4.37.1 $y^{″}(x)+3y(x)y^{\prime }(x)=f(x)+g(x)y(x)-y(x{)}^3$
4.37.2 $y^{″}(x)=(f(x)-3y(x))y^{\prime }(x)+f(x)y(x{)}^2-y(x{)}^3$
4.37.3 $y^{″}(x)=a(2y(x)y^{\prime }(x)+1)$
4.37.4 $a(y(x{)}^2-1)y^{\prime }(x)+by(x)+y^{″}(x)=0$
4.37.5 $y^{\prime }(x)f(x,y(x))+g(x,y(x))+y^{″}(x)=0$
4.37.6 $y^{″}(x)={(x^2-y^{\prime }(x))}^2+2x$
4.37.7 $y^{″}(x)+2y^{\prime }(x{)}^2\tan (y(x))+2\cot (x)y^{\prime }(x)=0$
4.37.8 $y^{″}(x)=a{y}^{\prime }(x{)}^2$
4.37.9 $y^{″}(x)=a^2+b^2{y}^{\prime }(x{)}^2$
4.37.10 $a{y}^{\prime }(x{)}^2+by(x)+y^{″}(x)=0$
4.37.11 $a{y}^{\prime }(x{)}^2+b\sin (y(x))+y^{″}(x)=0$
4.37.12 $a{y}^{\prime }(x{)}^2+b{y}^{\prime }(x)+cy(x)+y^{″}(x)=0$
4.37.13 $y^{″}(x)=e^x{y}^{\prime }(x{)}^2$
4.37.14 $f(x)y^{\prime }(x)+g(x)y^{\prime }(x{)}^2+y^{″}(x)=0$
4.37.15 $ay(x)y^{\prime }(x{)}^2+by(x)+y^{″}(x)=0$
4.37.16 $f(y(x))y^{\prime }(x{)}^2+g(y(x))+y^{″}(x)=0$
4.37.17 $f(x)y^{\prime }(x)+g(y(x))y^{\prime }(x{)}^2+y^{″}(x)=0$
4.37.18 $f(y(x))y^{\prime }(x)+g(y(x))y^{\prime }(x{)}^2+y^{″}(x)=0$
4.37.19 $f(y(x))y^{\prime }(x)+g(y(x))y^{\prime }(x{)}^2+h(y(x))+y^{″}(x)=0$
4.37.20 $y^{″}(x)+y^{\prime }(x{)}^3+y^{\prime }(x)=0$
4.37.21 $y^{″}(x)=(a-x)y^{\prime }(x{)}^3$
4.37.22 $y^{″}(x)+(e^{2y(x)}+x)y^{\prime }(x{)}^3=0$
4.37.23 $y^{″}(x)+4y^{\prime }(x{)}^3+2y^{\prime }(x)=0$
4.37.24 $a{y}^{\prime }(x{)}^3+y^{″}(x)=0$
4.37.25 $y^{″}(x)=x{y}^{\prime }(x{)}^3$
4.37.26 $y^{\prime }(x{)}^3(ax+by(x))+y^{″}(x)=0$
4.37.27 $ay(x){(y^{\prime }(x{)}^2+1)}^2+y^{″}(x)=0$
4.37.28 $y^{″}(x)=a{(x{y}^{\prime }(x)-y(x))}^k$
4.37.29 $f(x)y^{\prime }(x{)}^k+g(x)y^{\prime }(x)+y^{″}(x)=0$
4.37.30 $y^{″}(x)=A{x}^{a}y(x{)}^b{y}^{\prime }(x{)}^c$
4.37.31 $y^{″}(x)=a\sqrt{y^{\prime }(x{)}^2+1}$
4.37.32 $y^{″}(x)=a\sqrt{by(x{)}^2+y^{\prime }(x{)}^2}$
4.37.33 $y^{″}(x)=a{(y^{\prime }(x{)}^2+1)}^{3/2}$
4.37.34 $y^{″}(x)=ax{(y^{\prime }(x{)}^2+1)}^{3/2}$
4.37.35 $y^{″}(x)=ay(x){(y^{\prime }(x{)}^2+1)}^{3/2}$
4.37.36 $y^{″}(x)=ay(x){({(b-y^{\prime }(x))}^2+1)}^{3/2}$
4.37.37 $y^{″}(x)=a{(y^{\prime }(x{)}^2+1)}^{3/2}(b+cx+y(x))$
4.37.38 $y^{″}(x)+y(x{)}^3{y}^{\prime }(x)=y(x)y^{\prime }(x)\sqrt{4y^{\prime }(x)+y(x{)}^4}$
4.37.39 $y^{″}(x)=f(y^{\prime }(x))$
4.37.40 $y^{″}(x)=f(ax+by(x),y^{\prime }(x))$
4.37.41 $y^{″}(x)=y(x)f(x,\frac{y^{\prime }(x)}{y(x)})$
4.37.42 $y^{″}(x)=x^{n-2}f(x^{-n}y(x),x^{1-n}{y}^{\prime }(x))$
4.37.43 $2y^{″}(x)=12y(x{)}^2+1$
4.37.44 $2y^{″}(x)=y(x)(a-y(x{)}^2)$
4.37.45 $8y^{″}(x)+9y^{\prime }(x{)}^4=0$
4.37.46 $ax{e}^{y(x)}+x{y}^{″}(x)+y^{\prime }(x)=0$
4.37.47 $x{y}^{″}(x)+2y^{\prime }(x)+xy(x{)}^5=0$
4.37.48 $xy(x{)}^n+x{y}^{″}(x)+2y^{\prime }(x)=0$
4.37.49 $x^{m}y(x{)}^n+x{y}^{″}(x)+2y^{\prime }(x)=0$
4.37.50 $a{x}^{m}y(x{)}^n+x{y}^{″}(x)+2y^{\prime }(x)=0$