4.23.1 \(12 x^3+x y'(x)^4-2 y(x) y'(x)^3=0\)
4.23.2 \(a y'(x)^3+b y'(x)^2+y'(x)^5=c y(x)\)
4.23.3 \(a y'(x)^4+b y'(x)^3+c x y'(x)^2+y'(x)^5=c y(x)\)
4.23.4 \(3 y'(x)^5-y(x) y'(x)+1=0\)
4.23.5 \(y'(x)^6=(y(x)-a)^4 (y(x)-b)^3\)
4.23.6 \(f(x) (y(x)-a)^4 (y(x)-b)^3+y'(x)^6=0\)
4.23.7 \(f(x) (y(x)-a)^5 (y(x)-b)^3+y'(x)^6=0\)
4.23.8 \(f(x) (y(x)-a)^5 (y(x)-b)^4+y'(x)^6=0\)
4.23.9 \(f(x) (y(x)-a)^5 (y(x)-b)^4 (y(x)-c)^3+y'(x)^6=0\)
4.23.10 \(x^2 \left (y'(x)^6+3 y(x)^4+3 y(x)^2+1\right )=a^2\)
4.23.11 \(y'(x)^n=a x^r+b y'(x)^s\)
4.23.12 \(y'(x)^n=f(x)^n (y(x)-a)^{n+1} (y(x)-b)^{n-1}\)
4.23.13 \(y'(x)^n=f(x) (y(x)-a)^{n+1}\)
4.23.14 \(y'(x)^n=f(x) (y(x)-a)^{n-1} (y(x)-b)^{n-1}\)
4.23.15 \(f(x) g(x)+y'(x)^n=0\)
4.23.16 \(f(x,y(x))+y'(x)^n=0\)
4.23.17 \(a y'(x)+y'(x)^n=b y(x)\)
4.23.18 \(y'(x)^n+x y'(x)-y(x)=0\)
4.23.19 \(a y'(x)^m+y'(x)^n=b y(x)\)
4.23.20 \(\text {Y1}(y(x)) y'(x)^{n-1}+y'(x)^n=0\)
4.23.21 \(\text {X1}(x,y(x)) y'(x)^{n-1}+y'(x)^n=0\)
4.23.22 \(x^{n-1} y'(x)^n-n x y'(x)+y(x)=0\)
4.23.23 \(\text {X0}(x,y(x)) y'(x)^n+\text {X1}(x,y(x)) y'(x)^{n-1}=0\)
4.23.24 \(2 \sqrt {a y'(x)}+x y'(x)-y(x)=0\)
4.23.25 \((x-y(x)) \sqrt {y'(x)}=a \left (y'(x)+1\right )\)
4.23.26 \(3 x y'(x)+2 (y(x)+1)^{3/2}-3 y(x)=0\)
4.23.27 \(a y'(x)+\sqrt {y'(x)^2+1}=x\)
4.23.28 \(a y'(x)+\sqrt {y'(x)^2+1}=y(x)\)
4.23.29 \(\sqrt {y'(x)^2+1}=x y'(x)\)
4.23.30 \(-a y(x) y'(x)-a x+\sqrt {y'(x)^2+1}=0\)
4.23.31 \(-x y'(x)^2+\sqrt {y'(x)^2+1}+y(x)=0\)
4.23.32 \(\sqrt {a^2+b^2 y'(x)^2}+x y'(x)-y(x)=0\)
4.23.33 \(\sqrt {a c-b^2} \left (x y'(x)-y(x)\right )+\sqrt {a+2 b y'(x)+c y'(x)^2}=0\)
4.23.34 \(a \sqrt {y'(x)^2+1}+x y'(x)-y(x)=0\)
4.23.35 \(a x \sqrt {y'(x)^2+1}+x y'(x)-y(x)=0\)
4.23.36 \(-a y(x) y'(x)-a x+y(x) \sqrt {y'(x)^2+1}=0\)
4.23.37 \(y(x) \sqrt {y'(x)^2+1}=f\left (y(x) y'(x)+x\right )\)
4.23.38 \(\sqrt {\left (a x^2+y(x)^2\right ) \left (y'(x)^2+1\right )}-a x-y(x) y'(x)=0\)
4.23.39 \(a \sqrt [3]{y'(x)^3+1}+x y'(x)-y(x)=0\)
4.23.40 \(y'(x) \left (a+x \sqrt {y'(x)^2+1}\right )=y(x) \sqrt {y'(x)^2+1}\)
4.23.41 \(x y'(x)+\cos \left (y'(x)\right )=y(x)\)
4.23.42 \(a \cos \left (y'(x)\right )+b y'(x)+x=0\)
4.23.43 \(y'(x)+\sin \left (y'(x)\right )=x\)
4.23.44 \(y'(x) \sin \left (y'(x)\right )+\cos \left (y'(x)\right )=y(x)\)
4.23.45 \(y'(x)^2 \sin \left (y'(x)\right )=y(x)\)
4.23.46 \(y'(x)^2 \left (\sin \left (y'(x)\right )+x\right )=y(x)\)
4.23.47 \(\left (y'(x)^2+1\right ) \sin ^2\left (y(x)-x y'(x)\right )=1\)
4.23.48 \(-\sqrt {1-y'(x)^2}+y'(x) \left (\cos ^{-1}\left (y'(x)\right )-x\right )+y(x)=0\)
4.23.49 \(\left (y'(x)^2+1\right ) \left (a x+\tan ^{-1}\left (y'(x)\right )\right )+y'(x)=0\)
4.23.50 \(-y'(x)^2+e^{y'(x)-y(x)}+1=0\)