4 Listing of problems and solutions obtained by Mathematica and Maple

 4.1   \(y'(x)=a f(x)\)
 4.2   \(y'(x)=y(x)+x+\sin (x)\)
 4.3   \(y'(x)=x^2+2 y(x)+3 \cosh (x)\)
 4.4   \(y'(x)=a+b x+c y(x)\)
 4.5   \(y'(x)=a \cos (b x+c)+k y(x)\)
 4.6   \(y'(x)=a \sin (b x+c)+k y(x)\)
 4.7   \(y'(x)=a+b e^{k x}+c y(x)\)
 4.8   \(y'(x)=x \left (x^2-y(x)\right )\)
 4.9   \(y'(x)=x \left (a y(x)+e^{-x^2}\right )\)
 4.10   \(y'(x)=x^2 \left (a x^3+b y(x)\right )\)
 4.11   \(y'(x)=a x^n y(x)\)
 4.12   \(y'(x)=y(x) \cos (x)+\sin (x) \cos (x)\)
 4.13   \(y'(x)=y(x) \cos (x)+e^{\sin (x)}\)
 4.14   \(y'(x)=y(x) \cot (x)\)
 4.15   \(y'(x)=1-y(x) \cot (x)\)
 4.16   \(y'(x)=x \csc (x)-y(x) \cot (x)\)
 4.17   \(y'(x)=y(x) (\cot (x)+2 \csc (2 x))\)
 4.18   \(y'(x)=\sec (x)-y(x) \cot (x)\)
 4.19   \(y'(x)=y(x) \cot (x)+e^x \sin (x)\)
 4.20   \(y'(x)+2 y(x) \cot (x)+\csc (x)=0\)
 4.21   \(y'(x)=4 x \csc (x) \sec ^2(x)-2 y(x) \cot (2 x)\)
 4.22   \(y'(x)=2 \left (\cos (2 x) \cot ^2(x)-y(x) \csc (2 x)\right )\)
 4.23   \(y'(x)=4 x \csc (x) \left (y(x)+\sin ^3(x)\right )\)
 4.24   \(y'(x)=4 x \csc (x) \left (y(x)-\tan ^2(x)+1\right )\)
 4.25   \(y'(x)=y(x) \sec (x)\)
 4.26   \(y'(x)+\tan (x)=(1-y(x)) \sec (x)\)
 4.27   \(y'(x)=y(x) \tan (x)\)
 4.28   \(y'(x)=y(x) \tan (x)+\cos (x)\)
 4.29   \(y'(x)=\cos (x)-y(x) \tan (x)\)
 4.30   \(y'(x)=\sec (x)-y(x) \tan (x)\)
 4.31   \(y'(x)=y(x) \tan (x)+\sin (2 x)\)
 4.32   \(y'(x)=\sin (2 x)-y(x) \tan (x)\)
 4.33   \(y'(x)=2 y(x) \tan (x)+\sin (x)\)
 4.34   \(y'(x)=2 (y(x) \tan (2 x)+\sec (2 x)+1)\)
 4.35   \(y'(x)=3 y(x) \tan (x)+\csc (x)\)
 4.36   \(y'(x)=y(x) (a+\sin (\log (x))+\cos (\log (x)))\)
 4.37   \(y'(x)=6 e^{2 x}-y(x) \tanh (x)\)
 4.38   \(y'(x)=y(x) f'(x)+f(x) f'(x)\)
 4.39   \(y'(x)=f(x)+g(x) y(x)\)
 4.40   \(y'(x)=x^2-y(x)^2\)
 4.41   \(f(x)^2+y'(x)=f'(x)+y(x)^2\)
 4.42   \(y'(x)-x+1=y(x) (y(x)+x)\)
 4.43   \(y'(x)=(y(x)+x)^2\)
 4.44   \(y'(x)=(x-y(x))^2\)
 4.45   \(y'(x)=(x-y(x))^2+3 (y(x)-x+1)\)
 4.46   \(y'(x)=-\left (x^2+1\right ) y(x)+y(x)^2+2 x\)
 4.47   \(y'(x)=x \left (x^3+2\right )-\left (2 x^2-y(x)\right ) y(x)\)
 4.48   \(y'(x)=x \left (2-x^3\right )+\left (2 x^2-y(x)\right ) y(x)+1\)
 4.49   \(y'(x)=\cos (x)-y(x) (\sin (x)-y(x))\)
 4.50   \(y'(x)=y(x) (y(x)+\sin (2 x))+\cos (2 x)\)
 4.51   \(y'(x)=x f(x) y(x)+f(x)+y(x)^2\)
 4.52   \(y'(x)=(-4 y(x)+x+3)^2\)
 4.53   \(y'(x)=(9 y(x)+4 x+1)^2\)
 4.54   \(y'(x)=3 \left (a+b y(x)^2+b x\right )\)
 4.55   \(y'(x)=a+b y(x)^2\)
 4.56   \(y'(x)=a x+b y(x)^2\)
 4.57   \(y'(x)=a+b x+c y(x)^2\)
 4.58   \(y'(x)=a x^{n-1}+b x^{2 n}+c y(x)^2\)
 4.59   \(y'(x)=a x^2+b y(x)^2\)
 4.60   \(y'(x)=\text{a0}+\text{a1} y(x)+\text{a2} y(x)^2\)
 4.61   \(y'(x)=a y(x)+b y(x)^2+f(x)\)
 4.62   \(y'(x)=a (x-y(x)) y(x)+1\)
 4.63   \(y'(x)=a y(x)^2+f(x)+g(x) y(x)\)
 4.64   \(y'(x)=x y(x) (y(x)+3)\)
 4.65   \(y'(x)=-x^3+\left (2 x^2+1\right ) y(x)-x y(x)^2-x+1\)
 4.66   \(y'(x)=x \left (x^2 y(x)-y(x)^2+2\right )\)
 4.67   \(y'(x)=-(1-x) y(x)^2+(1-2 x) y(x)+x\)
 4.68   \(y'(x)=a x y(x)^2\)
 4.69   \(y'(x)=x^n \left (a+b y(x)^2\right )\)
 4.70   \(y'(x)=a x^m+b x^n y(x)^2\)
 4.71   \(y'(x)=y(x) (a+b y(x) \cos (k x))\)
 4.72   \(y'(x)=\sin (x) \left (2 \sec ^2(x)-y(x)\right )\)
 4.73   \(y'(x)+4 \csc (x)=y(x)^2 \sin (x)+y(x) (3-\cot (x))\)
 4.74   \(y'(x)=y(x) \sec (x)+(\sin (x)-1)^2\)
 4.75   \(y'(x)+\left (1-y(x)^2\right ) \tan (x)=0\)
 4.76   \(y'(x)=f(x)+g(x) y(x)+h(x) y(x)^2\)
 4.77   \(y'(x)=f(x) \left (a+b y(x)+c y(x)^2\right )\)
 4.78   \(y(x)^2 (a x+y(x))+y'(x)\)
 4.79   \(y'(x)=y(x)^2 \left (a e^x+y(x)\right )\)
 4.80   \(3 a (y(x)+2 x) y(x)^2+y'(x)=0\)
 4.81   \(y'(x)=y(x) \left (a+b y(x)^2\right )\)
 4.82   \(y'(x)=\text{a0}+\text{a1} y(x)+\text{a2} y(x)^2+\text{a3} y(x)^3\)
 4.83   \(y'(x)=x y(x)^3\)
 4.84   \(y'(x)+y(x) \left (1-x y(x)^2\right )=0\)
 4.85   \(y'(x)=y(x)^2 (a+b x y(x))\)
 4.86   \(y(x)^3 \left (a+4 b^2 x+3 b x^2\right )+y'(x)+3 x y(x)^2=0\)
 4.87   \(y'(x)=y(x)^2 \left (x^3 y(x)+1\right )\)
 4.88   \(2 x y(x) \left (a x y(x)^2+1\right )+y'(x)=0\)
 4.89   \(y'(x)=y(x)^2-a x \left (1-x^{n-1}\right ) y(x)^3\)
 4.90   \(y'(x)=a y(x)^2+x y(x)^3 \left (b+c x^{n-1}\right )\)
 4.91   \(y'(x)+y(x) \left (y(x)^2 \sec (x)+\tan (x)\right )=0\)
 4.92   \(y'(x)+y(x)^3 \tan (x) \sec (x)=0\)
 4.93   \(y'(x)=\text{f0}(x)+\text{f1}(x) y(x)+\text{f2}(x) y(x)^2+\text{f3}(x) y(x)^3\)
 4.94   \(y'(x)=y(x) \left (y(x)^3 \sec (x)+\tan (x)\right )\)
 4.95   \(y'(x)=a x^{\frac{n}{1-n}}+b y(x)^n\)
 4.96   \(y'(x)=f(x) y(x)+g(x) y(x)^k\)
 4.97   \(y'(x)=f(x)+g(x) y(x)+h(x) y(x)^n\)
 4.98   \(y'(x)=f(x) y(x)^m+g(x) y(x)^n\)
 4.99   \(y'(x)=\sqrt{\left | y(x)\right | }\)
 4.100   \(y'(x)=a+\sqrt{\text{A0}+\text{B0} y(x)}+b y(x)\)
 4.101   \(y'(x)=a x+b \sqrt{y(x)}\)
 4.102   \(x^3+y'(x)=x \sqrt{x^4+4 y(x)}\)
 4.103   \(y'(x)+2 \left (1-x \sqrt{y(x)}\right ) y(x)=0\)
 4.104   \(y'(x)=\sqrt{a+b y(x)^2}\)
 4.105   \(y'(x)=y(x) \sqrt{a+b y(x)}\)
 4.106   \(g(x) (f(x)-y(x)) \sqrt{(y(x)-a) (y(x)-b)}+y'(x)=0\)
 4.107   \(y'(x)=\sqrt{X Y}\)
 4.108   \(y'(x)=\text{R1}\left (x,\sqrt{X}\right ) \text{R2}\left (y(x),\sqrt{Y}\right )\)
 4.109   \(y'(x)=\cos ^2(x) \cos (y(x))\)
 4.110   \(y'(x)=\sec ^2(x) \text{Cosy}(y(x)) \cot (y(x))\)
 4.111   \(y'(x)=a+b \cos (A x+B y(x))\)
 4.112   \(y'(x)=-\left (1-f'(x)\right ) \cos (y(x))+f'(x)-f(x) \sin (y(x))+1\)
 4.113   \(g(x) \sin (a y(x))+h(x) \cos (a y(x))+f(x)+y'(x)=0\)
 4.114   \(y'(x)=a+b \cos (y(x))\)
 4.115   \(x \left (\sin (2 y(x))-x^2 \cos ^2(y(x))\right )+y'(x)=0\)
 4.116   \(y'(x)+\tan (x) \sec (x) \cos ^2(y(x))=0\)
 4.117   \(y'(x)=\cot (x) \cot (y(x))\)
 4.118   \(y'(x)+\cot (x) \cot (y(x))=0\)
 4.119   \(y'(x)=\sin (x) (\csc (y(x))-\cot (y(x)))\)
 4.120   \(y'(x)=\tan (x) \cot (y(x))\)
 4.121   \(y'(x)+\tan (x) \cot (y(x))=0\)
 4.122   \(y'(x)+\sin (2 x) \csc (2 y(x))=0\)
 4.123   \(y'(x)=\tan (x) (\tan (y(x))+\sec (x) \sec (y(x)))\)
 4.124   \(y'(x)=\cos (x) \sec ^2(y(x))\)
 4.125   \(y'(x)=\sec ^2(x) \sec ^3(y(x))\)
 4.126   \(y'(x)=a+b \sin (y(x))\)
 4.127   \(y'(x)=a+b \sin (A x+B y(x))\)
 4.128   \(y'(x)=\tan (y(x)) (\cos (x) \sin (y(x))+1)\)
 4.129   \(y'(x)+\csc (2 x) \sin (2 y(x))=0\)
 4.130   \(f(x)+g(x) \tan (y(x))+y'(x)=0\)
 4.131   \(y'(x)=\sqrt{a+b \cos (y(x))}\)
 4.132   \(y'(x)=e^{y(x)}+x\)
 4.133   \(y'(x)=e^{y(x)+x}\)
 4.134   \(y'(x)=e^x \left (a+b e^{-y(x)}\right )\)
 4.135   \(y'(x)+y(x) \log (x) \log (y(x))=0\)
 4.136   \(y'(x)=x^{m-1} y(x)^{1-n} f\left (a x^m+b y(x)^n\right )\)
 4.137   \(y'(x)=a f(y(x))\)
 4.138   \(y'(x)=f(a+b x+c y(x))\)
 4.139   \(y'(x)=f(x) g(y(x))\)
 4.140   \(y'(x)=\text{Csx}(x) y(x) \sec (x)+\sec ^2(x)\)
 4.141   \(2 y'(x)+2 \csc ^2(x)=y(x) \csc (x) \sec (x)-y(x)^2 \sec ^2(x)\)
 4.142   \(2 y'(x)=2 \sin ^2(y(x)) \tan (y(x))-x \sin (2 y(x))\)
 4.143   \(a x+2 y'(x)=\sqrt{a^2 x^2-4 b x^2-4 c y(x)}\)
 4.144   \(3 y'(x)=\sqrt{x^2-3 y(x)}+x\)
 4.145   \(x y'(x)=\sqrt{a^2-x^2}\)
 4.146   \(x y'(x)+y(x)+x=0\)
 4.147   \(x^2+x y'(x)-y(x)=0\)
 4.148   \(x y'(x)=x^3-y(x)\)
 4.149   \(x y'(x)=x^3+y(x)+1\)
 4.150   \(x y'(x)=x^m+y(x)\)
 4.151   \(x y'(x)=x \sin (x)-y(x)\)
 4.152   \(x y'(x)=x^2 \sin (x)+y(x)\)
 4.153   \(x y'(x)=x^n \log (x)-y(x)\)
 4.154   \(x y'(x)=\sin (x)-2 y(x)\)
 4.155   \(x y'(x)=a y(x)\)
 4.156   \(x y'(x)=a y(x)+x+1\)
 4.157   \(x y'(x)=a x+b y(x)\)
 4.158   \(x y'(x)=a x^2+b y(x)\)
 4.159   \(x y'(x)=a+b x^n+c y(x)\)
 4.160   \(x y'(x)+(3-x) y(x)+2=0\)
 4.161   \((a x+2) y(x)+x y'(x)+x=0\)
 4.162   \(y(x) (a+b x)+x y'(x)=0\)
 4.163   \(x y'(x)=x^3+\left (1-2 x^2\right ) y(x)\)
 4.164   \(x y'(x)=a x-\left (1-b x^2\right ) y(x)\)
 4.165   \(\left (2-a x^2\right ) y(x)+x y'(x)+x=0\)
 4.166   \(x^2+x y'(x)+y(x)^2=0\)
 4.167   \(x y'(x)=x^2+y(x) (y(x)+1)\)
 4.168   \(x y'(x)+y(x)^2-y(x)=x^{2/3}\)
 4.169   \(x y'(x)=a+b y(x)^2\)
 4.170   \(x y'(x)=a x^2+b y(x)^2+y(x)\)
 4.171   \(x y'(x)=a x^{2 n}+y(x) (b y(x)+n)\)
 4.172   \(x y'(x)=a x^n+b y(x)+c y(x)^2\)
 4.173   \(x y'(x)=a x^n+b y(x)+c y(x)^2+k\)
 4.174   \(a+x y'(x)+x y(x)^2=0\)
 4.175   \(x y'(x)+y(x) (1-x y(x))=0\)
 4.176   \(x y'(x)=y(x) (1-x y(x))\)
 4.177   \(x y'(x)=y(x) (x y(x)+1)\)
 4.178   \(x y'(x)=a x^3 y(x) (1-x y(x))\)
 4.179   \(x y'(x)=x^3+\left (2 x^2+1\right ) y(x)+x y(x)^2\)
 4.180   \(x y'(x)=y(x) (2 x y(x)+1)\)
 4.181   \(y(x) (a x y(x)+2)+b x+x y'(x)=0\)
 4.182   \(\text{a0}+\text{a1} x+y(x) (\text{a2}+\text{a3} x y(x))+x y'(x)=0\)
 4.183   \(a x^2 y(x)^2+x y'(x)+2 y(x)=b\)
 4.184   \(\frac{1}{2} (n-m) y(x)+x^m+x^n y(x)^2+x y'(x)=0\)
 4.185   \(y(x) \left (a+b x^n y(x)\right )+x y'(x)=0\)
 4.186   \(x y'(x)=a x^m-b y(x)-c x^n y(x)^2\)
 4.187   \(x y'(x)=a x^n (x-y(x))^2-y(x)+2 x\)
 4.188   \(y(x) (1-a y(x) \log (x))+x y'(x)=0\)
 4.189   \(x y'(x)=f(x) \left (x^2-y(x)^2\right )+y(x)\)
 4.190   \(x y'(x)=y(x) \left (y(x)^2+1\right )\)
 4.191   \(x y'(x)+y(x) \left (1-x y(x)^2\right )=0\)
 4.192   \(x y'(x)+y(x)=a \left (x^2+1\right ) y(x)^3\)
 4.193   \(x y'(x)=a y(x)+b \left (x^2+1\right ) y(x)^3\)
 4.194   \(x y'(x)+2 y(x)=a x^{2 k} y(x)^k\)
 4.195   \(x y'(x)=4 \left (y(x)-\sqrt{y(x)}\right )\)
 4.196   \(x y'(x)+2 y(x)=\sqrt{y(x)^2+1}\)
 4.197   \(x y'(x)=\sqrt{x^2+y(x)^2}+y(x)\)
 4.198   \(x y'(x)=\sqrt{x^2-y(x)^2}+y(x)\)
 4.199   \(x y'(x)=x \sqrt{x^2+y(x)^2}+y(x)\)
 4.200   \(x y'(x)=y(x)-x (x-y(x)) \sqrt{x^2+y(x)^2}\)
 4.201   \(x y'(x)=a \sqrt{b^2 x^2+y(x)^2}+y(x)\)
 4.202   \(\cos (y(x)) \left (\sin (y(x))-3 x^2 \cos (y(x))\right )+x y'(x)=0\)
 4.203   \(x y'(x)-y(x)+x \cos \left (\frac{y(x)}{x}\right )+x=0\)
 4.204   \(x y'(x)=y(x)-x \cos ^2\left (\frac{y(x)}{x}\right )\)
 4.205   \(x y'(x)=\left (1-2 x^2\right ) \cot ^2(y(x))\)
 4.206   \(x y'(x)=y(x)-\cot ^2(y(x))\)
 4.207   \(x y'(x)+y(x)+2 x \sec (x y(x))=0\)
 4.208   \(x y'(x)-y(x)+x \sec \left (\frac{y(x)}{x}\right )=0\)
 4.209   \(x y'(x)=y(x)+x \sec ^2\left (\frac{y(x)}{x}\right )\)
 4.210   \(x y'(x)=\sin (x-y(x))\)
 4.211   \(x y'(x)=y(x)+x \sin \left (\frac{y(x)}{x}\right )\)
 4.212   \(x y'(x)+\tan (y(x))=0\)
 4.213   \(x y'(x)+\tan (y(x)+x)+x=0\)
 4.214   \(x y'(x)=y(x)-x \tan \left (\frac{y(x)}{x}\right )\)
 4.215   \(x y'(x)=\left (y(x)^2+1\right ) \left (x^2+\tan ^{-1}(y(x))\right )\)
 4.216   \(x y'(x)=x e^{\frac{y(x)}{x}}+y(x)\)
 4.217   \(x y'(x)=x e^{\frac{y(x)}{x}}+y(x)+x\)
 4.218   \(x y'(x)=y(x) \log (y(x))\)
 4.219   \(x y'(x)=y(x) (-\log (y(x))+\log (x)+1)\)
 4.220   \(x y'(x)+y(x) (-\log (y(x))-\log (x)+1)=0\)
 4.221   \(x y'(x)=y(x)-2 x \tanh \left (\frac{y(x)}{x}\right )\)
 4.222   \(n y(x)+x y'(x)=f(x) g\left (x^n y(x)\right )\)
 4.223   \(x y'(x)=y(x) f\left (x^m y(x)^n\right )\)
 4.224   \((x+1) y'(x)=(3 x+4) x^3+y(x)\)
 4.225   \((x+1) y'(x)=2 y(x)+(x+1)^4\)
 4.226   \((x+1) y'(x)=n y(x)+e^x (x+1)^{n+1}\)
 4.227   \((x+1) y'(x)=a y(x)+b x y(x)^2\)
 4.228   \((x+1) y'(x)+(x+1)^4 y(x)^3+y(x)=0\)
 4.229   \((x+1) y'(x)=y(x) \left (1-x y(x)^3\right )\)
 4.230   \((x+1) y'(x)=(x+1) \sqrt{y(x)+1}+y(x)+1\)
 4.231   \((a+x) y'(x)=b x\)
 4.232   \((a+x) y'(x)=b x+y(x)\)
 4.233   \((a+x) y'(x)+b x^2+y(x)=0\)
 4.234   \((a+x) y'(x)=2 (a+x)^5+3 y(x)\)
 4.235   \((a+x) y'(x)=b+c y(x)\)
 4.236   \((a+x) y'(x)=b x+c y(x)\)
 4.237   \((a+x) y'(x)=y(x) (1-a y(x))\)
