y(x))+x\text{f2}(x,y(x)))=y(x)\text{f2}(x,y(x))+\text{f3}(x,y(x))$
4.15.22 $y^{\prime }(x)(a(y(x)+x)+1{)}^n+a(y(x)+x{)}^n=0$
4.15.23 $x{y}^{\prime }(x)(a+xy(x{)}^n)+by(x)=0$
4.15.24 $f(x)y(x{)}^m{y}^{\prime }(x)+g(x)y(x{)}^{m+1}+h(x)y(x{)}^n=0$
4.15.25 $\sqrt{b^2+y(x{)}^2}{y}^{\prime }(x)=\sqrt{a^2+x^2}$
4.15.26 $\sqrt{b^2-y(x{)}^2}{y}^{\prime }(x)=\sqrt{a^2-x^2}$
4.15.27 $\sqrt{Y}{y}^{\prime }(x)=\sqrt{X}$
4.15.28 $(\sqrt{y(x)+x}+1)y^{\prime }(x)+1=0$
4.15.29 $\sqrt{xy(x)}{y}^{\prime }(x)-y(x)+x=\sqrt{xy(x)}$
4.15.30 $(x-2\sqrt{xy(x)})y^{\prime }(x)=y(x)$
4.15.31 ${(x^2+1)}^{3/2}(y(x)+\sqrt{y(x{)}^2+1})y^{\prime }(x)=y(x{)}^2+1$
4.15.32 ${(x^2+1)}^{3/2}(y(x)+\sqrt{y(x{)}^2+1})y^{\prime }(x)=y(x{)}^2+1$
4.15.33 $(x-\sqrt{x^2+y(x{)}^2})y^{\prime }(x)=y(x)$
4.15.34 $x(1-\sqrt{x^2-y(x{)}^2})y^{\prime }(x)=y(x)$
4.15.35 $x(\sqrt{x^2+y(x{)}^2}+x)y^{\prime }(x)+\sqrt{x^2+y(x{)}^2}y(x)=0$
4.15.36 $xy(x)(\sqrt{x^2-y(x{)}^2}+x)y^{\prime }(x)=xy(x{)}^2-{(x^2-y(x{)}^2)}^{3/2}$
4.15.37 $(x-y(x{)}^2\sqrt{y(x{)}^2-x^2})y^{\prime }(x)=y(x)(x\sqrt{y(x{)}^2-x^2}+1)$
4.15.38 $(x\sqrt{x^2+y(x{)}^2+1}-y(x)(x^2+y(x{)}^2))y^{\prime }(x)=\sqrt{x^2+y(x{)}^2+1}y(x)+x(x^2+y(x{)}^2)$
4.15.39 $y^{\prime }(x)(x^2\sec (x)\cos (y(x))+1)-y(x)\tan (x)+\sec (x)\sin (y(x))=0$
4.15.40 $y^{\prime }(x)\cos (y(x))(\cos (y(x))-\sin (A)\sin (x))+\cos (x)(\cos (x)-\sin (A)\sin (y(x)))=0$
4.15.41 $y^{\prime }(x)(a\cos (ay(x)+bx)-b\sin (ax+by(x)))-a\sin (ax+by(x))+b\cos (ay(x)+bx)=0$
4.15.42 $y^{\prime }(x)(a\sin (xy(x))-\sin (y(x))+\cos (y(x)+x))+y(x)\sin (xy(x))+\cos (y(x)+x)+\cos (x)=0$
4.15.43 $y^{\prime }(x)(\cos (x)\sec (y(x))+x)+\tan (y(x))-y(x)\sin (x)\sec (y(x))=0$
4.15.44 $y^{\prime }(x)(x^2+2y(x)\sin (x)\sec (y(x)))+2x\tan (y(x))+y(x{)}^2\cos (x)\sec (y(x))=0$
4.15.45 $y^{\prime }(x)(x^2{\sec }^2(y(x))-6xy(x)+2)-3y(x{)}^2+2x\tan (y(x))=0$
4.15.46 $y^{\prime }(x)((y(x)+x)\tan (y(x))+1)+1=0$
4.15.47 $x{y}^{\prime }(x)(x-y(x)\tan \left(\frac{y(x)}{x}\right))+y(x)(y(x)\tan \left(\frac{y(x)}{x}\right)+x)=0$
4.15.48 $(x{e}^{y(x)}+e^x)y^{\prime }(x)+e^{x}y(x)+e^{y(x)}=0$
4.15.49 $y^{\prime }(x)(-\log (y(x))-2x+1)+2y(x)=0$
4.15.50 $y^{\prime }(x)(x\cosh (y(x))+\sinh (x))+\sinh (y(x))+y(x)\cosh (x)=0$