4.24.1 $y^{\prime }(x)+\log (y^{\prime }(x))=x$
4.24.2 $a+x{y}^{\prime }(x)+\log (y^{\prime }(x))=0$
4.24.3 $a+x{y}^{\prime }(x)+\log (y^{\prime }(x))=y(x)$
4.24.4 $a+by(x)+x{y}^{\prime }(x)+\log (y^{\prime }(x))=0$
4.24.5 $4x{y}^{\prime }(x)+\log (y^{\prime }(x))-2y(x)=0$
4.24.6 $a(x{y}^{\prime }(x)-y(x))+\log (y^{\prime }(x))=0$
4.24.7 $a(\log (y^{\prime }(x))-y^{\prime }(x))+y(x)-x=0$
4.24.8 $y^{\prime }(x)+y(x)\log (y^{\prime }(x))-xy(x)-y(x)\log (y(x))=0$
4.24.9 $-(x+1)y^{\prime }(x)+y^{\prime }(x)\log (y^{\prime }(x))+y(x)=0$
4.24.10 $\log (x{y}^{\prime }(x)-y(x))=y^{\prime }(x)$
4.24.11 $y^{\prime }(x)\log (\sqrt{a+y^{\prime }(x{)}^2}+y^{\prime }(x))-x{y}^{\prime }(x)-\sqrt{y^{\prime }(x{)}^2+1}+y(x)=0$
4.24.12 $y^{\prime }(x)\tan (y^{\prime }(x))+\log (\cos (y^{\prime }(x)))=y(x)$
4.24.13 $f(y^{\prime }(x))=0$
4.24.14 $f(x,y^{\prime }(x))=0$
4.24.15 $f(x{y}^{\prime }(x{)}^2)=y(x)-2x{y}^{\prime }(x)$
4.24.16 $f(y(x),y^{\prime }(x))=0$
4.24.17 $f(y^{\prime }(x))+x{y}^{\prime }(x)=y(x)$
4.24.18 $f(y^{\prime }(x))+xg(y^{\prime }(x))=y(x)$
4.24.19 $f(y^{\prime }(x),y(x)-x{y}^{\prime }(x))=0$
4.24.20 $f(x{y}^{\prime }(x),y(x))=0$
4.24.21 $x^{n}f(y^{\prime }(x),\frac{y(x)}{x})=0$
4.24.22 $f(y(x)y^{\prime }(x)+x)=y(x{)}^2(y^{\prime }(x{)}^2+1)$
4.24.23 $y(x)f(\frac{y^{\prime }(x)}{y(x)},x)=0$
4.24.24 $f(x,y(x),y^{\prime }(x))=0$
4.24.25 $y^{″}(x)=0$
4.24.26 $y^{″}(x)=x+\sin (x)$
4.24.27 $y^{″}(x)=\text{c1}\cos (ax)+\text{c2}\sin (bx)$
4.24.28 $y^{″}(x)=e^{x}x$
4.24.29 $y^{″}(x)=\text{c1}{e}^{ax}+\text{c2}{e}^{-bx}$
4.24.30 $y^{″}(x)+y(x)=0$
4.24.31 $y^{″}(x)-y(x)=0$
4.24.32 $y^{″}(x)+y(x)=ax$
4.24.33 $y^{″}(x)+y(x)=a\cos (bx)$
4.24.34 $y^{″}(x)+y(x)=8\cos (x)\cos (2x)$
4.24.35 $y^{″}(x)+y(x)=\sec (x)$
4.24.36 $y^{″}(x)+y(x)=a\sin (bx)$
4.24.37 $y^{″}(x)+y(x)=\sin (ax)\sin (bx)$
4.24.38 $y^{″}(x)+y(x)=4x\sin (x)$
4.24.39 $y^{″}(x)+y(x)=x(\cos (x)-x\sin (x))$
4.24.40 $y^{″}(x)+y(x)={\tan }^2(x)$
4.24.41 $y^{″}(x)+y(x)=e^{-x}$
4.24.42 $y^{″}(x)+y(x)=e^x(x^2-1)$
4.24.43 $y^{″}(x)+y(x)=e^x\sin (2x)$
4.24.44 $y^{″}(x)+y(x)=e^{2x}\cos (x)$
4.24.45 $y^{″}(x)-2y(x)=0$
4.24.46 $y^{″}(x)-2y(x)=4e^{x^2}{x}^2$
4.24.47 $y^{″}(x)+4y(x)=0$
4.24.48 $y^{″}(x)+4y(x)=x{\sin }^2(x)$
4.24.49 $y^{″}(x)+4y(x)=2\tan (x)$
4.24.50 $y^{″}(x)+4y(x)=2\tan (x)$