 4.238   \((a-x) y'(x)=y(x)^3 (b+c x)+y(x)\)
 4.239   \(2 x y'(x)=2 x^3-y(x)\)
 4.240   \(2 x y'(x)+1=y(x)^2+4 i x y(x)\)
 4.241   \(2 x y'(x)=y(x) \left (y(x)^2+1\right )\)
 4.242   \(2 x y'(x)+y(x) \left (y(x)^2+1\right )=0\)
 4.243   \(2 x y'(x)=y(x) \left (-6 y(x)^2+x+1\right )\)
 4.244   \(\sqrt{a^2-4 b-4 c y(x)}+a+2 x y'(x)+4 y(x)=0\)
 4.245   \((1-2 x) y'(x)=2 (-3 y(x)+16 x+8)\)
 4.246   \((2 x+1) y'(x)=4 e^{-y(x)}-2\)
 4.247   \(2 (1-x) y'(x)=y(x)+4 \sqrt{1-x} x\)
 4.248   \(2 (x+1) y'(x)+(x+1)^4 y(x)^3+2 y(x)=0\)
 4.249   \(3 x y'(x)=3 x^{2/3}+(1-3 y(x)) y(x)\)
 4.250   \(3 x y'(x)=y(x) \left (x y(x)^3+2\right )\)
 4.251   \(3 x y'(x)=y(x) \left (3 x y(x)^3 \log (x)+1\right )\)
 4.252   \(x^2 y'(x)=a-y(x)\)
 4.253   \(x^2 y'(x)=a+b x+c x^2+x y(x)\)
 4.254   \(x^2 y'(x)=a+b x+c x^2-x y(x)\)
 4.255   \(x^2 y'(x)+(1-2 x) y(x)=x^2\)
 4.256   \(x^2 y'(x)=a+b x y(x)\)
 4.257   \(x^2 y'(x)=y(x) (a+b x)\)
 4.258   \(x^2 y'(x)+(x+2) x y(x)=\left (1-e^{-2 x}\right ) x-2\)
 4.259   \(x^2 y'(x)+2 (1-x) x y(x)=e^x \left (2 e^x-1\right )\)
 4.260   \(x^2 y'(x)+x^2+x y(x)+y(x)^2=0\)
 4.261   \(x^2 y'(x)=(-y(x)+2 x+1)^2\)
 4.262   \(x^2 y'(x)=a+b y(x)^2\)
 4.263   \(x^2 y'(x)=y(x) (a y(x)+x)\)
 4.264   \(x^2 y'(x)=y(x) (a x+b y(x))\)
 4.265   \(a x^2+b x y(x)+c y(x)^2+x^2 y'(x)=0\)
 4.266   \(x^2 y'(x)=a+b x^n+x^2 y(x)^2\)
 4.267   \(x^2 y'(x)+x y(x) (x y(x)+4)+2=0\)
 4.268   \(a x (1-x y(x))+x^2 y'(x)+x^2 \left (-y(x)^2\right )+2=0\)
 4.269   \(x^2 y'(x)=a+b x^2 y(x)^2\)
 4.270   \(x^2 y'(x)=a+b x^n+c x^2 y(x)^2\)
 4.271   \(x^2 y'(x)=a+b x y(x)+c x^2 y(x)^2\)
 4.272   \(x^2 y'(x)=a+b x y(x)+c x^4 y(x)^2\)
 4.273   \(x^2 y'(x)+y(x) \left (x^2+y(x)^2-x\right )=0\)
 4.274   \(x^2 y'(x)=2 y(x) \left (x-y(x)^2\right )\)
 4.275   \(x^2 y'(x)=a x^2 y(x)^2-a y(x)^3\)
 4.276   \(a y(x)^2+b x^2 y(x)^3+x^2 y'(x)=0\)
 4.277   \(x^2 y'(x)=y(x) \left (a x+b y(x)^3\right )\)
 4.278   \(x^2 y'(x)+x y(x)+\sqrt{y(x)}=0\)
 4.279   \(x^2 y'(x)=3 x \tan (y(x))+\sec (y(x))\)
 4.280   \(\left (1-x^2\right ) y'(x)=-x^2+y(x)+1\)
 4.281   \(\left (1-x^2\right ) y'(x)+1=x y(x)\)
 4.282   \(\left (1-x^2\right ) y'(x)=5-x y(x)\)
 4.283   \(a+\left (x^2+1\right ) y'(x)+x y(x)=0\)
 4.284   \(a+\left (x^2+1\right ) y'(x)-x y(x)=0\)
 4.285   \(a+\left (1-x^2\right ) y'(x)-x y(x)=0\)
 4.286   \(\left (1-x^2\right ) y'(x)+x y(x)-x=0\)
 4.287   \(\left (1-x^2\right ) y'(x)-x^2+x y(x)=0\)
 4.288   \(\left (1-x^2\right ) y'(x)+x^2+x y(x)=0\)
 4.289   \(\left (x^2+1\right ) y'(x)=x \left (x^2+1\right )-x y(x)\)
 4.290   \(\left (x^2+1\right ) y'(x)=x \left (3 x^2-y(x)\right )\)
 4.291   \(\left (1-x^2\right ) y'(x)+2 x y(x)=0\)
 4.292   \(\left (x^2+1\right ) y'(x)=2 x (x-y(x))\)
 4.293   \(\left (x^2+1\right ) y'(x)=2 x \left (x^2+1\right )^2+2 x y(x)\)
 4.294   \(\left (1-x^2\right ) y'(x)+\cos (x)=2 x y(x)\)
 4.295   \(\left (x^2+1\right ) y'(x)=\tan (x)-2 x y(x)\)
 4.296   \(\left (1-x^2\right ) y'(x)=a+4 x y(x)\)
 4.297   \(\left (x^2+1\right ) y'(x)=y(x) (a+2 b x)\)
 4.298   \(\left (x^2+1\right ) y'(x)=y(x)^2+1\)
 4.299   \(\left (1-x^2\right ) y'(x)=1-y(x)^2\)
 4.300   \(\left (1-x^2\right ) y'(x)=1-(2 x-y(x)) y(x)\)
 4.301   \(\left (1-x^2\right ) y'(x)=n \left (y(x)^2-2 x y(x)+1\right )\)
 4.302   \(\left (x^2+1\right ) y'(x)+x (1-y(x)) y(x)=0\)
 4.303   \(\left (1-x^2\right ) y'(x)=x y(x) (a y(x)+1)\)
 4.304   \(\left (x^2+1\right ) y'(x)=y(x)^2-2 x \left (y(x)^2+1\right ) y(x)+1\)
 4.305   \(\left (x^2+1\right ) y'(x)+x \sin (y(x)) \cos (y(x))=x \left (x^2+1\right ) \cos ^2(y(x))\)
 4.306   \(\left (x^2+1\right ) y'(x)=x^2-y(x) \cot ^{-1}(x)+1\)
 4.307   \(\left (4-x^2\right ) y'(x)+4 y(x)=(x+2) y(x)^2\)
 4.308   \(\left (a^2+x^2\right ) y'(x)=b+x y(x)\)
 4.309   \(\left (a^2+x^2\right ) y'(x)=\left (\sqrt{a^2+x^2}+x\right ) (b+y(x))\)
 4.310   \(\left (a^2+x^2\right ) y'(x)+(x-y(x)) y(x)=0\)
 4.311   \(\left (a^2+x^2\right ) y'(x)=a^2-2 y(x)^2+3 x y(x)\)
 4.312   \(\left (a^2+x^2\right ) y'(x)+b x y(x)^2+x y(x)=0\)
 4.313   \((1-x) x y'(x)=a+(x+1) y(x)\)
 4.314   \((1-x) x y'(x)=2 (x y(x)+1)\)
 4.315   \((1-x) x y'(x)=2 (x y(x)-1)\)
 4.316   \(x (x+1) y'(x)=(1-2 x) y(x)\)
 4.317   \((1-x) x y'(x)+(2 x+1) y(x)=a\)
 4.318   \((1-x) x y'(x)=a+2 (2-x) y(x)\)
 4.319   \((1-x) x y'(x)-3 x y(x)+y(x)+2=0\)
 4.320   \(x (x+1) y'(x)=\left (x^2+x-1\right ) y(x)+(x+1) \left (x^2-1\right )\)
 4.321   \(x^2+(x-3) (x-2) y'(x)+3 x y(x)-8 y(x)=0\)
 4.322   \(x (a+x) y'(x)=y(x) (b+c y(x))\)
 4.323   \((a+x)^2 y'(x)=2 (a+x) (b+y(x))\)
 4.324   \(k (-a+y(x)+x)^2+(x-a)^2 y'(x)+y(x)^2=0\)
 4.325   \((x-a) (x-b) y'(x)+k y(x)=0\)
 4.326   \((x-a) (x-b) y'(x)=y(x) (-a-b+2 x)+(x-a) (x-b)\)
 4.327   \((x-a) (x-b) y'(x)=c y(x)^2\)
 4.328   \(k (y(x)-a) (y(x)-b)+(x-a) (x-b) y'(x)=0\)
 4.329   \(k (-a+y(x)+x) (-b+y(x)+x)+(x-a) (x-b) y'(x)+y(x)^2=0\)
 4.330   \(2 x^2 y'(x)=y(x)\)
 4.331   \(2 x^2 y'(x)+2 x^2 y(x) \cot (x)+x \cot (x)-1=0\)
 4.332   \(2 x^2 y'(x)+x^2 \left (-y(x)^2\right )+2 x y(x)+1=0\)
 4.333   \(2 x^2 y'(x)=\left (x^2-y(x)^2\right ) (1-x \cot (x))+2 x y(x)\)
 4.334   \(2 \left (1-x^2\right ) y'(x)=\sqrt{1-x^2}+(x+1) y(x)\)
 4.335   \((1-2 x) x y'(x)+(1-4 x) y(x)+1=0\)
 4.336   \((1-2 x) x y'(x)=y(x)^2-(4 x+1) y(x)+4 x\)
 4.337   \(2 (1-x) x y'(x)+(1-2 x) y(x)+x=0\)
 4.338   \(2 (1-x) x y'(x)+(1-x) y(x)^2+x=0\)
 4.339   \(2 \left (x^2+x+1\right ) y'(x)=8 x^2-(2 x+1) y(x)+1\)
 4.340   \(4 \left (x^2+1\right ) y'(x)-x^2-4 x y(x)=0\)
 4.341   \(a x^2 y'(x)=a x y(x)+b^2 y(x)^2+x^2\)
 4.342   \(\left (a+b x^2\right ) y'(x)=A+B y(x)^2\)
 4.343   \(\left (a+b x^2\right ) y'(x)=c x y(x) \log (y(x))\)
 4.344   \(x (a x+1) y'(x)+a-y(x)=0\)
 4.345   \((a+b x)^2 y'(x)+y(x)^3 (a+b x)+c y(x)^2=0\)
 4.346   \(x^3 y'(x)=a+b x^2 y(x)\)
 4.347   \(x^3 y'(x)=x^2 y(x)-x^2+3\)
 4.348   \(x^3 y'(x)=x^4+y(x)^2\)
 4.349   \(x^3 y'(x)=y(x) \left (x^2+y(x)\right )\)
 4.350   \(x^3 y'(x)=x^2 (y(x)-1)+y(x)^2\)
 4.351   \(x^3 y'(x)=(x+1) y(x)^2\)
 4.352   \(x^3 y'(x)+x^2 y(x) \left (1-x^2 y(x)\right )+20=0\)
 4.353   \(x^6 \left (-y(x)^2\right )+x^3 y'(x)+(3-2 x) x^2 y(x)+3=0\)
 4.354   \(x^3 y'(x)=y(x) \left (2 x^2+y(x)^2\right )\)
 4.355   \(x^3 y'(x)=\cos (y(x)) \left (\cos (y(x))-2 x^2 \sin (y(x))\right )\)
 4.356   \(x \left (x^2+1\right ) y'(x)=a x^2+y(x)\)
 4.357   \(x \left (1-x^2\right ) y'(x)=a x^2+y(x)\)
 4.358   \(x \left (x^2+1\right ) y'(x)=a x^3+y(x)\)
 4.359   \(x \left (x^2+1\right ) y'(x)=a-x^2 y(x)\)
 4.360   \(x \left (x^2+1\right ) y'(x)=\left (1-x^2\right ) y(x)\)
 4.361   \(x \left (1-x^2\right ) y'(x)=\left (x^2-x+1\right ) y(x)\)
 4.362   \(x \left (1-x^2\right ) y'(x)=a x^3+\left (1-2 x^2\right ) y(x)\)
 4.363   \(x \left (1-x^2\right ) y'(x)=\left (1-2 x^2\right ) y(x)+\left (1-x^2\right ) x^3\)
 4.364   \(x \left (x^2+1\right ) y'(x)=2 \left (1-2 x^2 y(x)\right )\)
 4.365   \(x \left (x^2+1\right ) y'(x)=x-\left (5 x^2+3\right ) y(x)\)
 4.366   \(\left (1-x^2\right ) x y'(x)+\left (1-x^2\right ) y(x)^2+x^2=0\)
 4.367   \((1-x) x^2 y'(x)=(2-x) x y(x)-y(x)^2\)
 4.368   \(2 x^3 y'(x)=y(x) \left (x^2-y(x)^2\right )\)
 4.369   \(2 x^3 y'(x)=y(x) \left (a y(x)^2+3 x^2\right )\)
 4.370   \(6 x^3 y'(x)=4 x^2 y(x)+(1-3 x) y(x)^4\)
 4.371   \(x y'(x) \left (a+b x+c x^2\right )-y(x) \left (a+b x+c x^2\right )+x^2=y(x)^2\)
 4.372   \(x^4 y'(x)=y(x) \left (x^3+y(x)\right )\)
 4.373   \(a^2+x^4 y'(x)+x^4 y(x)^2=0\)
 4.374   \(x^4 y'(x)+x^3 y(x)+\csc (x y(x))=0\)
 4.375   \(\left (1-x^4\right ) y'(x)=2 x \left (1-y(x)^2\right )\)
 4.376   \(x \left (1-x^3\right ) y'(x)=2 x-\left (1-4 x^3\right ) y(x)\)
 4.377   \(x \left (1-x^3\right ) y'(x)=x^2+y(x) (1-2 x y(x))\)
 4.378   \(x^2 \left (1-x^2\right ) y'(x)=y(x) \left (x-3 x^3 y(x)\right )\)
 4.379   \(x \left (1-2 x^3\right ) y'(x)=2 \left (1-x^3\right ) y(x)\)
 4.380   \(\left (y'(x)+y(x)^2\right ) \left (a+b x+c x^2\right )^2+A=0\)
 4.381   \(x^5 y'(x)=1-3 x^4 y(x)\)
 4.382   \(x \left (1-x^4\right ) y'(x)=\left (1-x^4\right ) y(x)+2 x \left (x^2-y(x)^2\right )\)
 4.383   \(x^7 y'(x)+5 x^3 y(x)^2+2 \left (x^2+1\right ) y(x)^3=0\)
 4.384   \(x^n y'(x)=a+b x^{n-1} y(x)\)
 4.385   \(x^n y'(x)=x^{2 n-1}-y(x)^2\)
 4.386   \(y(x) \left (x^{n-1}+y(x)\right )+x^n y'(x)+x^2=0\)
 4.387   \((1-n) x^{n-1}+x^{2 n-2}+x^n y'(x)+y(x)^2=0\)
 4.388   \(x^n y'(x)=a^2 x^{2 n-2}+b^2 y(x)^2\)
 4.389   \(x^n y'(x)=x^{n-1} \left (a x^{2 n}-b y(x)^2+n y(x)\right )\)
 4.390   \(x^{2 n} y'(x)=-n x^{n-1}+x^n y(x) \left (x^{2 n} y(x)^2-3 x^n y(x)+1\right )+1\)
 4.391   \(x^k y'(x)=a x^m+b y(x)^n\)
 4.392   \(\sqrt{x^2+1} y'(x)=2 x-y(x)\)
 4.393   \(\sqrt{1-x^2} y'(x)=y(x)^2+1\)
 4.394   \(\left (x-\sqrt{x^2+1}\right ) y'(x)=y(x)+\sqrt{y(x)^2+1}\)
 4.395   \(\sqrt{a^2+x^2} y'(x)+y(x)+x=\sqrt{a^2+x^2}\)
 4.396   \(\sqrt{b^2+x^2} y'(x)=\sqrt{a^2+y(x)^2}\)
 4.397   \(\sqrt{b^2-x^2} y'(x)=\sqrt{a^2-y(x)^2}\)
 4.398   \(x \sqrt{a^2+x^2} y'(x)=y(x) \sqrt{b^2+y(x)^2}\)
 4.399   \(x \sqrt{x^2-a^2} y'(x)=y(x) \sqrt{y(x)^2-b^2}\)
 4.400   \(\sqrt{X} y'(x)+\sqrt{Y}=0\)
 4.401   \(\sqrt{X} y'(x)=\sqrt{Y}\)
 4.402   \(x^{3/2} y'(x)=a+b x^{3/2} y(x)^2\)
 4.403   \(\sqrt{x^3+1} y'(x)=\sqrt{y(x)^3+1}\)
 4.404   \(\sqrt{(1-x) x (1-a x)} y'(x)=\sqrt{(1-y(x)) y(x) (1-a y(x))}\)
 4.405   \(\sqrt{1-x^4} y'(x)=\sqrt{1-y(x)^4}\)
 4.406   \(\sqrt{x^4+x^2+1} y'(x)=\sqrt{y(x)^4+y(x)^2+1}\)
 4.407   \(\sqrt{X} y'(x)=0\)
 4.408   \(\sqrt{X} y'(x)+\sqrt{Y}=0\)
 4.409   \(\sqrt{X} y'(x)=\sqrt{Y}\)
 4.410   \(\left (x^3+1\right )^{2/3} y'(x)+\left (y(x)^3+1\right )^{2/3}=0\)
 4.411   \(\left (\text{a0}+\text{a1} x+4 x^3\right )^{2/3} y'(x)+\left (\text{a0}+\text{a1} y(x)+4 y(x)^3\right )^{2/3}=0\)
 4.412   \(X^{2/3} y'(x)=Y^{2/3}\)
 4.413   \(\left (a+\cos ^2\left (\frac{x}{2}\right )\right ) y'(x)=y(x) \tan \left (\frac{x}{2}\right ) \left (a-y(x)+\cos ^2\left (\frac{x}{2}\right )+1\right )\)
 4.414   \(\left (1-4 \cos ^2(x)\right ) y'(x)=y(x) \left (4 \cos ^2(x)+1\right ) \tan (x)\)
 4.415   \((1-\sin (x)) y'(x)+y(x) \cos (x)=0\)
 4.416   \(y'(x) (\cos (x)-\sin (x))+y(x) (\sin (x)+\cos (x))=0\)
 4.417   \(y'(x) \left (\text{a0}+\text{a1} \sin ^2(x)\right )+\text{a2} x \left (\text{a1} \sin ^2(x)+\text{a3}\right )+\text{a1} y(x) \sin (2 x)=0\)
 4.418   \(\left (x-e^x\right ) y'(x)+\left (1-e^x\right ) y(x)+e^x x=0\)
 4.419   \(x \log (x) y'(x)=a x (\log (x)+1)-y(x)\)
 4.420   \(y(x) y'(x)+x=0\)
 4.421   \(e^{x^2} x+y(x) y'(x)=0\)
 4.422   \(x^3+y(x) y'(x)+y(x)=0\)
 4.423   \(a x+b y(x)+y(x) y'(x)=0\)
 4.424   \(y(x) y'(x)+e^{-x} x (y(x)+1)=0\)
 4.425   \(f(x)+y(x) y'(x)=g(x) y(x)\)
 4.426   \(y(x) y'(x)+y(x)^2+4 x (x+1)=0\)
 4.427   \(y(x) y'(x)=a x+b y(x)^2\)
 4.428   \(y(x) y'(x)=a y(x)^2+b \cos (c+x)\)
 4.429   \(y(x) y'(x)=\text{a0}+\text{a1} y(x)+\text{a2} y(x)^2\)
 4.430   \(y(x) y'(x)=a x+b x y(x)^2\)
 4.431   \(y(x) y'(x)=\csc ^2(x)-y(x)^2 \cot (x)\)
 4.432   \(y(x) y'(x)=\sqrt{a^2+y(x)^2}\)
 4.433   \(y(x) y'(x)=\sqrt{y(x)^2-a^2}\)
 4.434   \(g(x) f\left (x^2+y(x)^2\right )+y(x) y'(x)+x=0\)
 4.435   \((y(x)+1) y'(x)=y(x)+x\)
 4.436   \((y(x)+1) y'(x)=x^2 (1-y(x))\)
 4.437   \((y(x)+x) y'(x)+y(x)=0\)
 4.438   \((x-y(x)) y'(x)=y(x)\)
 4.439   \((y(x)+x) y'(x)-y(x)+x=0\)
 4.440   \((y(x)+x) y'(x)=x-y(x)\)
 4.441   \(1-y'(x)=y(x)+x\)
 4.442   \((x-y(x)) y'(x)=y(x) (2 x y(x)+1)\)
 4.443   \((y(x)+x) y'(x)+\tan (y(x))=0\)
 4.444   \((x-y(x)) y'(x)=\left (e^{-\frac{x}{y(x)}}+1\right ) y(x)\)
 4.445   \((y(x)+x+1) y'(x)+3 y(x)+4 x+1=0\)
 4.446   \((y(x)+x+2) y'(x)=-y(x)-x+1\)
 4.447   \((-y(x)-x+3) y'(x)=-3 y(x)+x+1\)
 4.448   \((y(x)-x+3) y'(x)=3 y(x)-4 x+11\)
 4.449   \((y(x)+2 x) y'(x)-2 y(x)+x=0\)
 4.450   \((-y(x)+2 x+2) y'(x)+3 (-y(x)+2 x+1)=0\)
 4.451   \((-y(x)+2 x+3) y'(x)+2=0\)
 4.452   \((-y(x)+2 x+4) y'(x)-2 y(x)+x+5=0\)
 4.453   \((-y(x)-2 x+5) y'(x)-2 y(x)-x+4=0\)
 4.454   \((y(x)-3 x+1) y'(x)=2 (x-y(x))\)
 4.455   \((y(x)-3 x+2) y'(x)-3 y(x)-2 x+5=0\)
 4.456   \((4 x-y(x)) y'(x)-5 y(x)+2 x=0\)
 4.457   \((-y(x)-4 x+6) y'(x)=2 x-y(x)\)
 4.458   \((-y(x)+5 x+1) y'(x)-5 y(x)+x+5=0\)
 4.459   \(y'(x) (a+b x+y(x))+a-b x-y(x)=0\)
 4.460   \(\left (x^2-y(x)\right ) y'(x)+x=0\)
 4.461   \(\left (x^2-y(x)\right ) y'(x)=4 x y(x)\)
 4.462   \(y'(x) (y(x)-\cot (x) \csc (x))+y(x) \csc (x) (y(x) \cos (x)+1)=0\)
 4.463   \(x^2+2 y(x) y'(x)+y(x)^2+2 x=0\)
 4.464   \(2 y(x) y'(x)=x^3+x y(x)^2\)
 4.465   \((x-2 y(x)) y'(x)=y(x)\)
 4.466   \((2 y(x)+x) y'(x)-y(x)+2 x=0\)
 4.467   \((x-2 y(x)) y'(x)+y(x)+2 x=0\)
 4.468   \((-2 y(x)+x+1) y'(x)=-y(x)+2 x+1\)
 4.469   \((2 y(x)+x+1) y'(x)-2 y(x)-x+1=0\)
 4.470   \((2 y(x)+x+1) y'(x)-4 y(x)+x+7=0\)
 4.471   \(x^2+2 (y(x)+x) y'(x)+2 y(x)=0\)
 4.472   \((-2 y(x)+2 x+3) y'(x)=-2 y(x)+6 x+1\)
 4.473   \((-2 y(x)-4 x+1) y'(x)+y(x)+2 x=0\)
 4.474   \((6 x-2 y(x)) y'(x)=-y(x)+3 x+2\)
 4.475   \((2 y(x)+9 x+19) y'(x)-6 y(x)-2 x+18=0\)
 4.476   \(\left (x^3+2 y(x)\right ) y'(x)=3 x (2-x y(x))\)
 4.477   \(y'(x) (\tan (x) \sec (x)-2 y(x))+\sec (x) (2 y(x) \sin (x)+1)=0\)
 4.478   \(\left (e^{-x} x-2 y(x)\right ) y'(x)=2 e^{-2 x} x-\left (-2 y(x)+e^{-x} x+e^{-x}\right ) y(x)\)
 4.479   \(3 y(x) y'(x)+5 \cot (x) \cos ^2(y(x)) \cot (y(x))=0\)
 4.480   \(3 (2-y(x)) y'(x)+x y(x)=0\)
 4.481   \((x-3 y(x)) y'(x)-y(x)+3 x+4=0\)
 4.482   \((-3 y(x)-x+4) y'(x)-3 y(x)-x+3=0\)
 4.483   \((3 y(x)+2 x+2) y'(x)=-3 y(x)-2 x+1\)
 4.484   \((-3 y(x)-2 x+5) y'(x)-3 y(x)-2 x+1=0\)
 4.485   \((-3 y(x)+9 x+1) y'(x)-y(x)+3 x+2=0\)
 4.486   \((4 y(x)+x) y'(x)-y(x)+4 x=0\)
 4.487   \((4 y(x)+2 x+3) y'(x)=2 y(x)+x+1\)
 4.488   \((-4 y(x)+2 x+5) y'(x)=-2 y(x)+x+3\)
 4.489   \((-4 y(x)+3 x+5) y'(x)=-3 y(x)+7 x+2\)
 4.490   \(4 (-y(x)-x+1) y'(x)-x+2=0\)
 4.491   \((-4 y(x)-11 x+11) y'(x)=-25 y(x)-8 x+62\)
 4.492   \((5 y(x)+3 x+6) y'(x)=7 y(x)+x+2\)
 4.493   \((5 y(x)+7 x) y'(x)+8 y(x)+10 x=0\)
 4.494   \(\left (4 x^3+5 y(x)+x\right ) y'(x)+7 x^3+3 x^2 y(x)+4 y(x)=0\)
 4.495   \((6 y(x)-x+5) y'(x)=4 y(x)-x+3\)
 4.496   \(3 (2 y(x)+x) y'(x)=-2 y(x)-x+1\)
 4.497   \((7 y(x)-3 x+3) y'(x)+3 y(x)-7 x+7=0\)
 4.498   \((9 y(x)+x+1) y'(x)+5 y(x)+x+1=0\)
 4.499   \((-12 y(x)+5 x+8) y'(x)=-5 y(x)+2 x+3\)
 4.500   \((-16 y(x)+7 x+140) y'(x)+y(x)+8 x+25=0\)
 4.501   \((21 y(x)+9 x+3) y'(x)=-5 y(x)+7 x+45\)
 4.502   \(y'(x) (a x+b y(x))+x=0\)
 4.503   \(y'(x) (a x+b y(x))+y(x)=0\)
 4.504   \(y'(x) (a x+b y(x))+a y(x)+b x=0\)
 4.505   \(y'(x) (a x+b y(x))=a y(x)+b x\)
 4.506   \(\text{a1}+y'(x) (\text{a2}+b x+\text{c2} y(x))+b y(x)+\text{b1} x=0\)
 4.507   \(y'(x) (\text{a2}+\text{b2} y(x)+\text{c2} y(x))=\text{a1}+\text{b1} x+\text{c1} y(x)\)
 4.508   \(x y(x) y'(x)+y(x)^2+1=0\)
 4.509   \(x y(x) y'(x)=y(x)^2+x\)
 4.510   \(x^2+x y(x) y'(x)+y(x)^2=0\)
 4.511   \(x^4+x y(x) y'(x)-y(x)^2=0\)
 4.512   \(x y(x) y'(x)=a x^3 \cos (x)+y(x)^2\)
 4.513   \(x y(x) y'(x)=x^2-x y(x)+y(x)^2\)
 4.514   \(2 x^2+x y(x) y'(x)-2 x y(x)-y(x)^2=0\)
 4.515   \(x y(x) y'(x)=a+b y(x)^2\)
 4.516   \(x y(x) y'(x)=a x^n+b y(x)^2\)
 4.517   \(x y(x) y'(x)=\left (x^2+1\right ) \left (1-y(x)^2\right )\)
 4.518   \(x^2 \cot ^{-1}\left (\frac{y(x)}{x}\right )+x y(x) y'(x)-y(x)^2=0\)
 4.519   \(x^2 e^{-\frac{2 y(x)}{x}}+x y(x) y'(x)-y(x)^2=0\)
 4.520   \((x y(x)+1) y'(x)+y(x)^2=0\)
 4.521   \(x (y(x)+1) y'(x)-(1-x) y(x)=0\)
 4.522   \(x (1-y(x)) y'(x)+(x+1) y(x)=0\)
 4.523   \(x (1-y(x)) y'(x)+(1-x) y(x)=0\)
 4.524   \(a x+x (y(x)+2) y'(x)=0\)
 4.525   \((x (-y(x))+3 x+2) y'(x)+y(x)=0\)
 4.526   \(x (y(x)+4) y'(x)=y(x)^2+2 y(x)+2 x\)
 4.527   \(x (a+y(x)) y'(x)+b x+c y(x)=0\)
 4.528   \(x (a+y(x)) y'(x)=y(x) (A+B x)\)
 4.529   \(x (y(x)+x) y'(x)+y(x)^2=0\)
 4.530   \(x (x-y(x)) y'(x)+y(x)^2=0\)
 4.531   \(x (y(x)+x) y'(x)=x^2+y(x)^2\)
 4.532   \(2 x^2+x (x-y(x)) y'(x)+3 x y(x)-y(x)^2=0\)
 4.533   \(x \sqrt{x^2-y(x)^2}+x (y(x)+x) y'(x)-y(x) (y(x)+x)=0\)
 4.534   \((a+x (y(x)+x)) y'(x)=b y(x) (y(x)+x)\)
 4.535   \(x (y(x)+2 x) y'(x)=x^2+x y(x)-y(x)^2\)
 4.536   \(4 x^2+x (4 x-y(x)) y'(x)-6 x y(x)-y(x)^2=0\)
 4.537   \(x \left (x^3+y(x)\right ) y'(x)=\left (x^3-y(x)\right ) y(x)\)
 4.538   \(x \left (2 x^3+y(x)\right ) y'(x)=\left (2 x^3-y(x)\right ) y(x)\)
 4.539   \(x \left (2 x^3+y(x)\right ) y'(x)=6 y(x)^2\)
 4.540   \((1-x) y(x) y'(x)+x (1-y(x))=0\)
 4.541   \((a+x) (b+x) y'(x)=x y(x)\)
 4.542   \(-2 x^3+2 x y(x) y'(x)-y(x)^2+1=0\)
 4.543   \(a+2 x y(x) y'(x)+y(x)^2=0\)
 4.544   \(2 x y(x) y'(x)=a x+y(x)^2\)
 4.545   \(x^2+2 x y(x) y'(x)+y(x)^2=0\)
 4.546   \(2 x y(x) y'(x)=x^2+y(x)^2\)
 4.547   \(2 x y(x) y'(x)=4 (2 x+1) x^2+y(x)^2\)
 4.548   \(x^2 \left (a x^3+1\right )+2 x y(x) y'(x)=6 y(x)^2\)
 4.549   \(3 x^2+(2 x y(x)-x+3) y'(x)+y(x)^2-y(x)=0\)
 4.550   \(x (x-2 y(x)) y'(x)+y(x)^2=0\)
 4.551   \(x (2 y(x)+x) y'(x)+(2 x-y(x)) y(x)=0\)
 4.552   \(x (x-2 y(x)) y'(x)+(2 x-y(x)) y(x)=0\)
 4.553   \(x (-2 y(x)+x+1) y'(x)+y(x) (y(x)-2 x+1)=0\)
 4.554   \(x (-2 y(x)-x+1) y'(x)+y(x) (y(x)+2 x+1)=0\)
 4.555   \(2 x \left (2 x^2+y(x)\right ) y'(x)+y(x) \left (12 x^2+y(x)\right )=0\)
 4.556   \(-3 x^2+2 (x+1) y(x) y'(x)+y(x)^2+2 x=0\)
 4.557   \(x (3 y(x)+2 x) y'(x)=y(x)^2\)
 4.558   \(x (3 y(x)+2 x) y'(x)+3 (y(x)+x)^2=0\)
 4.559   \(\left (x^2+6 x y(x)+3\right ) y'(x)+3 y(x)^2+2 x y(x)+2 x=0\)
 4.560   \(x^3+3 x (2 y(x)+x) y'(x)+3 y(x) (y(x)+2 x)=0\)
 4.561   \(a x y(x) y'(x)=x^2+y(x)^2\)
 4.562   \(a x y(x) y'(x)+x^2-y(x)^2=0\)
 4.563   \(x y'(x) (a+b y(x))=c y(x)\)
 4.564   \(x (x-a y(x)) y'(x)=y(x) (y(x)-a x)\)
 4.565   \(y'(x) (x (A x+B y(x))+\text{a0}+\text{a1} x+\text{a2} y(x))=y(x) (A x+B y(x))+\text{b0}+\text{b1} x+\text{b2} y(x)\)
 4.566   \(y'(x) (x (\text{a1}+\text{b2} x+\text{c2} y(x))+\text{a1}+\text{b1} x+\text{c1} y(x))=y(x) (\text{a2}+\text{b2} x+\text{c2} y(x))+\text{a3}+\text{b3} x+\text{c2} y(x)\)
 4.567   \(x y'(x) \left (a y(x)+x^n\right )+y(x)^2 (b+c y(x))=0\)
 4.568   \(\left (1-x^2 y(x)\right ) y'(x)-x y(x)^2+1=0\)
 4.569   \(\left (1-x^2 y(x)\right ) y'(x)+x y(x)^2-1=0\)
 4.570   \(x (1-x y(x)) y'(x)+y(x) (x y(x)+1)=0\)
 4.571   \(x (x y(x)+2) y'(x)=2 x^3-x y(x)^2-2 y(x)+3\)
 4.572   \(x (2-x y(x)) y'(x)-x (x y(x)+1) y(x)^2+2 y(x)=0\)
 4.573   \(x (3-x y(x)) y'(x)=y(x) (x y(x)-1)\)
 4.574   \(x^2 (1-y(x)) y'(x)+(1-x) y(x)=0\)
 4.575   \(x^2 (1-y(x)) y'(x)+(x+1) y(x)^2=0\)
 4.576   \(\left (x^2+1\right ) y(x) y'(x)+x \left (1-y(x)^2\right )=0\)
 4.577   \(\left (1-x^2\right ) y(x) y'(x)+2 x^2+x y(x)^2=0\)
 4.578   \(2 x^2 y(x) y'(x)=x^2 (2 x+1)-y(x)^2\)
 4.579   \(x (1-2 x y(x)) y'(x)+y(x) (2 x y(x)+1)=0\)
 4.580   \(x (2 x y(x)+1) y'(x)+y(x) (3 x y(x)+2)=0\)
 4.581   \(y(x) \left (-x^2 y(x)^2+2 x y(x)+1\right )+x (2 x y(x)+1) y'(x)=0\)
 4.582   \(x^2 (x-2 y(x)) y'(x)=2 x^3-4 x y(x)^2+y(x)^3\)
 4.583   \(2 x (x+1) y(x) y'(x)=y(x)^2+1\)
 4.584   \(3 x^2 y(x) y'(x)+2 x y(x)^2+1=0\)
 4.585   \(x^2 (4 x-3 y(x)) y'(x)=y(x) \left (6 x^2-3 x y(x)+2 y(x)^2\right )\)
 4.586   \(\left (1-x^3 y(x)\right ) y'(x)=x^2 y(x)^2\)
 4.587   \(a+2 x^3 y(x) y'(x)+3 x^2 y(x)^2=0\)
 4.588   \(x \left (3-2 x^2 y(x)\right ) y'(x)=3 x^2 y(x)^2-3 y(x)+4 x\)
 4.589   \(x \left (2 x^2 y(x)+3\right ) y'(x)+y(x) \left (3 x^2 y(x)+4\right )=0\)
 4.590   \(3 x^4+8 x^3 y(x) y'(x)-6 x^2 y(x)^2-y(x)^4=0\)
 4.591   \(x y(x) \left (a+b x^2\right ) y'(x)=A+B y(x)^2\)
 4.592   \(3 x^4 y(x) y'(x)=1-2 x^3 y(x)^2\)
 4.593   \(x^7 y(x) y'(x)=5 x^3 y(x)+2 \left (x^2+1\right )\)
 4.594   \(\sqrt{x^2+1} y(x) y'(x)+x \sqrt{y(x)^2+1}=0\)
 4.595   \(\sqrt{x^2+1} (y(x)+1) y'(x)=y(x)^3\)
 4.596   \(y'(x) (\text{g0}(x)+\text{g1}(x) y(x))=\text{f0}(x)+\text{f1}(x) y(x)+\text{f2}(x) y(x)^2+\text{f3}(x) y(x)^3\)
 4.597   \(y(x)^2 y'(x)+x (2-y(x))=0\)
 4.598   \(y(x)^2 y'(x)=x \left (y(x)^2+1\right )\)
 4.599   \(\left (y(x)^2+x\right ) y'(x)+y(x)=a+b x\)
 4.600   \(\left (x-y(x)^2\right ) y'(x)=x^2-y(x)\)
 4.601   \(\left (x^2+y(x)^2\right ) y'(x)+x y(x)=0\)
 4.602   \(\left (x^2+y(x)^2\right ) y'(x)=x y(x)\)
 4.603   \(\left (x^2-y(x)^2\right ) y'(x)=2 x y(x)\)
 4.604   \(\left (x^2-y(x)^2\right ) y'(x)+x (2 y(x)+x)=0\)
 4.605   \(\left (x^2+y(x)^2\right ) y'(x)+2 x (y(x)+2 x)=0\)
 4.606   \(\left (-x^2+y(x)^2+1\right ) y'(x)=x^2-y(x)^2+1\)
 4.607   \(\left (a^2+x^2+y(x)^2\right ) y'(x)+2 x y(x)=0\)
 4.608   \(\left (a^2+x^2+y(x)^2\right ) y'(x)+b^2+x^2+2 x y(x)=0\)
 4.609   \(\left (x^2+y(x)^2+x\right ) y'(x)=y(x)\)
 4.610   \(\left (3 x^2-y(x)^2\right ) y'(x)=2 x y(x)\)
 4.611   \(\left (x^4+y(x)^2\right ) y'(x)=4 x^3 y(x)\)
 4.612   \(y(x) (y(x)+1) y'(x)=x (x+1)\)
 4.613   \(\left (y(x)^2+2 y(x)+x\right ) y'(x)+y(x)^2 (y(x)+x)^2+y(x) (y(x)+1)=0\)
 4.614   \(\left (x^2+y(x)^2+2 y(x)\right ) y'(x)+2 x=0\)
 4.615   \(\left (x^3-y(x)^2+2 y(x)\right ) y'(x)+3 x^2 y(x)=0\)
 4.616   \(\left (y(x)^2+x y(x)+y(x)+1\right ) y'(x)+y(x)+1=0\)
 4.617   \((y(x)+x)^2 y'(x)=a^2\)
 4.618   \((x-y(x))^2 y'(x)=a^2\)
 4.619   \(\left (x^2+2 x y(x)-y(x)^2\right ) y'(x)+x^2-2 x y(x)+y(x)^2=0\)
 4.620   \((x-y(x))^2 y'(x)=(-y(x)+x+1)^2\)
 4.621   \((y(x)+x)^2 y'(x)=(y(x)+x+2)^2\)
 4.622   \((y(x)+x)^2 y'(x)=x^2-2 x y(x)+5 y(x)^2\)
 4.623   \(y'(x) (a+b+y(x)+x)^2=2 (a+y(x))^2\)
 4.624   \(\left (2 x^2+4 x y(x)-y(x)^2\right ) y'(x)=x^2-4 x y(x)-2 y(x)^2\)
 4.625   \((y(x)+3 x)^2 y'(x)=4 y(x) (2 y(x)+3 x)\)
 4.626   \((-y(x)-3 x+1)^2 y'(x)=(-4 y(x)-6 x+3) (1-2 y(x))\)
 4.627   \(y'(x) \left (\cot (x)-2 y(x)^2\right )=y(x)^3 \csc (x) \sec (x)\)
 4.628   \(3 y(x)^2 y'(x)=a y(x)^3+x+1\)
 4.629   \(\left (x^2-3 y(x)^2\right ) y'(x)+2 x y(x)+1=0\)
 4.630   \(\left (2 x^2+3 y(x)^2\right ) y'(x)+x (y(x)+3 x)=0\)
 4.631   \(3 \left (x^2-y(x)^2\right ) y'(x)-2 y(x)^3+6 x (x+1) y(x)+3 e^x=0\)
 4.632   \(\left (3 x^2+2 x y(x)+4 y(x)^2\right ) y'(x)+2 x^2+6 x y(x)+y(x)^2=0\)
 4.633   \((2 y(x)-3 x+1)^2 y'(x)=(-3 y(x)+2 x+4)^2\)
 4.634   \(\left (-3 x^2 y(x)+6 y(x)^2+1\right ) y'(x)+x^2-3 x y(x)^2=0\)
 4.635   \(a+(x-6 y(x))^2 y'(x)-6 y(x)^2+2 x y(x)=0\)
 4.636   \(\left (a y(x)^2+x^2\right ) y'(x)=x y(x)\)
 4.637   \(\left (a y(x)^2+x^2+x y(x)\right ) y'(x)=a x^2+x y(x)+y(x)^2\)
 4.638   \(\left (a x^2-a y(x)^2+2 x y(x)\right ) y'(x)-2 a x y(x)+x^2-y(x)^2=0\)
 4.639   \(y'(x) \left (x^2 (a+2 b)+2 x (2 b+c) y(x)+3 c y(x)^2\right )+2 x (a+2 b) y(x)+3 a x^2+(2 b+c) y(x)^2=0\)
 4.640   \(y'(x) \left (a x^2+2 b x y(x)+c y(x)^2\right )+2 a x y(x)+b y(x)^2+k x^2=0\)
 4.641   \(x \left (1-y(x)^2\right ) y'(x)=\left (x^2+1\right ) y(x)\)
 4.642   \(x \left (3 x-y(x)^2\right ) y'(x)+y(x) \left (5 x-2 y(x)^2\right )=0\)
 4.643   \(x \left (x^2+y(x)^2\right ) y'(x)=y(x) \left (x^4+x^2+y(x)^2\right )\)
 4.644   \(x \left (-x^2+y(x)^2+1\right ) y'(x)+y(x) \left (x^2-y(x)^2+1\right )=0\)
 4.645   \(x \left (a-x^2-y(x)^2\right ) y'(x)+y(x) \left (a+x^2+y(x)^2\right )=0\)
 4.646   \(x \left (2 x^2+y(x)^2\right ) y'(x)=y(x) \left (2 x^2+3 y(x)^2\right )\)
 4.647   \(\left (x \left (a-x^2-y(x)^2\right )+y(x)\right ) y'(x)-y(x) \left (a-x^2-y(x)^2\right )+x=0\)
 4.648   \(x (a+y(x))^2 y'(x)=b y(x)^2\)
 4.649   \(x \left (x^2-x y(x)+y(x)^2\right ) y'(x)+y(x) \left (x^2+x y(x)+y(x)^2\right )=0\)
 4.650   \(x \left (x^2-x y(x)-y(x)^2\right ) y'(x)=y(x) \left (x^2+x y(x)-y(x)^2\right )\)
 4.651   \(x \left (a x y(x)+x^2+y(x)^2\right ) y'(x)=y(x) \left (b x y(x)+x^2+y(x)^2\right )\)
 4.652   \(x \left (x^2-2 y(x)^2\right ) y'(x)=y(x) \left (2 x^2-y(x)^2\right )\)
 4.653   \(x \left (x^2+2 y(x)^2\right ) y'(x)=y(x) \left (2 x^2+3 y(x)^2\right )\)
 4.654   \(2 x \left (5 x^2+y(x)^2\right ) y'(x)=x^2 y(x)-y(x)^3\)
 4.655   \(x \left (a x y(x)+x^2+2 y(x)^2\right ) y'(x)=y(x)^2 (a x+2 y(x))\)
 4.656   \(3 x y(x)^2 y'(x)=2 x-y(x)^3\)
 4.657   \(\left (3 x y(x)^2-4 x+1\right ) y'(x)=y(x) \left (2-y(x)^2\right )\)
 4.658   \(x \left (x-3 y(x)^2\right ) y'(x)+y(x) \left (2 x-y(x)^2\right )=0\)
 4.659   \(x^3+3 x \left (y(x)^2+x\right ) y'(x)-3 x y(x)-2 y(x)^3=0\)
 4.660   \(x \left (-3 x^3 y(x)+x^3+4 y(x)^2\right ) y'(x)=6 y(x)^3\)
 4.661   \(6 x y(x)^2 y'(x)+2 y(x)^3+x=0\)
 4.662   \(x \left (6 y(x)^2+x\right ) y'(x)-3 y(x)^3+x y(x)=0\)
 4.663   \(x \left (x^2-6 y(x)^2\right ) y'(x)=4 y(x) \left (x^2+3 y(x)^2\right )\)
 4.664   \(x \left (3 x-7 y(x)^2\right ) y'(x)+y(x) \left (5 x-3 y(x)^2\right )=0\)
 4.665   \(x^3+x^2 y(x)^2 y'(x)-x+1=0\)
 4.666   \(\left (1-x^2 y(x)^2\right ) y'(x)=x y(x)^3\)
 4.667   \(\left (1-x^2 y(x)^2\right ) y'(x)=y(x)^2 (x y(x)+1)\)
 4.668   \(x \left (x y(x)^2+1\right ) y'(x)+y(x)=0\)
 4.669   \(x \left (x y(x)^2+1\right ) y'(x)=y(x) \left (2-3 x y(x)^2\right )\)
 4.670   \(x^2 (a+y(x))^2 y'(x)=\left (x^2+1\right ) \left (a^2+y(x)^2\right )\)
 4.671   \(\left (x^2+1\right ) \left (y(x)^2+1\right ) y'(x)+2 x y(x) \left (1-y(x)^2\right )=0\)
 4.672   \(\left (x^2+1\right ) \left (y(x)^2+1\right ) y'(x)+2 x y(x) (1-y(x))^2=0\)
 4.673   \(\left (-x^3+6 x^2 y(x)^2+1\right ) y'(x)=x \left (-4 y(x)^3+3 x y(x)+6\right )\)
 4.674   \(x \left (4 x^2 y(x)-12 x y(x)^2+5 x+3\right ) y'(x)+y(x) \left (6 x^2 y(x)-8 x y(x)^2+10 x+3\right )=0\)
 4.675   \(x^3 \left (y(x)^2+1\right ) y'(x)+3 x^2 y(x)=0\)
 4.676   \(y(x) \left (x^2 y(x)^2+1\right )+x (1-x y(x))^2 y'(x)=0\)
 4.677   \(\left (1-x^4 y(x)^2\right ) y'(x)=x^3 y(x)^3\)
 4.678   \(\left (3 x-y(x)^3\right ) y'(x)=x^2-3 y(x)\)
 4.679   \(\left (x^3-y(x)^3\right ) y'(x)+x^2 y(x)=0\)
 4.680   \(x^2 (a x+3 y(x))+\left (x^3+y(x)^3\right ) y'(x)=0\)
 4.681   \(\left (-x^2 y(x)-y(x)^3+x\right ) y'(x)=x^3+x y(x)^2-y(x)\)
 4.682   \(\left (a^2 x+y(x) \left (x^2-y(x)^2\right )\right ) y'(x)+x \left (x^2-y(x)^2\right )=a^2 y(x)\)
 4.683   \(y(x) \left (a+x^2+y(x)^2\right ) y'(x)=x \left (a-x^2-y(x)^2\right )\)
 4.684   \(y(x) \left (3 x^2+y(x)^2\right ) y'(x)+x \left (x^2+3 y(x)^2\right )=0\)
 4.685   \(y(x) \left (a-3 x^2-y(x)^2\right ) y'(x)+x \left (a-x^2+y(x)^2\right )=0\)
 4.686   \(2 y(x)^3 y'(x)=x^3-x y(x)^2\)
 4.687   \(y(x) \left (2 y(x)^2+1\right ) y'(x)=x \left (2 x^2+1\right )\)
 4.688   \(x^3+y(x) \left (3 x^2+2 y(x)^2\right ) y'(x)=0\)
 4.689   \(y(x) \left (5 x^2+2 y(x)^2\right ) y'(x)+x \left (x^2+5 y(x)^2\right )=0\)
 4.690   \(2 x^3+3 x^2 y(x)+\left (-x^3+x^2+3 x y(x)^2+2 y(x)^3\right ) y'(x)-y(x)^3+y(x)^2=0\)
 4.691   \(4 x^3+9 x^2 y(x)+\left (3 x^3+6 x^2 y(x)-3 x y(x)^2+20 y(x)^3\right ) y'(x)+6 x y(x)^2-y(x)^3=0\)
 4.692   \(\left (a y(x)^3+x^3\right ) y'(x)=x^2 y(x)\)
 4.693   \(y'(x) \left (a x^2-b x^3+3 c x y(x)^2+2 c y(x)^3\right )+a y(x)^2+2 b x^3+3 b x^2 y(x)-c y(x)^3=0\)
 4.694   \(x y(x)^3 y'(x)=\left (1-x^2\right ) \left (y(x)^2+1\right )\)
 4.695   \(x \left (x-y(x)^3\right ) y'(x)=y(x) \left (y(x)^3+3 x\right )\)
 4.696   \(x \left (2 x^3+y(x)^3\right ) y'(x)=y(x) \left (2 x^3-x^2 y(x)+y(x)^3\right )\)
 4.697   \(x \left (2 x^3-y(x)^3\right ) y'(x)=y(x) \left (x^3-2 y(x)^3\right )\)
 4.698   \(x \left (x^3+3 x^2 y(x)+y(x)^3\right ) y'(x)=y(x)^2 \left (3 x^2+y(x)^2\right )\)
 4.699   \(x \left (x^3-2 y(x)^3\right ) y'(x)=y(x) \left (2 x^3-y(x)^3\right )\)
 4.700   \(x \left (x^4-2 y(x)^3\right ) y'(x)+y(x) \left (2 x^4+y(x)^3\right )=0\)
 4.701   \(x \left (2 y(x)^3+y(x)+x\right ) y'(x)=(x-y(x)) y(x)\)
 4.702   \(\left (-7 x y(x)^3-y(x)+5 x\right ) y'(x)-y(x)^4+5 y(x)=0\)
 4.703   \(y(x) \left (1-2 x^3 y(x)\right )+x \left (1-2 x y(x)^3\right ) y'(x)=0\)
 4.704   \(x \left (-2 x y(x)^3-x y(x)^2+2\right ) y'(x)+2 y(x)+1=0\)
 4.705   \(\left (-10 x^2 y(x)^3+3 y(x)^2+2\right ) y'(x)=x \left (5 y(x)^4+1\right )\)
 4.706   \(x y'(x) \left (a+b x y(x)^3\right )+y(x) \left (a+c x^3 y(x)\right )=0\)
 4.707   \(y(x) \left (1-2 x^3 y(x)^2\right )+x \left (1-2 x^2 y(x)^3\right ) y'(x)=0\)
 4.708   \(x (1-x y(x)) \left (1-x^2 y(x)^2\right ) y'(x)+y(x) (x y(x)+1) \left (x^2 y(x)^2+1\right )=0\)
 4.709   \(\left (x^2-y(x)^4\right ) y'(x)=x y(x)\)
 4.710   \(\left (x^3-y(x)^4\right ) y'(x)=3 x^2 y(x)\)
 4.711   \(\left (a^2 x^2+\left (x^2+y(x)^2\right )^2\right ) y'(x)=a^2 x y(x)\)
 4.712   \(2 \left (x-y(x)^4\right ) y'(x)=y(x)\)
 4.713   \(\left (-2 y(x)^4-x y(x)^3+4 x\right ) y'(x)=y(x) \left (y(x)^3+2\right )\)
 4.714   \(y(x) y'(x) \left ((a x+b y(x))^3+a x^3\right )+x \left ((a x+b y(x))^3+b y(x)^3\right )=0\)
 4.715   \(\left (2 x^2 y(x)^3+x y(x)^4+2 y(x)+x\right ) y'(x)+y(x) \left (y(x)^4+1\right )=0\)
 4.716   \(2 x \left (x^3+y(x)^4\right ) y'(x)=y(x) \left (x^3+2 y(x)^4\right )\)
 4.717   \(x \left (1-x^2 y(x)^4\right ) y'(x)+y(x)=0\)
 4.718   \(\left (x^2-y(x)^5\right ) y'(x)=2 x y(x)\)
 4.719   \(x \left (x^3+y(x)^5\right ) y'(x)=y(x) \left (x^3-y(x)^5\right )\)
 4.720   \(y(x)^3 \left (3 x^5 y(x)^5-1\right )+x^3 \left (5 x^3 y(x)^7+1\right ) y'(x)=0\)
 4.721   \(y'(x) (\text{f1}(x,y(x))+x \text{f2}(x,y(x)))=y(x) \text{f2}(x,y(x))+\text{f3}(x,y(x))\)
 4.722   \(y'(x) (a (y(x)+x)+1)^n+a (y(x)+x)^n=0\)
 4.723   \(x y'(x) \left (a+x y(x)^n\right )+b y(x)=0\)
 4.724   \(f(x) y(x)^m y'(x)+g(x) y(x)^{m+1}+h(x) y(x)^n=0\)
 4.725   \(\sqrt{b^2+y(x)^2} y'(x)=\sqrt{a^2+x^2}\)
 4.726   \(\sqrt{b^2-y(x)^2} y'(x)=\sqrt{a^2-x^2}\)
 4.727   \(\sqrt{Y} y'(x)=\sqrt{X}\)
 4.728   \(\left (\sqrt{y(x)+x}+1\right ) y'(x)+1=0\)
 4.729   \(\sqrt{x y(x)} y'(x)-y(x)+x=\sqrt{x y(x)}\)
 4.730   \(\left (x-2 \sqrt{x y(x)}\right ) y'(x)=y(x)\)
 4.731   \(\left (x^2+1\right )^{3/2} \left (y(x)+\sqrt{y(x)^2+1}\right ) y'(x)=y(x)^2+1\)
 4.732   \(\left (x^2+1\right )^{3/2} \left (y(x)+\sqrt{y(x)^2+1}\right ) y'(x)=y(x)^2+1\)
 4.733   \(\left (x-\sqrt{x^2+y(x)^2}\right ) y'(x)=y(x)\)
 4.734   \(x \left (1-\sqrt{x^2-y(x)^2}\right ) y'(x)=y(x)\)
 4.735   \(x \left (\sqrt{x^2+y(x)^2}+x\right ) y'(x)+\sqrt{x^2+y(x)^2} y(x)=0\)
 4.736   \(x y(x) \left (\sqrt{x^2-y(x)^2}+x\right ) y'(x)=x y(x)^2-\left (x^2-y(x)^2\right )^{3/2}\)
 4.737   \(\left (x-y(x)^2 \sqrt{y(x)^2-x^2}\right ) y'(x)=y(x) \left (x \sqrt{y(x)^2-x^2}+1\right )\)
 4.738   \(\left (x \sqrt{x^2+y(x)^2+1}-y(x) \left (x^2+y(x)^2\right )\right ) y'(x)=\sqrt{x^2+y(x)^2+1} y(x)+x \left (x^2+y(x)^2\right )\)
 4.739   \(y'(x) \left (x^2 \sec (x) \cos (y(x))+1\right )-y(x) \tan (x)+\sec (x) \sin (y(x))=0\)
 4.740   \(y'(x) \cos (y(x)) (\cos (y(x))-\sin (A) \sin (x))+\cos (x) (\cos (x)-\sin (A) \sin (y(x)))=0\)
 4.741   \(y'(x) (a \cos (a y(x)+b x)-b \sin (a x+b y(x)))-a \sin (a x+b y(x))+b \cos (a y(x)+b x)=0\)
 4.742   \(y'(x) (a \sin (x y(x))-\sin (y(x))+\cos (y(x)+x))+y(x) \sin (x y(x))+\cos (y(x)+x)+\cos (x)=0\)
 4.743   \(y'(x) (\cos (x) \sec (y(x))+x)+\tan (y(x))-y(x) \sin (x) \sec (y(x))=0\)
 4.744   \(y'(x) \left (x^2+2 y(x) \sin (x) \sec (y(x))\right )+2 x \tan (y(x))+y(x)^2 \cos (x) \sec (y(x))=0\)
 4.745   \(y'(x) \left (x^2 \sec ^2(y(x))-6 x y(x)+2\right )-3 y(x)^2+2 x \tan (y(x))=0\)
 4.746   \(y'(x) ((y(x)+x) \tan (y(x))+1)+1=0\)
 4.747   \(x y'(x) \left (x-y(x) \tan \left (\frac{y(x)}{x}\right )\right )+y(x) \left (y(x) \tan \left (\frac{y(x)}{x}\right )+x\right )=0\)
 4.748   \(\left (x e^{y(x)}+e^x\right ) y'(x)+e^x y(x)+e^{y(x)}=0\)
 4.749   \(y'(x) (-\log (y(x))-2 x+1)+2 y(x)=0\)
 4.750   \(y'(x) (x \cosh (y(x))+\sinh (x))+\sinh (y(x))+y(x) \cosh (x)=0\)
 4.751   \((\sinh (x)+1) y'(x) \sinh (y(x))+\cosh (x) (\cosh (y(x))-1)=0\)
 4.752   \(y'(x)^2=a x^n\)
 4.753   \(y'(x)^2=y(x)\)
 4.754   \(y'(x)^2=x-y(x)\)
 4.755   \(y'(x)^2=x^2+y(x)\)
 4.756   \(x^2+y'(x)^2=4 y(x)\)
 4.757   \(3 x^2+y'(x)^2=8 y(x)\)
 4.758   \(a x^2+b y(x)+y'(x)^2=0\)
 4.759   \(y'(x)^2=y(x)^2+1\)
 4.760   \(y'(x)^2=1-y(x)^2\)
 4.761   \(y'(x)^2=a^2-y(x)^2\)
 4.762   \(y'(x)^2=a^2 y(x)^2\)
 4.763   \(y'(x)^2=a+b y(x)^2\)
 4.764   \(y'(x)^2=x^2 y(x)^2\)
 4.765   \(y'(x)^2=(y(x)-1) y(x)^2\)
 4.766   \(y'(x)^2=(y(x)-a) (y(x)-b) (y(x)-c)\)
 4.767   \(y'(x)^2=a^2 y(x)^n\)
 4.768   \(y'(x)^2=a^2 y(x)^2 \left (1-\log ^2(y(x))\right )\)
 4.769   \(f(x) (y(x)-a) (y(x)-b)+y'(x)^2=0\)
 4.770   \(f(x) (y(x)-a)^2 (y(x)-b)+y'(x)^2=0\)
 4.771   \(f(x) (y(x)-a) (y(x)-b) (y(x)-c)+y'(x)^2=0\)
 4.772   \(f(x) (y(x)-a)^2 (y(x)-b) (y(x)-c)+y'(x)^2=0\)
 4.773   \(f(x) (y(x)-\text{a1}) (y(x)-\text{a2}) (y(x)-\text{a3}) (y(x)-\text{a4})+y'(x)^2=0\)
 4.774   \(y'(x)^2=f(x)^2 (y(x)-a) (y(x)-b) (y(x)-c)^2\)
 4.775   \(y'(x)^2=f(x)^2 (y(x)-a) (y(x)-b) (y(x)-u(x))^2\)
 4.776   \(y'(x)^2+2 y'(x)+x=0\)
 4.777   \(a (x-y(x))+y'(x)^2-2 y'(x)=0\)
 4.778   \(y'(x)^2-2 y'(x)-y(x)^2=0\)
 4.779   \(y'(x)^2-5 y'(x)+6=0\)
 4.780   \(y'(x)^2-7 y'(x)+12=0\)
 4.781   \(a y'(x)+b+y'(x)^2=0\)
 4.782   \(a y'(x)+b x+y'(x)^2=0\)
 4.783   \(a y'(x)+b y(x)+y'(x)^2=0\)
 4.784   \(y'(x)^2+x y'(x)+1=0\)
 4.785   \(y'(x)^2+x y'(x)-y(x)=0\)
 4.786   \(y'(x)^2-x y'(x)+y(x)=0\)
 4.787   \(y'(x)^2-x y'(x)-y(x)=0\)
 4.788   \(y'(x)^2+x y'(x)-y(x)+x=0\)
 4.789   \(y'(x)^2+(1-x) y'(x)+y(x)=0\)
 4.790   \(y'(x)^2-(x+1) y'(x)+y(x)=0\)
 4.791   \(y'(x)^2-(2-x) y'(x)-y(x)+1=0\)
 4.792   \((a+x) y'(x)+y'(x)^2-y(x)=0\)
 4.793   \(y'(x)^2-2 x y'(x)+1=0\)
 4.794   \(-3 x^2+2 x y'(x)+y'(x)^2=0\)
 4.795   \(y'(x)^2+2 x y'(x)-y(x)=0\)
 4.796   \(y'(x)^2+2 x y'(x)-y(x)=0\)
 4.797   \(y'(x)^2-2 x y'(x)+2 y(x)=0\)
 4.798   \(y'(x)^2-(2 x+1) y'(x)-(1-x) x=0\)
 4.799   \(y'(x)^2+2 (1-x) y'(x)-2 (x-y(x))=0\)
 4.800   \(y'(x)^2+3 x y'(x)-y(x)=0\)
 4.801   \(y'(x)^2-4 (x+1) y'(x)+4 y(x)=0\)
 4.802   \(a x y'(x)+y'(x)^2=b c x^2\)
 4.803   \(-a x y'(x)+a y(x)+y'(x)^2=0\)
 4.804   \(a x y'(x)+b x^2+c y(x)+y'(x)^2=0\)
 4.805   \((a+b x) y'(x)+c+y'(x)^2=b y(x)\)
 4.806   \(-2 x^2 y'(x)+2 x y'(x)+y'(x)^2=0\)
 4.807   \(a x^2 y'(x)+b x y(x)+y'(x)^2=0\)
 4.808   \(a x^3 y'(x)-2 a x^2 y(x)+y'(x)^2=0\)
 4.809   \(-2 a x^3 y'(x)+4 a x^2 y(x)+y'(x)^2=0\)
 4.810   \(4 x^5 y'(x)-12 x^4 y(x)+y'(x)^2=0\)
 4.811   \(y'(x)^2-2 \cosh (x) y'(x)+1=0\)
 4.812   \(y'(x)^2+y(x) y'(x)=x (y(x)+x)\)
 4.813   \(y'(x)^2-y(x) y'(x)+e^x=0\)
 4.814   \(y'(x)^2+(y(x)+x) y'(x)+x y(x)=0\)
 4.815   \(y'(x)^2-2 y(x) y'(x)-2 x=0\)
 4.816   \(y'(x)^2+(2 y(x)+1) y'(x)+(y(x)-1) y(x)=0\)
 4.817   \(y'(x)^2-2 (x-y(x)) y'(x)-4 x y(x)=0\)
 4.818   \(y'(x)^2-(4 y(x)+1) y'(x)+y(x) (4 y(x)+1)=0\)
 4.819   \(y'(x)^2-2 (1-3 y(x)) y'(x)-(4-9 y(x)) y(x)=0\)
 4.820   \(y(x) (3 a+b+9 y(x))+(a+6 y(x)) y'(x)+y'(x)^2=0\)
 4.821   \(a y(x) y'(x)-a x+y'(x)^2=0\)
 4.822   \(-a y(x) y'(x)-a x+y'(x)^2=0\)
 4.823   \(y'(x) (a x+b y(x))+a b x y(x)+y'(x)^2=0\)
 4.824   \(y(x)^2 \log (a y(x))-x y(x) y'(x)+y'(x)^2=0\)
 4.825   \(y'(x)^2-(2 x y(x)+1) y'(x)+2 x y(x)=0\)
 4.826   \(y'(x)^2-\left (y(x)^2+4\right ) y'(x)+y(x)^2+4=0\)
 4.827   \(-(x-y(x)) y(x) y'(x)+y'(x)^2-x y(x)^3=0\)
 4.828   \(x y(x)^2 y'(x)+y'(x)^2+y(x)^3=0\)
 4.829   \(-2 x^3 y(x)^2 y'(x)-4 x^2 y(x)^3+y'(x)^2=0\)
 4.830   \(x^4 y(x)^4-x \left (x^2+y(x)^2\right ) y(x) y'(x)+y'(x)^2=0\)
 4.831   \(2 x y(x)^3 y'(x)+y'(x)^2+y(x)^4=0\)
 4.832   \(y'(x)^2+2 y(x) \cot (x) y'(x)-y(x)^2=0\)
 4.833   \(y'(x)^2-3 x y(x)^{2/3} y'(x)+9 y(x)^{5/3}=0\)
 4.834   \(y'(x)^2=e^{4 x-2 y(x)} \left (y'(x)-1\right )\)
 4.835   \(2 y'(x)^2+x y'(x)-2 y(x)=0\)
 4.836   \(2 y'(x)^2-(1-x) y'(x)-y(x)=0\)
 4.837   \(-2 x^2 y'(x)+2 y'(x)^2+3 x y(x)=0\)
 4.838   \(2 y'(x)^2+2 (6 y(x)-1) y'(x)+3 y(x) (6 y(x)-1)=0\)
 4.839   \(3 y'(x)^2-2 x y'(x)+y(x)=0\)
 4.840   \(x^2+4 x y'(x)+3 y'(x)^2-y(x)=0\)
 4.841   \(4 y'(x)^2=9 x\)
 4.842   \(4 y'(x)^2+2 x e^{-2 y(x)} y'(x)-e^{-2 y(x)}=0\)
 4.843   \(4 y'(x)^2+2 e^{2 x-2 y(x)} y'(x)-e^{2 x-2 y(x)}=0\)
 4.844   \(5 y'(x)^2+3 x y'(x)-y(x)=0\)
 4.845   \(5 y'(x)^2+6 x y'(x)-2 y(x)=0\)
 4.846   \(3 x y(x)^4 y'(x)+9 y'(x)^2+y(x)^5=0\)
 4.847   \(x y'(x)^2=a\)
 4.848   \(x y'(x)^2=a-x^2\)
 4.849   \(x y'(x)^2=y(x)\)
 4.850   \(x y'(x)^2-2 y(x)+x=0\)
 4.851   \(x y'(x)^2+y'(x)=y(x)\)
 4.852   \(x y'(x)^2+2 y'(x)-y(x)=0\)
 4.853   \(x y'(x)^2-2 y'(x)-y(x)=0\)
 4.854   \(x y'(x)^2+4 y'(x)-2 y(x)=0\)
 4.855   \(x y'(x)^2+x y'(x)-y(x)=0\)
 4.856   \(-\left (x^2+1\right ) y'(x)+x y'(x)^2+x=0\)
 4.857   \(a+x y'(x)^2+y(x) y'(x)=0\)
 4.858   \(a+x y'(x)^2-y(x) y'(x)=0\)
 4.859   \(a x+x y'(x)^2-y(x) y'(x)=0\)
 4.860   \(-x^2+x y'(x)^2+y(x) y'(x)=0\)
 4.861   \(x^3+x y'(x)^2+y(x) y'(x)=0\)
 4.862   \(a y(x)+x y'(x)^2-y(x) y'(x)=0\)
 4.863   \(y(x) y'(x)+x y'(x)^2-y(x)^4=0\)
 4.864   \((a-y(x)) y'(x)+b+x y'(x)^2=0\)
 4.865   \(x y'(x)^2+(x-y(x)) y'(x)-y(x)+1=0\)
 4.866   \((a-y(x)+x) y'(x)+x y'(x)^2-y(x)=0\)
 4.867   \(x y'(x)^2-(3 x-y(x)) y'(x)+y(x)=0\)
 4.868   \(a-b y(x)+b x+x y'(x)^2-y(x)=0\)
 4.869   \(a+x y'(x)^2-2 y(x) y'(x)=0\)
 4.870   \(x y'(x)^2+2 y(x) y'(x)-x=0\)
 4.871   \(a x+x y'(x)^2-2 y(x) y'(x)=0\)
 4.872   \(x y'(x)^2-2 y(x) y'(x)+2 y(x)+x=0\)
 4.873   \(9 x^2+x y'(x)^2-3 y(x) y'(x)=0\)
 4.874   \(x y'(x)^2-(3 y(x)+2 x) y'(x)+6 y(x)=0\)
 4.875   \(-a y(x) y'(x)+b+x y'(x)^2=0\)
 4.876   \(a y(x) y'(x)+b x+x y'(x)^2=0\)
 4.877   \(x y'(x)^2-(x y(x)+1) y'(x)+y(x)=0\)
 4.878   \((1-x) y(x) y'(x)+x y'(x)^2-y(x)^2=0\)
 4.879   \(\left (1-x^2 y(x)\right ) y'(x)+x y'(x)^2-x y(x)=0\)
 4.880   \((x+1) y'(x)^2=y(x)\)
 4.881   \((x+1) y'(x)^2-(y(x)+x) y'(x)+y(x)=0\)
 4.882   \((a-x) y'(x)^2-b+y(x) y'(x)=0\)
 4.883   \((a+x) y'(x)^2+y'(x) (\text{a1}+\text{b1} x+\text{c1} y(x))+\text{a2}+\text{b2} x+\text{c2} y(x)=0\)
 4.884   \(2 x y'(x)^2+(2 x-y(x)) y'(x)-y(x)+1=0\)
 4.885   \(3 x y'(x)^2-6 y(x) y'(x)+2 y(x)+x=0\)
 4.886   \((3 x+1) y'(x)^2-3 (y(x)+2) y'(x)+9=0\)
 4.887   \((3 x+5) y'(x)^2-(3 y(x)+3) y'(x)+y(x)=0\)
 4.888   \(4 x y'(x)^2=(a-3 x)^2\)
 4.889   \(4 x y'(x)^2+2 x y'(x)-y(x)=0\)
 4.890   \(4 x y'(x)^2-3 y(x) y'(x)+3=0\)
 4.891   \(4 x y'(x)^2+4 y(x) y'(x)=1\)
 4.892   \(4 y(x) y'(x)+4 x y'(x)^2-y(x)^4=0\)
 4.893   \(4 (2-x) y'(x)^2+1=0\)
 4.894   \(8 y(x) y'(x)+16 x y'(x)^2+y(x)^6=0\)
 4.895   \(x^2 y'(x)^2=a^2\)
 4.896   \(x^2 y'(x)^2=y(x)^2\)
 4.897   \(x^2 y'(x)^2+x^2-y(x)^2=0\)
 4.898   \(x^2 y'(x)^2=(x-y(x))^2\)
 4.899   \(x^2 y'(x)^2-y(x)^4+y(x)^2=0\)
 4.900   \(x^2 y'(x)^2-x y'(x)+(1-y(x)) y(x)=0\)
 4.901   \(a^2+2 a x y'(x)-2 a y(x)+x^2 y'(x)^2+x^2=0\)
 4.902   \(x^2 y'(x)^2-2 x y(x) y'(x)+y(x) (y(x)+1)-x=0\)
 4.903   \(-x^4+x^2 y'(x)^2+\left (1-x^2\right ) y(x)^2-2 x y(x) y'(x)=0\)
 4.904   \(x^2 y'(x)^2-(2 x y(x)+1) y'(x)+y(x)^2+1=0\)
 4.905   \(-(a+2 x y(x)) y'(x)+x^2 y'(x)^2+y(x)^2=0\)
 4.906   \(x^2 y'(x)^2-x (x-2 y(x)) y'(x)+y(x)^2=0\)
 4.907   \(-4 a+x^2 y'(x)^2+2 x (y(x)+2 x) y'(x)+y(x)^2=0\)
 4.908   \(x \left (x^3-2 y(x)\right ) y'(x)-\left (2 x^3-y(x)\right ) y(x)+x^2 y'(x)^2=0\)
 4.909   \(x^2 y'(x)^2+3 x y(x) y'(x)+2 y(x)^2=0\)
 4.910   \(x^3+x^2 y'(x)^2-3 x y(x) y'(x)+2 y(x)^2=0\)
 4.911   \(x^2 y'(x)^2+4 x y(x) y'(x)-5 y(x)^2=0\)
 4.912   \(x^2 y'(x)^2-4 x (y(x)+2) y'(x)+4 y(x) (y(x)+2)=0\)
 4.913   \(x^2 y'(x)^2-5 x y(x) y'(x)+6 y(x)^2=0\)
 4.914   \(x^2 y'(x)^2+x \left (x^2+x y(x)-2 y(x)\right ) y'(x)+(1-x) \left (x^2-y(x)\right ) y(x)=0\)
 4.915   \(x^2 y'(x)^2+(y(x)+2 x) y(x) y'(x)+y(x)^2=0\)
 4.916   \(x^2 y'(x)^2+(2 x-y(x)) y(x) y'(x)+y(x)^2=0\)
 4.917   \(y'(x) \left (a+b x^2 y(x)^3\right )+a b y(x)^3+x^2 y'(x)^2=0\)
 4.918   \(\left (1-x^2\right ) y'(x)^2=1-y(x)^2\)
 4.919   \(\left (1-x^2\right ) y'(x)^2+4 x^2+2 x y(x) y'(x)=0\)
 4.920   \(\left (a^2+x^2\right ) y'(x)^2=b^2\)
 4.921   \(\left (a^2-x^2\right ) y'(x)^2+b^2=0\)
 4.922   \(\left (a^2-x^2\right ) y'(x)^2=b^2\)
 4.923   \(\left (a^2-x^2\right ) y'(x)^2=x^2\)
 4.924   \(\left (a^2-x^2\right ) y'(x)^2+x^2+2 x y(x) y'(x)=0\)
 4.925   \(\left (a^2-x^2\right ) y'(x)^2-2 x y(x) y'(x)-y(x)^2=0\)
 4.926   \(\left (a^2+x^2\right ) y'(x)^2+b-2 x y(x) y'(x)+y(x)^2=0\)
 4.927   \(\left (2 x^2+1\right ) y'(x)^2+\left (x^2+2 x y(x)+y(x)^2+2\right ) y'(x)+2 y(x)^2+1=0\)
 4.928   \(4 x^2 y'(x)^2-4 x y(x) y'(x)=8 x^3-y(x)^2\)
 4.929   \(a x^2 y'(x)^2+(1-a) a x^2-2 a x y(x) y'(x)+y(x)^2=0\)
 4.930   \(\left (1-a^2\right ) x^2 y'(x)^2-a^2 x^2-2 x y(x) y'(x)+y(x)^2=0\)
 4.931   \(x^3 y'(x)^2=a\)
 4.932   \(x^3 y'(x)^2+x y'(x)-y(x)=0\)
 4.933   \(a+x^3 y'(x)^2+x^2 y(x) y'(x)=0\)
 4.934   \(x^3 y'(x)^2-\left (2 x^2 y(x)+1\right ) y'(x)+x y(x)^2=0\)
 4.935   \(x \left (1-x^2\right ) y'(x)^2-2 \left (1-x^2\right ) y(x) y'(x)+x \left (1-y(x)^2\right )=0\)
 4.936   \(4 x (a-x) (b-x) y'(x)^2=\left (-2 x (a+b)+a b+2 x^2\right )^2\)
 4.937   \(x^4 y'(x)^2-x y'(x)-y(x)=0\)
 4.938   \(x^4 y'(x)^2+2 x^3 y(x) y'(x)-4=0\)
 4.939   \(x^4 y'(x)^2+x y(x)^2 y'(x)-y(x)^3=0\)
 4.940   \(x^2 \left (a^2-x^2\right ) y'(x)^2+1=0\)
 4.941   \(3 x^4 y'(x)^2-x y(x)-y(x)=0\)
 4.942   \(4 x^5 y'(x)^2+12 x^4 y(x) y'(x)+9=0\)
 4.943   \(x^6 y'(x)^2-2 x y'(x)-4 y(x)=0\)
 4.944   \(x^8 y'(x)^2+3 x y'(x)+9 y(x)=0\)
 4.945   \(y(x) y'(x)^2=a\)
 4.946   \(y(x) y'(x)^2=a^2 x\)
 4.947   \(y(x) y'(x)^2=e^{2 x}\)
 4.948   \(2 a x y'(x)-a y(x)+y(x) y'(x)^2=0\)
 4.949   \(-4 a^2 x y'(x)+a^2 y(x)+y(x) y'(x)^2=0\)
 4.950   \(a x y'(x)+b y(x)+y(x) y'(x)^2=0\)
 4.951   \(-(a-2 b x) y'(x)-b y(x)+y(x) y'(x)^2=0\)
 4.952   \(x^3 y'(x)-x^2 y(x)+y(x) y'(x)^2=0\)
 4.953   \(y(x) y'(x)^2+(x-y(x)) y'(x)-x=0\)
 4.954   \(y(x) y'(x)^2-(y(x)+x) y'(x)+y(x)=0\)
 4.955   \(y(x) y'(x)^2-(x y(x)+1) y'(x)+x=0\)
 4.956   \(y(x) y'(x)^2+\left (x-y(x)^2\right ) y'(x)-x y(x)=0\)
 4.957   \(y(x) y'(x)^2+y(x)=a\)
 4.958   \((y(x)+x) y'(x)^2+2 x y'(x)-y(x)=0\)
 4.959   \((2 x-y(x)) y'(x)^2-2 (1-x) y'(x)-y(x)+2=0\)
 4.960   \(2 y(x) y'(x)^2+(5-4 x) y'(x)+2 y(x)=0\)
 4.961   \(4 x^3 y'(x)-4 x^2 y(x)+9 y(x) y'(x)^2=0\)
 4.962   \((1-a y(x)) y'(x)^2=a y(x)\)
 4.963   \(y'(x)^2 (\text{a0}+\text{b0} x+\text{c0} y(x))+y'(x) (\text{a1}+\text{b1} x+\text{c1} y(x))+\text{a2}+\text{b2} x+\text{c2} y(x)=0\)
 4.964   \(\left (x^2-a y(x)\right ) y'(x)^2-2 x y(x) y'(x)=0\)
 4.965   \(x y(x) y'(x)^2+(y(x)+x) y'(x)+1=0\)
 4.966   \(\left (x^2+y(x)^2\right ) y'(x)+x y(x) y'(x)^2+x y(x)=0\)
 4.967   \(\left (x^2-y(x)^2\right ) y'(x)+x y(x) y'(x)^2-x y(x)=0\)
 4.968   \(-\left (x^2-y(x)^2\right ) y'(x)+x y(x) y'(x)^2-x y(x)=0\)
 4.969   \(\left (a+x^2-y(x)^2\right ) y'(x)+x y(x) y'(x)^2-x y(x)=0\)
 4.970   \(-y'(x) \left (a-b x^2+y(x)^2\right )-b x y(x)+x y(x) y'(x)^2=0\)
 4.971   \(\left (3 x^2-2 y(x)^2\right ) y'(x)+x y(x) y'(x)^2-6 x y(x)=0\)
 4.972   \(-2 x y(x) y'(x)+x (x-2 y(x)) y'(x)^2+y(x)^2-2 x y(x)=0\)
 4.973   \(6 x y(x) y'(x)+x (x-2 y(x)) y'(x)^2+y(x)^2-2 x y(x)=0\)
 4.974   \(y(x)^2 y'(x)^2=a^2\)
 4.975   \(-a^2+y(x)^2 y'(x)^2+y(x)^2=0\)
 4.976   \(y(x)^2 y'(x)^2-3 x y'(x)+y(x)=0\)
 4.977   \(-6 x^3 y'(x)+4 x^2 y(x)+y(x)^2 y'(x)^2=0\)
 4.978   \(4 a^2-4 a y(x) y'(x)-4 a x+y(x)^2 y'(x)^2+y(x)^2=0\)
 4.979   \(y(x)^2 y'(x)^2-(x+1) y(x) y'(x)+x=0\)
 4.980   \(x^2+2 x y(x) y'(x)+y(x)^2 y'(x)^2=0\)
 4.981   \(a+y(x)^2 y'(x)^2+2 x y(x) y'(x)-y(x)^2=0\)
 4.982   \(-x^2-2 x y(x) y'(x)+y(x)^2 y'(x)^2+2 y(x)^2=0\)
 4.983   \(a-x^2-2 x y(x) y'(x)+y(x)^2 y'(x)^2+2 y(x)^2=0\)
 4.984   \((a-1) b+a x^2+2 a x y(x) y'(x)+(1-a) y(x)^2+y(x)^2 y'(x)^2=0\)
 4.985   \(\left (1-y(x)^2\right ) y'(x)^2=1\)
 4.986   \(\left (a^2-y(x)^2\right ) y'(x)^2=y(x)^2\)
 4.987   \(\left (a^2-2 a x y(x)+y(x)^2\right ) y'(x)^2+2 a y(x) y'(x)+y(x)^2=0\)
 4.988   \(\left (a^2 x^2-y(x)^2\right ) y'(x)^2+\left (a^2-1\right ) x^2-2 x y(x) y'(x)=0\)
 4.989   \(\left ((1-a) x^2+y(x)^2\right ) y'(x)^2+2 a x y(x) y'(x)+(1-a) y(x)^2+x^2=0\)
 4.990   \(\left (\left (1-4 a^2\right ) x^2+y(x)^2\right ) y'(x)^2-8 a^2 x y(x) y'(x)+\left (1-4 a^2\right ) y(x)^2+x^2=0\)
 4.991   \(\left (\left (1-a^2\right ) x^2+y(x)^2\right ) y'(x)^2+2 a^2 x y(x) y'(x)+\left (1-a^2\right ) y(x)^2+x^2=0\)
 4.992   \((y(x)+x)^2 y'(x)^2=y(x)^2\)
 4.993   \(-\left (x^2-x y(x)-2 y(x)^2\right ) y'(x)+(y(x)+x)^2 y'(x)^2-(x-y(x)) y(x)=0\)
 4.994   \(2 a^2 y'(x)+\left (a^2-(x-y(x))^2\right ) y'(x)^2+a^2-(x-y(x))^2=0\)
 4.995   \(x^2+2 x y(x) y'(x)+2 y(x)^2 y'(x)^2+y(x)^2-1=0\)
 4.996   \(-x^2-2 x y(x) y'(x)+3 y(x)^2 y'(x)^2+4 y(x)^2=0\)
 4.997   \(3 x^3+2 (3 x+1) x y(x) y'(x)+4 y(x)^2 y'(x)^2=0\)
 4.998   \(\left (x^2-4 y(x)^2\right ) y'(x)^2-4 x^2+6 x y(x) y'(x)+y(x)^2=0\)
 4.999   \(9 y(x)^2 y'(x)^2-3 x y'(x)+y(x)=0\)
 4.1000   \((2-3 y(x))^2 y'(x)^2=4 (1-y(x))\)
 4.1001   \(a^2 \left (-x^2\right )-3 a^2 x y(x) y'(x)+\left (1-a^2\right ) y(x)^2 y'(x)^2+y(x)^2=0\)
 4.1002   \((a-b) y(x)^2 y'(x)^2-a b+a y(x)^2-b x^2-2 b x y(x) y'(x)=0\)
 4.1003   \(a^2 y'(x)^2 \left (b^2-(c x-a y(x))^2\right )+c^2 \left (b^2-(c x-a y(x))^2\right )+2 a b^2 c y'(x)=0\)
 4.1004   \(a^2 x+y(x)^3 \left (-y'(x)\right )+x y(x)^2 y'(x)^2=0\)
 4.1005   \(\left (a-x^3-y(x)^3\right ) y'(x)+x^2 y(x)+x y(x)^2 y'(x)^2=0\)
 4.1006   \(-x \left (x^2-2 y(x)^2\right )-2 y(x)^3 y'(x)+x y(x)^2 y'(x)^2=0\)
 4.1007   \(-a+y(x)^3 \left (-y'(x)\right )+2 x y(x)^2 y'(x)^2=0\)
 4.1008   \(4 x^2 y(x)^2 y'(x)^2=\left (x^2+y(x)^2\right )^2\)
 4.1009   \(-2 x \left (x^3+2 y(x)^2\right ) y(x) y'(x)+\left (2 x^3+y(x)^2\right ) y(x)^2+4 x^2 y(x)^2 y'(x)^2=0\)
 4.1010   \(4 y(x)^3 y'(x)^2-4 x y'(x)+y(x)=0\)
 4.1011   \(x y(x) \left (x^2+y(x)^2\right ) y'(x)^2-x y(x) \left (x^2+y(x)^2\right )-\left (x^4+x^2 y(x)^2+y(x)^4\right ) y'(x)=0\)
 4.1012   \(x \left (a^2 x+y(x) \left (x^2-y(x)^2\right )\right ) y'(x)^2+\left (2 a^2 x y(x)+\left (x^2-y(x)^2\right )^2\right ) y'(x)+a^2 y(x)^2-x \left (x^2-y(x)^2\right ) y(x)=0\)
 4.1013   \(x \left (a^2 x+y(x) \left (x^2-y(x)^2\right )\right ) y'(x)^2-\left (2 a^2 x y(x)-\left (x^2-y(x)^2\right )^2\right ) y'(x)+a^2 y(x)^2-x \left (x^2-y(x)^2\right ) y(x)=0\)
 4.1014   \(\left (x^2-y(x)^2 \left (x^2+y(x)^2\right )\right ) y'(x)^2-2 x y(x) y'(x)+y(x)^2=0\)
 4.1015   \(-2 x \left (x^2+2 y(x)^2\right ) y(x) y'(x)+\left (x^4+y(x)^2 \left (x^2-y(x)^2\right )\right ) y'(x)^2+y(x)^4=0\)
 4.1016   \(y(x)^5 \left (-y'(x)\right )+3 x y(x)^4 y'(x)^2+1=0\)
 4.1017   \(-a-3 y(x)^5 y'(x)+9 x y(x)^4 y'(x)^2=0\)
 4.1018   \(9 \left (1-x^2\right ) y(x)^4 y'(x)^2+4 x^2+6 x y(x)^5 y'(x)=0\)
 4.1019   \(y'(x)^2 \left (a^2 r(x,y(x))-x^2\right )+a^2 r(x,y(x))+2 x y(x) y'(x)-y(x)^2=0\)
 4.1020   \(y'(x)^2 \left (a r(x,y(x))-x^2\right )+a r(x,y(x))+2 x y(x) y'(x)-y(x)^2=0\)
 4.1021   \(y'(x)^3=a+b x\)
 4.1022   \(y'(x)^3=a x^n\)
 4.1023   \(y'(x)^3-y(x)+x=0\)
 4.1024   \(y'(x)^3=f(x) \left (a+b y(x)+c y(x)^2\right )\)
 4.1025   \(y'(x)^3=(y(x)-a)^2 (y(x)-b)^2\)
 4.1026   \(f(x) (y(x)-a)^2 (y(x)-b)^2+y'(x)^3=0\)
 4.1027   \(f(x) (y(x)-a)^2 (y(x)-b)^2 (y(x)-c)^2+y'(x)^3=0\)
 4.1028   \(a-b x+y'(x)^3+y'(x)=0\)
 4.1029   \(y'(x)^3+y'(x)-y(x)=0\)
 4.1030   \(y'(x)^3+y'(x)=e^{y(x)}\)
 4.1031   \(y'(x)^3-7 y'(x)+6=0\)
 4.1032   \(a y(x)+y'(x)^3-x y'(x)=0\)
 4.1033   \(y'(x)^3+2 x y'(x)-y(x)=0\)
 4.1034   \(y'(x)^3-2 x y'(x)-y(x)=0\)
 4.1035   \(-a x y'(x)+x^3+y'(x)^3=0\)
 4.1036   \(a x y'(x)-a y(x)+y'(x)^3=0\)
 4.1037   \(-(a+b x) y'(x)+b y(x)+y'(x)^3=0\)
 4.1038   \(y'(x)^3-y(x) y'(x)-x=0\)
 4.1039   \(y'(x)^3-(y(x)+3) y'(x)+x=0\)
 4.1040   \(y'(x)^3-2 y(x) y'(x)+y(x)^2=0\)
 4.1041   \(-a x y(x) y'(x)+2 a y(x)^2+y'(x)^3=0\)
 4.1042   \(-\left (x^3+x y(x)+y(x)^2\right ) y'(x)+y'(x)^3+x y(x) (y(x)+x)=0\)
 4.1043   \(-x y(x)^4 y'(x)+y'(x)^3-y(x)^5=0\)
 4.1044   \(y'(x)^3+e^{3 x-2 y(x)} \left (y'(x)-1\right )=0\)
 4.1045   \(y'(x)^3+\left (e^{2 x}+e^{3 x}\right ) e^{-2 y(x)} y'(x)-e^{3 x-2 y(x)}=0\)
 4.1046   \(y'(x)^3+y'(x)^2-y(x)=0\)
 4.1047   \(y'(x)^3-y'(x)^2+y(x)^2=0\)
 4.1048   \(y'(x)^3-y'(x)^2+x y'(x)-y(x)=0\)
 4.1049   \(a b x-a y'(x)^2+b y(x)+y'(x)^3=0\)
 4.1050   \(\text{a0} y'(x)^2+\text{a1} y'(x)+\text{a2}+\text{a3} y(x)+y'(x)^3=0\)
 4.1051   \(y'(x)^3+x y'(x)^2-y(x)=0\)
 4.1052   \(-x^3-(1-3 x) x y'(x)+y'(x)^3+(1-3 x) y'(x)^2-1=0\)
 4.1053   \(y'(x)^3-y(x) y'(x)^2+y(x)^2=0\)
 4.1054   \(y'(x)^3+y'(x)^2 (\cos (x) \cot (x)-y(x))-y'(x) (y(x) \cos (x) \cot (x)+1)+y(x)=0\)
 4.1055   \(y'(x)^3+\left (2 x-y(x)^2\right ) y'(x)^2-2 x y(x)^2 y'(x)=0\)
 4.1056   \(\left (x^2+2 x y(x)^2-y(x)^2\right ) y'(x)-y(x)^2 \left (x^2-y(x)^2\right )+y'(x)^3-\left (y(x)^2+2 x\right ) y'(x)^2=0\)
 4.1057   \(-x^3 y(x)^3+x \left (x^2+x y(x)+y(x)^2\right ) y(x) y'(x)-\left (x^2+x y(x)+y(x)^2\right ) y'(x)^2+y'(x)^3=0\)
 4.1058   \(-x^3 y(x)^6+x \left (x^2+y(x)^4+x y(x)^2\right ) y(x)^2 y'(x)-\left (x^2+y(x)^4+x y(x)^2\right ) y'(x)^2+y'(x)^3=0\)
 4.1059   \(2 y'(x)^3+x y'(x)-2 y(x)=0\)
 4.1060   \(2 y'(x)^3+y'(x)^2-y(x)=0\)
 4.1061   \(x^4 \left (-y'(x)\right )+2 x^3 y(x)+3 y'(x)^3=0\)
 4.1062   \(4 y'(x)^3+4 y'(x)=x\)
 4.1063   \(8 y'(x)^3+12 y'(x)^2=27 (y(x)+x)\)
 4.1064   \(a+x y'(x)^3-y(x) y'(x)^2=0\)
 4.1065   \(x y'(x)^3+(2 x-y(x)) y'(x)^2+(2-2 y(x)) y'(x)-y(x)+1=0\)
 4.1066   \(-\left (x^2+y(x)+x\right ) y'(x)^2+\left (x^2+x y(x)+y(x)\right ) y'(x)+x y'(x)^3-x y(x)=0\)
 4.1067   \(4 x^2+x y'(x)^3-2 y(x) y'(x)^2=0\)
 4.1068   \(2 x y'(x)^3-3 y(x) y'(x)^2-x=0\)
 4.1069   \(4 x y'(x)^3-6 y(x) y'(x)^2+3 y(x)-x=0\)
 4.1070   \(8 x y'(x)^3-12 y(x) y'(x)^2+9 y(x)=0\)
 4.1071   \(x^2 y'(x)^3-2 x y(x) y'(x)^2+y(x)^2 y'(x)+1=0\)
 4.1072   \(b x \left (a^2-x^2\right ) y'(x)^2+\left (a^2-x^2\right ) y'(x)^3-b x-y'(x)=0\)
 4.1073   \(x \left (x^5+3 y(x)^2\right ) y'(x)-2 x^5 y(x)-3 x^2 y(x) y'(x)^2+x y'(x)^3-y(x)^3=0\)
 4.1074   \(2 x^3 y'(x)^3+6 x^2 y(x) y'(x)^2-(1-6 x y(x)) y(x) y'(x)+2 y(x)^3=0\)
 4.1075   \(8 x^3 y'(x)^3+12 x^2 y(x) y'(x)^2-\left (1-6 x y(x)^2\right ) y'(x)+y(x)^3=0\)
 4.1076   \(x^4 y'(x)^3-x^3 y(x) y'(x)^2-x^2 y(x)^2 y'(x)+x y(x)^3=1\)
 4.1077   \(x^6 y'(x)^3-x y'(x)-y(x)=0\)
 4.1078   \(y(x) y'(x)^3-3 x y'(x)+3 y(x)=0\)
 4.1079   \(2 y(x) y'(x)^3-3 x y'(x)+2 y(x)=0\)
 4.1080   \(2 y(x) y'(x)^3+3 y(x) y'(x)+x=0\)
 4.1081   \(2 y(x) y'(x)^3-y(x) y'(x)^2+2 x y'(x)-x=0\)
 4.1082   \((2 y(x)+x) y'(x)^3+3 (y(x)+x) y'(x)^2+(y(x)+2 x) y'(x)=0\)
 4.1083   \(y(x)^2 y'(x)^3-x y'(x)+y(x)=0\)
 4.1084   \(y(x)^2 y'(x)^3+2 x y'(x)-y(x)=0\)
 4.1085   \(4 y(x)^2 y'(x)^3-2 x y'(x)+y(x)=0\)
 4.1086   \(16 y(x)^2 y'(x)^3+2 x y'(x)-y(x)=0\)
 4.1087   \(x \left (x^2+1\right ) y'(x)-x^2 y(x)+y(x)^3 \left (-y'(x)^2\right )+x y(x)^2 y'(x)^3=0\)
 4.1088   \(x^7 y(x)^2 y'(x)^3+\left (1-3 x^6 y(x)^3\right ) y'(x)^2+3 x^5 y(x)^4 y'(x)-x^4 y(x)^5=0\)
 4.1089   \(y(x)^3 y'(x)^3-x y'(x)+y(x)=0\)
 4.1090   \(x^3+3 x^2 y(x) y'(x)+y(x)^3 y'(x)^3-(1-3 x) y(x)^2 y'(x)^2-y(x)^2=0\)
 4.1091   \(y(x)^4 y'(x)^3-6 x y'(x)+2 y(x)=0\)
 4.1092   \(y'(x)^4=(y(x)-a)^3 (y(x)-b)^2\)
 4.1093   \(f(x) (y(x)-a)^3 (y(x)-b)^2+y'(x)^4=0\)
 4.1094   \(f(x) (y(x)-a)^3 (y(x)-b)^3+y'(x)^4=0\)
 4.1095   \(f(x) (y(x)-a)^3 (y(x)-b)^3 (y(x)-c)^2+y'(x)^4=0\)
 4.1096   \(y'(x)^4+x y'(x)-3 y(x)=0\)
 4.1097   \(y'(x)^4-3 (1-x) y'(x)^2+3 (1-2 y(x)) y'(x)+3 x=0\)
 4.1098   \(-4 x^2 y(x) y'(x)^2+y'(x)^4+16 x y(x)^2 y'(x)-16 y(x)^3=0\)
 4.1099   \(y'(x)^4+4 y(x) y'(x)^3+6 y(x)^2 y'(x)^2-\left (1-4 y(x)^3\right ) y'(x)-y(x) \left (3-y(x)^3\right )=0\)
 4.1100   \(2 y'(x)^4-y(x) y'(x)-2=0\)
 4.1101   \(12 x^3+x y'(x)^4-2 y(x) y'(x)^3=0\)
 4.1102   \(a y'(x)^3+b y'(x)^2+y'(x)^5=c y(x)\)
 4.1103   \(a y'(x)^4+b y'(x)^3+c x y'(x)^2+y'(x)^5=c y(x)\)
 4.1104   \(3 y'(x)^5-y(x) y'(x)+1=0\)
 4.1105   \(y'(x)^6=(y(x)-a)^4 (y(x)-b)^3\)
 4.1106   \(f(x) (y(x)-a)^4 (y(x)-b)^3+y'(x)^6=0\)
 4.1107   \(f(x) (y(x)-a)^5 (y(x)-b)^3+y'(x)^6=0\)
 4.1108   \(f(x) (y(x)-a)^5 (y(x)-b)^4+y'(x)^6=0\)
 4.1109   \(f(x) (y(x)-a)^5 (y(x)-b)^4 (y(x)-c)^3+y'(x)^6=0\)
 4.1110   \(x^2 \left (y'(x)^6+3 y(x)^4+3 y(x)^2+1\right )=a^2\)
 4.1111   \(y'(x)^n=a x^r+b y'(x)^s\)
 4.1112   \(y'(x)^n=f(x)^n (y(x)-a)^{n+1} (y(x)-b)^{n-1}\)
 4.1113   \(y'(x)^n=f(x) (y(x)-a)^{n+1}\)
 4.1114   \(y'(x)^n=f(x) (y(x)-a)^{n-1} (y(x)-b)^{n-1}\)
 4.1115   \(f(x) g(x)+y'(x)^n=0\)
 4.1116   \(f(x,y(x))+y'(x)^n=0\)
 4.1117   \(a y'(x)+y'(x)^n=b y(x)\)
 4.1118   \(y'(x)^n+x y'(x)-y(x)=0\)
 4.1119   \(a y'(x)^m+y'(x)^n=b y(x)\)
 4.1120   \(\text{Y1}(y(x)) y'(x)^{n-1}+y'(x)^n=0\)
 4.1121   \(\text{X1}(x,y(x)) y'(x)^{n-1}+y'(x)^n=0\)
 4.1122   \(x^{n-1} y'(x)^n-n x y'(x)+y(x)=0\)
 4.1123   \(\text{X0}(x,y(x)) y'(x)^n+\text{X1}(x,y(x)) y'(x)^{n-1}=0\)
 4.1124   \(2 \sqrt{a y'(x)}+x y'(x)-y(x)=0\)
 4.1125   \((x-y(x)) \sqrt{y'(x)}=a \left (y'(x)+1\right )\)
 4.1126   \(3 x y'(x)+2 (y(x)+1)^{3/2}-3 y(x)=0\)
 4.1127   \(a y'(x)+\sqrt{y'(x)^2+1}=x\)
 4.1128   \(a y'(x)+\sqrt{y'(x)^2+1}=y(x)\)
 4.1129   \(\sqrt{y'(x)^2+1}=x y'(x)\)
 4.1130   \(-a y(x) y'(x)-a x+\sqrt{y'(x)^2+1}=0\)
 4.1131   \(-x y'(x)^2+\sqrt{y'(x)^2+1}+y(x)=0\)
 4.1132   \(\sqrt{a^2+b^2 y'(x)^2}+x y'(x)-y(x)=0\)
 4.1133   \(\sqrt{a c-b^2} \left (x y'(x)-y(x)\right )+\sqrt{a+2 b y'(x)+c y'(x)^2}=0\)
 4.1134   \(a \sqrt{y'(x)^2+1}+x y'(x)-y(x)=0\)
 4.1135   \(a x \sqrt{y'(x)^2+1}+x y'(x)-y(x)=0\)
 4.1136   \(-a y(x) y'(x)-a x+y(x) \sqrt{y'(x)^2+1}=0\)
 4.1137   \(y(x) \sqrt{y'(x)^2+1}=f\left (y(x) y'(x)+x\right )\)
 4.1138   \(\sqrt{\left (a x^2+y(x)^2\right ) \left (y'(x)^2+1\right )}-a x-y(x) y'(x)=0\)
 4.1139   \(a \sqrt [3]{y'(x)^3+1}+x y'(x)-y(x)=0\)
 4.1140   \(y'(x) \left (a+x \sqrt{y'(x)^2+1}\right )=y(x) \sqrt{y'(x)^2+1}\)
 4.1141   \(x y'(x)+\cos \left (y'(x)\right )=y(x)\)
 4.1142   \(a \cos \left (y'(x)\right )+b y'(x)+x=0\)
 4.1143   \(y'(x)+\sin \left (y'(x)\right )=x\)
 4.1144   \(y'(x) \sin \left (y'(x)\right )+\cos \left (y'(x)\right )=y(x)\)
 4.1145   \(y'(x)^2 \sin \left (y'(x)\right )=y(x)\)
 4.1146   \(y'(x)^2 \left (\sin \left (y'(x)\right )+x\right )=y(x)\)
 4.1147   \(\left (y'(x)^2+1\right ) \sin ^2\left (y(x)-x y'(x)\right )=1\)
 4.1148   \(-\sqrt{1-y'(x)^2}+y'(x) \left (\cos ^{-1}\left (y'(x)\right )-x\right )+y(x)=0\)
 4.1149   \(\left (y'(x)^2+1\right ) \left (a x+\tan ^{-1}\left (y'(x)\right )\right )+y'(x)=0\)
 4.1150   \(-y'(x)^2+e^{y'(x)-y(x)}+1=0\)
 4.1151   \(y'(x)+\log \left (y'(x)\right )=x\)
 4.1152   \(a+x y'(x)+\log \left (y'(x)\right )=0\)
 4.1153   \(a+x y'(x)+\log \left (y'(x)\right )=y(x)\)
 4.1154   \(a+b y(x)+x y'(x)+\log \left (y'(x)\right )=0\)
 4.1155   \(4 x y'(x)+\log \left (y'(x)\right )-2 y(x)=0\)
 4.1156   \(a \left (x y'(x)-y(x)\right )+\log \left (y'(x)\right )=0\)
 4.1157   \(a \left (\log \left (y'(x)\right )-y'(x)\right )+y(x)-x=0\)
 4.1158   \(y'(x)+y(x) \log \left (y'(x)\right )-x y(x)-y(x) \log (y(x))=0\)
 4.1159   \(-(x+1) y'(x)+y'(x) \log \left (y'(x)\right )+y(x)=0\)
 4.1160   \(\log \left (x y'(x)-y(x)\right )=y'(x)\)
 4.1161   \(y'(x) \log \left (\sqrt{a+y'(x)^2}+y'(x)\right )-x y'(x)-\sqrt{y'(x)^2+1}+y(x)=0\)
 4.1162   \(y'(x) \tan \left (y'(x)\right )+\log \left (\cos \left (y'(x)\right )\right )=y(x)\)
 4.1163   \(f\left (y'(x)\right )=0\)
 4.1164   \(f\left (x,y'(x)\right )=0\)
 4.1165   \(f\left (x y'(x)^2\right )=y(x)-2 x y'(x)\)
 4.1166   \(f\left (y(x),y'(x)\right )=0\)
 4.1167   \(f\left (y'(x)\right )+x y'(x)=y(x)\)
 4.1168   \(f\left (y'(x)\right )+x g\left (y'(x)\right )=y(x)\)
 4.1169   \(f\left (y'(x),y(x)-x y'(x)\right )=0\)
 4.1170   \(f\left (x y'(x),y(x)\right )=0\)
 4.1171   \(x^n f\left (y'(x),\frac{y(x)}{x}\right )=0\)
 4.1172   \(f\left (y(x) y'(x)+x\right )=y(x)^2 \left (y'(x)^2+1\right )\)
 4.1173   \(y(x) f\left (\frac{y'(x)}{y(x)},x\right )=0\)
 4.1174   \(f\left (x,y(x),y'(x)\right )=0\)
 4.1175   \(y''(x)=0\)
 4.1176   \(y''(x)=x+\sin (x)\)
 4.1177   \(y''(x)=\text{c1} \cos (a x)+\text{c2} \sin (b x)\)
 4.1178   \(y''(x)=e^x x\)
 4.1179   \(y''(x)=\text{c1} e^{a x}+\text{c2} e^{-b x}\)
 4.1180   \(y''(x)+y(x)=0\)
 4.1181   \(y''(x)-y(x)=0\)
 4.1182   \(y''(x)+y(x)=a x\)
 4.1183   \(y''(x)+y(x)=a \cos (b x)\)
 4.1184   \(y''(x)+y(x)=8 \cos (x) \cos (2 x)\)
 4.1185   \(y''(x)+y(x)=\sec (x)\)
 4.1186   \(y''(x)+y(x)=a \sin (b x)\)
 4.1187   \(y''(x)+y(x)=\sin (a x) \sin (b x)\)
 4.1188   \(y''(x)+y(x)=4 x \sin (x)\)
 4.1189   \(y''(x)+y(x)=x (\cos (x)-x \sin (x))\)
 4.1190   \(y''(x)+y(x)=\tan ^2(x)\)
 4.1191   \(y''(x)+y(x)=e^{-x}\)
 4.1192   \(y''(x)+y(x)=e^x \left (x^2-1\right )\)
 4.1193   \(y''(x)+y(x)=e^x \sin (2 x)\)
 4.1194   \(y''(x)+y(x)=e^{2 x} \cos (x)\)
 4.1195   \(y''(x)-2 y(x)=0\)
 4.1196   \(y''(x)-2 y(x)=4 e^{x^2} x^2\)
 4.1197   \(y''(x)+4 y(x)=0\)
 4.1198   \(y''(x)+4 y(x)=x \sin ^2(x)\)
 4.1199   \(y''(x)+4 y(x)=2 \tan (x)\)
 4.1200   \(y''(x)+4 y(x)=2 \tan (x)\)
 4.1201   \(y''(x)-a^2 y(x)=x+1\)
 4.1202   \(y''(x)=a x+b y(x)\)
 4.1203   \(a^2 y(x)+y''(x)=x^2+x+1\)
 4.1204   \(a^2 y(x)+y''(x)=\cos (b x)\)
 4.1205   \(a^2 y(x)+y''(x)=\cot (a x)\)
 4.1206   \(a^2 y(x)+y''(x)=\sin (b x)\)
 4.1207   \(y''(x)+x y(x)=0\)
 4.1208   \(y(x) (a+b x)+y''(x)=0\)
 4.1209   \(\left (a+x^2\right ) y(x)+y''(x)=0\)
 4.1210   \(\left (a-x^2\right ) y(x)+y''(x)=0\)
 4.1211   \(y''(x)=\left (a+x^2\right ) y(x)\)
 4.1212   \(y(x) \left (a+b^2 x^2\right )+y''(x)=0\)
 4.1213   \(y(x) \left (a+b x+c x^2\right )+y''(x)=0\)
 4.1214   \(y(x) \left (\text{a0}+\text{a1} x^2+x^4\right )+y''(x)=0\)
 4.1215   \(a x^k y(x)+y''(x)=0\)
 4.1216   \(y(x) \left (\text{a0}+\text{a1} x+\text{a2} x^2+\text{a3} x^3+\text{a4} x^4+x^8\right )+y''(x)=0\)
 4.1217   \(y(x) (a+b \cos (2 x))+y''(x)=0\)
 4.1218   \(y(x) (a+b \cos (2 x)+k \cos (4 x))+y''(x)=0\)
 4.1219   \(y(x) \left (\DOTSB \sum@ \slimits@ _{n=0}^m a(n) \cos (2 n x)\right )+y''(x)=0\)
 4.1220   \(y''(x)=2 y(x) \csc ^2(x)\)
 4.1221   \(a y(x) \csc ^2(x)+y''(x)=0\)
 4.1222   \(y(x) \left (\text{a0}+\text{a1} \cos ^2(x)+\text{a2} \csc ^2(x)\right )+y''(x)=0\)
 4.1223   \(y''(x)=y(x) \left (a^2+(p-1) p \csc ^2(x)+(q-1) q \sec ^2(x)\right )\)
 4.1224   \(y(x) \left (a+b \sin ^2(x)\right )+y''(x)=0\)
 4.1225   \(y''(x)=y(x) \left (2 \tan ^2(x)+1\right )\)
 4.1226   \(y''(x)-y(x) \left (a^2-b e^x\right )=0\)
 4.1227   \(y''(x)-\left (a^2-e^{2 x}\right ) y(x)=0\)
 4.1228   \(y(x) \left (a+b e^x+c e^{2 x}\right )+y''(x)=0\)
 4.1229   \(a e^{b x} y(x)+y''(x)=0\)
 4.1230   \(y(x) \left (a+b \cosh ^2(x)\right )+y''(x)=0\)
 4.1231   \(y(x) \left (a+b \sinh ^2(x)\right )+y''(x)=0\)
 4.1232   \(y(x) \left (a+b \sin ^2(x)\right )+y''(x)=0\)
 4.1233   \(\frac{(a+b) y(x)}{x^2}+y''(x)=0\)
 4.1234   \(y''(x)-y'(x)+x y(x)=0\)
 4.1235   \(y''(x)+2 y'(x)+y(x)=0\)
 4.1236   \(y''(x)-2 y'(x)+y(x)=(x-6) x^2\)
 4.1237   \(y''(x)-2 y'(x)+y(x)=e^x\)
 4.1238   \(y''(x)-2 y'(x)+y(x)=e^x \left (3 x^2+2 x+1\right )\)
 4.1239   \(y''(x)-2 y'(x)+y(x)=e^x \sin (x)\)
 4.1240   \(y''(x)+2 y'(x)+y(x)=x^2+3 e^{2 x}-\cos (x)\)
 4.1241   \(y''(x)-2 y'(x)+y(x)=8 e^{3 x} x^2\)
 4.1242   \(y''(x)-2 y'(x)+y(x)=50 \cos (x) \cosh (x)\)
 4.1243   \(y''(x)+2 y'(x)+3 y(x)=0\)
 4.1244   \(y''(x)+2 y'(x)+y(x)=e^{-x} \cos (x)\)
 4.1245   \(y''(x)+2 y'(x)+5 y(x)=0\)
 4.1246   \(y''(x)+2 y'(x)+5 y(x)=8 \sinh (x)\)
 4.1247   \(-2 \tan (a) y'(x)+\csc ^2(a) y(x)+y''(x)=0\)
 4.1248   \(-2 \tan (a) y'(x)+\csc ^2(a) y(x)+y''(x)=x^2 e^{x \tan (a)}\)
 4.1249   \(y''(x)+3 y'(x)+2 y(x)=0\)
 4.1250   \(y''(x)+3 y'(x)+2 y(x)=\cos (a x)\)
 4.1251   \(y''(x)+3 y'(x)+2 y(x)=e^x+\sin (x)\)
 4.1252   \(y''(x)-3 y'(x)+2 y(x)=x^2+2 e^{-x}\)
 4.1253   \(y''(x)-3 y'(x)+2 y(x)=x e^{a x}\)
 4.1254   \(y''(x)-3 y'(x)-4 y(x)=0\)
 4.1255   \(y''(x)-3 y'(x)-4 y(x)=10 \cos (2 x)\)
 4.1256   \(y''(x)-4 y'(x)+4 y(x)=0\)
 4.1257   \(y''(x)-4 y'(x)+4 y(x)=e^{2 x} \cos ^2(x)\)
 4.1258   \(y''(x)+4 y'(x)+5 y(x)=0\)
 4.1259   \(y''(x)+4 y'(x)+5 y(x)=\sin (x)\)
 4.1260   \(y''(x)-4 y'(x)+13 y(x)=0\)
 4.1261   \(y''(x)-5 y'(x)+6 y(x)=0\)
 4.1262   \(y''(x)-5 y'(x)+6 y(x)=4 e^x x^2\)
 4.1263   \(y''(x)-5 y'(x)+6 y(x)=e^{a x}\)
 4.1264   \(y''(x)+6 y'(x)+9 y(x)=0\)
 4.1265   \(y''(x)+6 y'(x)+9 y(x)=e^{-3 x} \cosh (x)\)
 4.1266   \(y''(x)-7 y'(x)+12 y(x)=0\)
 4.1267   \(y''(x)-7 y'(x)+12 y(x)=x\)
 4.1268   \(y''(x)+8 y'(x)+16 y(x)=0\)
 4.1269   \(y''(x)+8 y'(x)+16 y(x)=4 e^x-e^{2 x}\)
 4.1270   \(y''(x)-9 y'(x)+20 y(x)=0\)
 4.1271   \(y''(x)-9 y'(x)+20 y(x)=e^{3 x} x^2\)
 4.1272   \(2 a y'(x)+b^2 y(x)+y''(x)=0\)
 4.1273   \(2 a y'(x)+b^2 y(x)+y''(x)=c \sin (k x)\)
 4.1274   \(a^2 y(x)-2 a y'(x)+y''(x)=e^x\)
 4.1275   \(\left (a^2+b^2\right )^2 y(x)-4 a b y'(x)+y''(x)=0\)
 4.1276   \(a y'(x)+b y(x)+y''(x)=0\)
 4.1277   \(a y'(x)+b y(x)+y''(x)=f(x)\)
 4.1278   \(a y'(x)+y(x) (b+c x)+y''(x)=0\)
 4.1279   \(a y'(x)+y(x) \left (b+c x^2\right )+y''(x)=0\)
 4.1280   \(a y'(x)+y(x) \left (b+c e^x\right )+y''(x)=0\)
 4.1281   \(b e^{2 a x} y(x)+a y'(x)+y''(x)=0\)
 4.1282   \(a y'(x)+b e^{k x} y(x)+y''(x)=0\)
 4.1283   \(y''(x)+x y'(x)+y(x)=0\)
 4.1284   \(y''(x)+x y'(x)-y(x)=0\)
 4.1285   \(y''(x)-x y'(x)+2 y(x)=0\)
 4.1286   \(n y(x)+y''(x)-x y'(x)=0\)
 4.1287   \(-a y(x)+y''(x)-x y'(x)=0\)
 4.1288   \(y''(x)-x y'(x)-(1-x) y(x)=0\)
 4.1289   \(y''(x)-2 x y'(x)+6 y(x)=0\)
 4.1290   \(y''(x)+2 x y'(x)-8 y(x)=0\)
 4.1291   \(2 n y(x)+y''(x)-2 x y'(x)=0\)
 4.1292   \(-\left (-x^2-x+1\right ) y(x)+y''(x)-(2 x+1) y'(x)=0\)
 4.1293   \(2 \left (2 x^2+1\right ) y(x)+y''(x)+4 x y'(x)=0\)
 4.1294   \(-\left (3-4 x^2\right ) y(x)+y''(x)-4 x y'(x)=0\)
 4.1295   \(-\left (3-4 x^2\right ) y(x)+y''(x)-4 x y'(x)=e^{x^2}\)
 4.1296   \(a^2 x^2 y(x)-2 a x y'(x)+y''(x)=0\)
 4.1297   \(a x y'(x)+b y(x)+y''(x)=0\)
 4.1298   \((a+b x) y'(x)+c y(x)+y''(x)=0\)
 4.1299   \((\text{a0}+\text{b0} x) y'(x)+y(x) (\text{a1}+\text{b1} x)+y''(x)=0\)
 4.1300   \((\text{a0}+\text{b0} x) y'(x)+y(x) \left (\text{a1}+\text{b1} x+\text{c1} x^2\right )+y''(x)=0\)
 4.1301   \(-2 a \left (1-2 a x^2\right ) y(x)-4 a x y'(x)+y''(x)=0\)
 4.1302   \(x^2 \left (-y'(x)\right )+y''(x)+x y(x)=0\)
 4.1303   \(x^2 \left (-y'(x)\right )+y''(x)+x y(x)=x\)
 4.1304   \(x^2 y'(x)+y''(x)-4 x y(x)=0\)
 4.1305   \(x^4 y'(x)-x^3 y(x)+y''(x)=0\)
 4.1306   \(a (k+1) x^{k-1} y(x)+a x^k y'(x)+y''(x)=0\)
 4.1307   \(a k x^{k-1} y(x)+a x^k y'(x)+y''(x)=0\)
 4.1308   \(-a x^{k-1} y(x)+a x^k y'(x)+y''(x)=0\)
 4.1309   \(a x^k y'(x)+b x^{k-1} y(x)+y''(x)=0\)
 4.1310   \(y''(x)-\cot (x) y'(x)+2 y(x)=0\)
 4.1311   \(k (k+1) y(x)+y''(x)+\cot (x) y'(x)=0\)
 4.1312   \(y''(x)+\cot (x) y'(x)-y(x) \csc ^2(x)=0\)
 4.1313   \(y(x) \left (p (p+1)-k^2 \csc ^2(x)\right )+y''(x)+\cot (x) y'(x)=0\)
 4.1314   \(y(x) \left (\text{a0}+4 \text{a1} \sin ^2(x)-\text{a2} \csc ^2(x)\right )+y''(x)+\cot (x) y'(x)=0\)
 4.1315   \(y''(x)+2 \cot (x) y'(x)+3 y(x)=0\)
 4.1316   \(y''(x)+2 \cot (x) y'(x)+3 y(x)=e^x \csc (x)\)
 4.1317   \(a \cot (x) y'(x)+y(x) \left (b+k^2 \cos ^2(x)\right )+y''(x)=0\)
 4.1318   \(y(x) \left (a \cot ^2(x)+b \cot (x) \csc (x)+c \csc ^2(x)\right )+k \cot (x) y'(x)+y''(x)=0\)
 4.1319   \(y''(x)-\cot (2 x) y'(x)+2 y(x)=0\)
 4.1320   \(a y(x) \tan ^2(x)+y''(x)-2 \cot (2 x) y'(x)=0\)
 4.1321   \(a \cot (b x) y'(x)+c y(x)+y''(x)=0\)
 4.1322   \(\left (b^2-a^2\right ) y(x)+2 a \cot (a x) y'(x)+y''(x)=0\)
 4.1323   \(a y(x) \tan ^2\left (\frac{x}{2}\right )+y''(x)-\csc (x) y'(x)=0\)
 4.1324   \(y''(x)+y'(x) (\cot (x)+\csc (x))=a \csc (x)+1\)
 4.1325   \(y''(x)-\csc (2 x) y'(x)+y(x) \left (\sin ^2(x)+2\right ) \csc ^2(x)=0\)
 4.1326   \(a y(x) \csc ^2(x)+y''(x)+(\cos (x)+2) \csc (x) y'(x)=0\)
 4.1327   \(y''(x)-(3 \cos (x)+2) \csc (x) y'(x)-2 y(x) (\cos (x)+1) \sec (x)=0\)
 4.1328   \(y''(x)-y'(x) (\cot (x)-\sin (x))+y(x) \sin ^2(x)=0\)
 4.1329   \(y''(x)-\sin (x) y'(x)+y(x) (-\cos (x))=a-x+x \log (x)\)
 4.1330   \(-2 \csc (2 x) \left (1-a \sin ^2(x)\right ) y'(x)+b y(x) \tan ^2(x)+y''(x)=0\)
 4.1331   \(a y(x) \cos ^2(x)+y''(x)+\tan (x) y'(x)=0\)
 4.1332   \(a y(x) \cot ^2(x)+y''(x)+\tan (x) y'(x)=0\)
 4.1333   \(-a (a+1) y(x) \csc ^2(x)+y''(x)-\tan (x) y'(x)=0\)
 4.1334   \(y(x) \left (a \cos ^2(x)-\sec ^2(x)\right )+y''(x)-\tan (x) y'(x)=0\)
 4.1335   \(y''(x)+2 \tan (x) y'(x)-y(x)=0\)
 4.1336   \(y''(x)+2 \tan (x) y'(x)-y(x)=(x+1) \sec (x)\)
 4.1337   \(y''(x)+2 \tan (x) y'(x)+3 y(x)=0\)
 4.1338   \(b y(x)+y''(x)-2 \tan (x) y'(x)=0\)
 4.1339   \(-\left (a^2+1\right ) y(x)+y''(x)-2 \tan (x) y'(x)=0\)
 4.1340   \(-\left (a^2+1\right ) y(x)+y''(x)-2 \tan (x) y'(x)=\sin (x)\)
 4.1341   \(a \tan (x) y'(x)+b y(x)+y''(x)=0\)
 4.1342   \(y''(x)-\left (2 e^x+1\right ) y'(x)+e^{2 x} y(x)=0\)
 4.1343   \(y(x) \left (\text{a0}+4 \text{a1} \sinh ^2(x)-\text{a2} \text{csch}^2(x)\right )+y''(x)+\coth (x) y'(x)=0\)
 4.1344   \(y(x) \left (\text{a0}+4 \text{a1} \cosh ^2(x)-\text{a2} \text{sech}^2(x)\right )+y''(x)+\tanh (x) y'(x)=0\)
 4.1345   \(b y(x)+y''(x)+2 \tanh (x) y'(x)=0\)
 4.1346   \(a \tanh (x) y'(x)+b y(x)+y''(x)=0\)
 4.1347   \(f(x) y'(x)+y''(x)=0\)
 4.1348   \(a k x^{k-1} y(x)+2 a x^k y'(x)+2 y''(x)=0\)
 4.1349   \(3 y''(x)-10 y'(x)+3 y(x)=0\)
 4.1350   \(4 y''(x)=\left (a+x^2\right ) y(x)\)
 4.1351   \(\left (4 a-x^2+2\right ) y(x)+4 y''(x)=0\)
 4.1352   \(4 y''(x)-8 y'(x)+3 y(x)=0\)
 4.1353   \(x y''(x)+y(x)=0\)
 4.1354   \((a+x) y(x)+x y''(x)=0\)
 4.1355   \(x y''(x)+y'(x)=0\)
 4.1356   \(x y''(x)+y'(x)=x^n\)
 4.1357   \(x y''(x)+y'(x)-y(x)=0\)
 4.1358   \(x y''(x)+y'(x)-(x+1) y(x)=0\)
 4.1359   \(4 x^3 y(x)+x y''(x)-y'(x)=0\)
 4.1360   \(-a^2 x^3 y(x)+x y''(x)-y'(x)=0\)
 4.1361   \(x^3 \left (e^{x^2}-k^2\right ) y(x)+x y''(x)-y'(x)=0\)
 4.1362   \(x y''(x)+2 y'(x)=0\)
 4.1363   \(x y''(x)+2 y'(x)=0\)
 4.1364   \(x y''(x)+2 y'(x)-x y(x)=e^x\)
 4.1365   \(a x y(x)+x y''(x)+2 y'(x)=0\)
 4.1366   \(a x^2 y(x)+x y''(x)+2 y'(x)=0\)
 4.1367   \(a y'(x)+x y''(x)=0\)
 4.1368   \((a+1) y'(x)+x y''(x)+y(x)=0\)
 4.1369   \((1-a) y'(x)+x y''(x)+y(x)=0\)
 4.1370   \((a+1) y'(x)+x y''(x)-y(x)=0\)
 4.1371   \(2 n y'(x)+x y''(x)-y(x)=0\)
 4.1372   \(a y'(x)+b y(x)+x y''(x)=0\)
 4.1373   \(a y'(x)+b x y(x)+x y''(x)=0\)
 4.1374   \(a y'(x)+y(x) (\text{b1}+\text{b2} x)+x y''(x)=0\)
 4.1375   \(a y'(x)+y(x) \left (\text{a1}+\text{b1} x+\text{c1} x^2\right )+x y''(x)=0\)
 4.1376   \(a y'(x)+b x^k y(x)+x y''(x)=0\)
 4.1377   \(x y''(x)-(x+1) y'(x)+y(x)=0\)
 4.1378   \(n y(x)+x y''(x)+(1-x) y'(x)=0\)
 4.1379   \((k-x+1) y'(x)+n y(x)+x y''(x)=0\)
 4.1380   \(x y''(x)-(x+1) y'(x)+2 (1-x) y(x)=0\)
 4.1381   \(x y''(x)-(2-x) y'(x)-y(x)=0\)
 4.1382   \(x y''(x)-(x+3) y'(x)+y(x)=0\)
 4.1383   \(x y''(x)-(x+3) y'(x)+3 y(x)=0\)
 4.1384   \((a+x) y'(x)+b y(x)+x y''(x)=0\)
 4.1385   \(-a y(x)+(c-x) y'(x)+x y''(x)=0\)
 4.1386   \(x y''(x)+(1-2 x) y'(x)-(1-x) y(x)=0\)
 4.1387   \(x y''(x)-(2 x+1) y'(x)+(x+1) y(x)=0\)
 4.1388   \(x y''(x)-(2 x+1) y'(x)+(x+1) y(x)=x^2-x-1\)
 4.1389   \((a+b x) y'(x)+c y(x)+x y''(x)=0\)
 4.1390   \((\text{a1}+\text{b1} x) y'(x)+y(x) (\text{a2}+\text{b2} x)+x y''(x)=0\)
 4.1391   \(-2 (a+b x) y'(x)+y(x) (2 a+b x)+x y''(x)=0\)
 4.1392   \(y'(x) (x (a+b)+m+n)+y(x) (a b x+a n+b m)+x y''(x)=0\)
 4.1393   \(x y''(x)-\left (1-x^2\right ) y'(x)=0\)
 4.1394   \(-\left (4-x^2\right ) y'(x)+x y''(x)+2 x y(x)=0\)
 4.1395   \(x^3 y(x)-\left (2 x^2+1\right ) y'(x)+x y''(x)=0\)
 4.1396   \(-8 x^3 y(x)-\left (2 x^2+1\right ) y'(x)+x y''(x)=0\)
 4.1397   \(-8 x^3 y(x)-\left (2 x^2+1\right ) y'(x)+x y''(x)=4 e^{-x^2} x^3\)
 4.1398   \(\left (4 x^2+1\right ) y'(x)+4 x \left (x^2+1\right ) y(x)+x y''(x)=0\)
 4.1399   \(-\left (1-2 a x^3\right ) y'(x)+a x^2 \left (a x^3+1\right ) y(x)+x y''(x)=0\)
 4.1400   \((x f(x)+2) y'(x)+f(x) y(x)+x y''(x)=0\)
 4.1401   \((1-x) y''(x)+x y'(x)-y(x)=0\)
 4.1402   \((1-x) y''(x)+x y'(x)-y(x)=(1-x)^2\)
 4.1403   \((3-x) y''(x)-(9-4 x) y'(x)+3 (2-x) y(x)=0\)
 4.1404   \((a-x) y''(x)-2 y'(x)=0\)
 4.1405   \((a+x) y''(x)+(\text{a1}+\text{b1} x) y'(x)+y(x) (\text{a2}+\text{b2} x)=0\)
 4.1406   \(2 x y''(x)+y'(x)=0\)
 4.1407   \(a y(x)+2 x y''(x)+y'(x)=0\)
 4.1408   \(-a y(x)+2 x y''(x)+y'(x)=0\)
 4.1409   \(y(x) (a+b x)+2 x y''(x)+y'(x)=0\)
 4.1410   \(-\left (2 x^2+1\right ) y'(x)+2 x y''(x)-x y(x)=0\)
 4.1411   \((1-2 x) y''(x)-(x+2) y'(x)-y(x)=0\)
 4.1412   \((1-2 x) y''(x)-(4-3 x) y'(x)+(3-x) y(x)=0\)
 4.1413   \(4 y''(x)+2 y'(x)+y(x)=0\)
 4.1414   \(4 y''(x)-2 y'(x)-y(x)=0\)
 4.1415   \(4 x y''(x)+4 \coth (x) y'(x)+y(x)=0\)
 4.1416   \(y(x) (a+b x)+16 x y''(x)+8 y'(x)=0\)
 4.1417   \((a+b x) y''(x)+c y'(x)=0\)
 4.1418   \((\text{a0}+\text{b0} x) y''(x)+(\text{a1}+\text{b1} x) y'(x)+y(x) (\text{a2}+\text{b2} x)=0\)
 4.1419   \((1-x \cot (x)) y''(x)-x y'(x)+y(x)=0\)
 4.1420   \(x^2 y''(x)=a+b x\)
 4.1421   \(x^2 y''(x)=2 y(x)\)
 4.1422   \(x^2 y''(x)=6 y(x)\)
 4.1423   \(x^2 y''(x)=12 y(x)\)
 4.1424   \(a y(x)+x^2 y''(x)=0\)
 4.1425   \(y(x) (a+b x)+x^2 y''(x)=0\)
 4.1426   \(x^2 y''(x)-\left (2-x^2\right ) y(x)=0\)
 4.1427   \(x^2 y''(x)-\left (2-x^2\right ) y(x)=x^4\)
 4.1428   \(x^2 y''(x)-\left (a^2 x^2+2\right ) y(x)=0\)
 4.1429   \(x^2 y''(x)-\left (6-a^2 x^2\right ) y(x)=0\)
 4.1430   \(x^2 y''(x)-y(x) \left (a^2 x^2+n (n+1)\right )=0\)
 4.1431   \(x^2 y''(x)-y(x) \left ((n-1) n-a^2 x^2\right )=0\)
 4.1432   \(y(x) \left (a+b x+c x^2\right )+x^2 y''(x)=0\)
 4.1433   \(x^2 y''(x)-y(x) \left ((a-1) a-b x^k\right )=0\)
 4.1434   \(x^k y(x) \left (a+b x^k\right )+x^2 y''(x)=0\)
 4.1435   \(-b y(x) \left (a+b x^2\right )+a y'(x)+x^2 y''(x)=0\)
 4.1436   \(x^2 y''(x)+x y'(x)+y(x)=0\)
 4.1437   \(x^2 y''(x)+x y'(x)-y(x)=0\)
 4.1438   \(x^2 y''(x)-x y'(x)+y(x)=0\)
 4.1439   \(x^2 y''(x)+x y'(x)-y(x)=a x^2\)
 4.1440   \(x^2 y''(x)-x y'(x)+y(x)=x^2 (x+3)\)
 4.1441   \(x^2 y''(x)-x y'(x)+y(x)=3 x^3\)
 4.1442   \(x^2 y''(x)+x y'(x)+y(x)=\log (x)\)
 4.1443   \(x^2 y''(x)-x y'(x)+2 y(x)=0\)
 4.1444   \(x^2 y''(x)-x y'(x)+2 y(x)=x \log (x)\)
 4.1445   \(x^2 y''(x)-x y'(x)-3 y(x)=0\)
 4.1446   \(a^2 (-y(x))+x^2 y''(x)+x y'(x)=0\)
 4.1447   \(y(x) (a+b x)+x^2 y''(x)+x y'(x)=0\)
 4.1448   \(-\left (p^2-x^2\right ) y(x)+x^2 y''(x)+x y'(x)=0\)
 4.1449   \(-\left (p^2+x^2\right ) y(x)+x^2 y''(x)+x y'(x)=0\)
 4.1450   \(-\left (p^2+i x^2\right ) y(x)+x^2 y''(x)+x y'(x)=0\)
 4.1451   \(-y(x) \left (p^2-a^2 x^2\right )+x^2 y''(x)+x y'(x)=0\)
 4.1452   \(-y(x) \left (a+b x+c x^2\right )+x^2 y''(x)+x y'(x)=0\)
 4.1453   \(-y(x) \left (4 a x^2+n^2-x^4\right )+x^2 y''(x)+x y'(x)=0\)
 4.1454   \(-y(x) \left (a^2+b^2 x^2+c^2 x^4\right )+x^2 y''(x)+x y'(x)=0\)
 4.1455   \((m+1) a(m) x^m y(x)+x^2 y''(x)+x y'(x)=0\)
 4.1456   \((a+x) y'(x)+x^2 y''(x)-y(x)=0\)
 4.1457   \(x^2 y''(x)-2 x y'(x)+2 y(x)=0\)
 4.1458   \(x^2 y''(x)-2 x y'(x)+2 y(x)=4 x^3\)
 4.1459   \(x^2 y''(x)-2 x y'(x)+2 y(x)=x^3 \sin (x)\)
 4.1460   \(x^2 y''(x)-2 x y'(x)+2 y(x)=2 x \log (x)\)
 4.1461   \(x^2 y''(x)-2 x y'(x)+2 y(x)=x^5 \log (x)\)
 4.1462   \(x^2 y''(x)+2 x y'(x)-6 y(x)=0\)
 4.1463   \(x^2 y''(x)+2 x y'(x)-6 y(x)=2-x\)
 4.1464   \(\left (a^2 x^2+2\right ) y(x)+x^2 y''(x)-2 x y'(x)=0\)
 4.1465   \(-y(x) \left (n (n+1)-a^2 x^2\right )+x^2 y''(x)+2 x y'(x)=0\)
 4.1466   \(y(x) \left (a+b x^2\right )+x^2 y''(x)+2 x y'(x)=0\)
 4.1467   \(a y(x)+x^2 y''(x)-2 (1-x) y'(x)=0\)
 4.1468   \(x^2 y''(x)+3 x y'(x)+y(x)=0\)
 4.1469   \(x^2 y''(x)+3 x y'(x)+y(x)=x\)
 4.1470   \(x^2 y''(x)+3 x y'(x)+y(x)=a-x+x \log (x)\)
 4.1471   \(x^2 y''(x)-3 x y'(x)+4 y(x)=0\)
 4.1472   \(x^2 y''(x)-3 x y'(x)+4 y(x)=5 x\)
 4.1473   \(x^2 y''(x)-3 x y'(x)-5 y(x)=0\)
 4.1474   \(x^2 y''(x)-3 x y'(x)-5 y(x)=x^2 \log (x)\)
 4.1475   \(x^2 y''(x)+4 x y'(x)+2 y(x)=0\)
 4.1476   \(x^2 y''(x)+4 x y'(x)+2 y(x)=e^x\)
 4.1477   \(x^2 y''(x)+4 x y'(x)+2 y(x)=\log (x+1)\)
 4.1478   \(x^2 y''(x)-4 x y'(x)+6 y(x)=0\)
 4.1479   \(x^2 y''(x)-4 x y'(x)+6 y(x)=x^2 \left (x^2-1\right )\)
 4.1480   \(x^2 y''(x)+\left (2-x^2\right ) y(x)+4 x y'(x)=0\)
 4.1481   \(x^2 y''(x)+\left (x^2+6\right ) y(x)+4 x y'(x)=0\)
 4.1482   \(x^2 y''(x)+5 x y'(x)+13 y(x)=0\)
 4.1483   \(x^2 y''(x)-7 x y'(x)+16 y(x)=0\)
 4.1484   \(y(x) \left (a (a+1)+b^2 x^2\right )-2 a x y'(x)+x^2 y''(x)=0\)
 4.1485   \(\text{a1} x y'(x)+\text{a2} y(x)+x^2 y''(x)=0\)
 4.1486   \(\text{a1} x y'(x)+y(x) (\text{a2}+\text{b2} x)+x^2 y''(x)=0\)
 4.1487   \(\text{a1} x y'(x)+y(x) \left (\text{a2}+\text{b2} x^2\right )+x^2 y''(x)=0\)
 4.1488   \(\text{a1} x y'(x)+y(x) \left (\text{a2}+\text{b2} x+\text{c2} x^2\right )+x^2 y''(x)=0\)
 4.1489   \(a x y'(x)+y(x) \left (b+c x^3\right )+x^2 y''(x)=0\)
 4.1490   \(a x y'(x)+x^2 y(x) \left (\text{a1}+\text{b1} x^2\right )+x^2 y''(x)=0\)
 4.1491   \(a x y'(x)+y(x) \left (b+c x^{2 k}\right )+x^2 y''(x)=0\)
 4.1492   \((a+b x) y'(x)+c y(x)+x^2 y''(x)=0\)
 4.1493   \(-2 a x y'(x)+a (a+1) y(x)+x^2 y''(x)=0\)
 4.1494   \(-2 a x y'(x)+a (a+1) y(x)+x^2 y''(x)=e^x x^{a+2}\)
 4.1495   \(y(x) \left (a (a+1)+b^2 x^2\right )-2 a x y'(x)+x^2 y''(x)=0\)
 4.1496   \(y(x) (a+b x)+2 a x y'(x)+x^2 y''(x)=0\)
 4.1497   \(x^2 y''(x)-x^2 y'(x)-2 x^2 y(x)=2 x^2 \log (x)+x+1\)
 4.1498   \(y(x) \left (a+b x^2\right )+x^2 y''(x)+x^2 y'(x)=0\)
 4.1499   \(x^2 y''(x)-\left (1-x^2\right ) y'(x)-y(x)=0\)
 4.1500   \(x^2 y''(x)+(1-x) x y'(x)-(1-x) y(x)=0\)
 4.1501   \(x^2 y''(x)-(x+2) x y'(x)+(x+2) y(x)=0\)
 4.1502   \(x^2 y''(x)-(x+2) x y'(x)+(x+2) y(x)=x^3\)
 4.1503   \(x^2 y''(x)+(2-x) x y'(x)-(3 x+2) y(x)=0\)
 4.1504   \(x^2 y''(x)+(x+3) x y'(x)-y(x)=0\)
 4.1505   \(x^2 y''(x)-2 (x+1) x y'(x)+2 (x+1) y(x)=0\)
 4.1506   \(a x^2 y'(x)+x^2 y''(x)-2 y(x)=0\)
 4.1507   \(-x (a x+5) y'(x)+(3 a x+5) y(x)+x^2 y''(x)=0\)
 4.1508   \(x (\text{a1}+\text{b1} x) y'(x)+y(x) \left (\text{a2}+\text{b2} x+\text{c2} x^2\right )+x^2 y''(x)=0\)
 4.1509   \(x^3 y'(x)+x^2 y''(x)-\left (2-x^2\right ) y(x)=0\)
 4.1510   \(x^2 y''(x)+\left (1-x^2\right ) x y'(x)-\left (x^2+1\right ) y(x)=0\)
 4.1511   \(4 x^3 y'(x)+x^2 y''(x)+\left (4 x^4+2 x^2+1\right ) y(x)=0\)
 4.1512   \(x y'(x) \left (\text{a0}+\text{b0} x^k\right )+y(x) \left (\text{a1}+\text{b1} x^k+\text{c1} x^{2 k}\right )+x^2 y''(x)=0\)
 4.1513   \(x y'(x) \left (\text{a0}+\text{a1} x^r+\text{a2} x^s\right )+y(x) \left (\text{b0}+\text{b1} x^r+\text{b2} x^{2 r}+\text{b3} x^s+\text{b4} x^{2 s}+\text{b5} x^{r+s}\right )+x^2 y''(x)=0\)
 4.1514   \(a y(x)+x^2 y''(x)+2 x^2 \cot (x) y'(x)=0\)
 4.1515   \(-y(x) (a-x \cot (x))+x^2 y''(x)+x (2 x \cot (x)+1) y'(x)=0\)
 4.1516   \(a y(x)+x^2 y''(x)-2 x^2 \tan (x) y'(x)=0\)
 4.1517   \(-y(x) (a+x \tan (x))+x^2 y''(x)+x (1-2 x \tan (x)) y'(x)=0\)
 4.1518   \(y(x) \left (f(x) \left (\text{a1}+\text{b1} x^k-1\right )+\text{a2}+\text{b2} x^k+\text{c2} x^{2 k}+f'(x)+f(x)^2\right )+x y'(x) \left (\text{a1}+\text{b1} x^k+2 f(x)\right )+x^2 y''(x)=0\)
 4.1519   \(\left (x^2+1\right ) y''(x)-2 y(x)=0\)
 4.1520   \(a+\left (x^2+1\right ) y''(x)-x y'(x)=0\)
 4.1521   \(\left (1-x^2\right ) y''(x)+x y'(x)=x\)
 4.1522   \(\left (x^2+1\right ) y''(x)-x y'(x)+y(x)=0\)
 4.1523   \(\left (1-x^2\right ) y''(x)+x y'(x)-y(x)=0\)
 4.1524   \(\left (1-x^2\right ) y''(x)-x y'(x)+y(x)=0\)
 4.1525   \(\left (1-x^2\right ) y''(x)-x y'(x)-y(x)=0\)
 4.1526   \(\left (1-x^2\right ) y''(x)+x y'(x)-y(x)=x \left (1-x^2\right )^{3/2}\)
 4.1527   \(\left (1-x^2\right ) y''(x)+x y'(x)+3 y(x)=0\)
 4.1528   \(\left (x^2+1\right ) y''(x)+x y'(x)-4 y(x)=0\)
 4.1529   \(\left (x^2+1\right ) y''(x)+x y'(x)-4 y(x)=0\)
 4.1530   \(n^2 y(x)+\left (1-x^2\right ) y''(x)-x y'(x)=0\)
 4.1531   \(a^2 y(x)+\left (x^2+1\right ) y''(x)+x y'(x)=0\)
 4.1532   \(a^2 y(x)+\left (1-x^2\right ) y''(x)-x y'(x)=0\)
 4.1533   \(y(x) \left (a+b x^2\right )+\left (1-x^2\right ) y''(x)-x y'(x)=0\)
 4.1534   \(y(x) \left (\DOTSB \sum@ \slimits@ _{m=0}^n a(m) x^{2 m}\right )+\left (1-x^2\right ) y''(x)-x y'(x)=0\)
 4.1535   \(\left (1-x^2\right ) y''(x)-2 x y'(x)=0\)
 4.1536   \(a+\left (1-x^2\right ) y''(x)-2 x y'(x)=0\)
 4.1537   \(\left (x^2+1\right ) y''(x)+2 x y'(x)-2 y(x)=0\)
 4.1538   \(\left (x^2+1\right ) y''(x)-2 x y'(x)+2 y(x)=0\)
 4.1539   \(\left (1-x^2\right ) y''(x)+2 x y'(x)-2 y(x)=\left (1-x^2\right )^2\)
 4.1540   \(n (n+1) y(x)+\left (1-x^2\right ) y''(x)-2 x y'(x)=0\)
 4.1541   \(n (n+1) y(x)+\left (1-x^2\right ) y''(x)-2 x y'(x)=\frac{2 ((-n-1) x P_n(x)+(n+1) P_{n+1}(x))}{x^2-1}\)
 4.1542   \(-p (p+1) y(x)+\left (x^2+1\right ) y''(x)+2 x y'(x)=0\)
 4.1543   \(p (p+1) y(x)+\left (1-x^2\right ) y''(x)-2 x y'(x)=0\)
 4.1544   \(n (n+2) y(x)+\left (1-x^2\right ) y''(x)-3 x y'(x)=0\)
 4.1545   \(-a y(x)+\left (1-x^2\right ) y''(x)-3 x y'(x)=0\)
 4.1546   \(\left (x^2+1\right ) y''(x)+4 x y'(x)+2 y(x)=2 (\cos (x)-x)\)
 4.1547   \(\left (x^2+1\right ) y''(x)-4 x y'(x)+6 y(x)=0\)
 4.1548   \(\left (1-x^2\right ) y''(x)-\left (x^2+1\right ) y(x)-4 x y'(x)=0\)
 4.1549   \(\left (1-x^2\right ) y''(x)-6 x y'(x)-4 y(x)=0\)
 4.1550   \(n y(x) (a+b+n+1)+(-x (a+b+2)-a+b) y'(x)+\left (1-x^2\right ) y''(x)=0\)
 4.1551   \(p (2 k+p) y(x)-(2 k+1) x y'(x)+\left (1-x^2\right ) y''(x)=0\)
 4.1552   \(n y(x) (a+b+n+1)+(-x (a+b+2)-a+b) y'(x)+\left (1-x^2\right ) y''(x)=0\)
 4.1553   \(-(k-p) (k+p+1) y(x)-2 (k+1) x y'(x)+\left (1-x^2\right ) y''(x)=0\)
 4.1554   \(-2 a x y'(x)+(1-a) a y(x)+\left (1-x^2\right ) y''(x)=0\)
 4.1555   \(a x y'(x)-(2-a) y(x)+\left (x^2+1\right ) y''(x)=0\)
 4.1556   \(a x y'(x)+b y(x)+\left (1-x^2\right ) y''(x)=0\)
 4.1557   \(a x y'(x)+y(x) \left (\text{a0}+\text{b0} x+\text{c0} x^2\right )+\left (1-x^2\right ) y''(x)=0\)
 4.1558   \((a+b x) y'(x)+c y(x)+\left (1-x^2\right ) y''(x)=0\)
 4.1559   \(\left (a^2-x^2\right ) y''(x)+y(x) \left (b^2+c^2 x^2\right )-x y'(x)=0\)
 4.1560   \(\left (a^2-x^2\right ) y''(x)-8 x y'(x)-12 y(x)=0\)
 4.1561   \((1-x) x y''(x)+2 y'(x)+y(x)=0\)
 4.1562   \((1-x) x y''(x)-2 y'(x)+2 y(x)=0\)
 4.1563   \((1-x) x y''(x)+2 y'(x)+6 y(x)=0\)
 4.1564   \((1-x) x y''(x)-2 y'(x)+6 y(x)=0\)
 4.1565   \((1-x) x y''(x)+3 y'(x)+2 y(x)=0\)
 4.1566   \((1-x) x y''(x)-3 y'(x)+2 y(x)=0\)
 4.1567   \((1-x) x y''(x)-3 y'(x)+2 y(x)=x \left (3 x^3+1\right )\)
 4.1568   \(-a y'(x)+(1-x) x y''(x)+2 y(x)=0\)
 4.1569   \(x (x+1) y''(x)+(1-x) y'(x)+y(x)=0\)
 4.1570   \((1-x) x y''(x)-(x+1) y'(x)+y(x)=0\)
 4.1571   \((1-x) x y''(x)-(x+4) y'(x)+4 y(x)=0\)
 4.1572   \((1-x) x y''(x)+2 x y'(x)-2 y(x)=0\)
 4.1573   \((1-x) x y''(x)+(1-2 x) y'(x)+6 y(x)=0\)
 4.1574   \(p (p+1) y(x)+(1-x) x y''(x)+(1-2 x) y'(x)=0\)
 4.1575   \((1-x) x y''(x)+(1-x) y'(x)+2 y(x)=0\)
 4.1576   \((1-x) x y''(x)-3 x y'(x)-y(x)=0\)
 4.1577   \(x (x+1) y''(x)+(3 x+2) y'(x)+y(x)=0\)
 4.1578   \((1-x) x y''(x)+(1-4 x) y'(x)-2 y(x)=0\)
 4.1579   \((1-x) x y''(x)-2 (2 x+1) y'(x)-2 y(x)=0\)
 4.1580   \((1-x) x y''(x)-2 (1-2 x) y'(x)-6 y(x)=0\)
 4.1581   \((p-k) (k+p+1) y(x)+(k+1) (1-2 x) y'(x)+(1-x) x y''(x)=0\)
 4.1582   \((c-(a+1) x) y'(x)+n (a+n) y(x)+(1-x) x y''(x)=0\)
 4.1583   \((a+b x) y'(x)+c y(x)+x (x+1) y''(x)=0\)
 4.1584   \(y'(x) (c-x (a+b+1))-a b y(x)+(1-x) x y''(x)=0\)
 4.1585   \(-(a-(2-a) x) y'(x)-a y(x)+x (x+1) y''(x)=0\)
 4.1586   \(-(a-(2-a) x) y'(x)-a y(x)+x (x+1) y''(x)=0\)
 4.1587   \((a+b x) y'(x)+c y(x)+(1-x) x y''(x)=0\)
 4.1588   \(y(x) \left (\DOTSB \sum@ \slimits@ _{m=0}^n a(m) x^m\right )+a (1-2 x) y'(x)+x (x+1) y''(x)=0\)
 4.1589   \(\left (-x^2-x+2\right ) y''(x)+(1-x) x y'(x)+x (6 x+7) y(x)=0\)
 4.1590   \((2-x) x y''(x)+2 (1-x) y'(x)+2 y(x)=0\)
 4.1591   \(-\left (2-x^2\right ) y'(x)+(2-x) x y''(x)+2 (1-x) y(x)=0\)
 4.1592   \((1-x)^2 y''(x)-4 (1-x) y'(x)+2 y(x)=0\)
 4.1593   \((1-x)^2 y''(x)-4 (1-x) y'(x)+2 y(x)=\cos (x)\)
 4.1594   \((x+1)^2 y''(x)-4 (x+1) y'(x)+6 y(x)=0\)
 4.1595   \((x+1)^2 y''(x)-4 (x+1) y'(x)+6 y(x)=x\)
 4.1596   \(-\left (-x^2-x+1\right ) y'(x)+(x+1)^2 y''(x)-(x+2) y(x)=0\)
 4.1597   \((1-x)^2 y''(x)-2 (1-x)^2 y'(x)+(1-x)^2 y(x)=e^x\)
 4.1598   \(\left (x^2+3 x+4\right ) y''(x)+\left (x^2+x+1\right ) y'(x)-(2 x+3) y(x)=0\)
 4.1599   \((x+2)^2 y''(x)-(x+2) y'(x)+2 y(x)=0\)
 4.1600   \((2-x)^2 y''(x)+(2-x) y'(x)-3 y(x)=0\)
 4.1601   \(x (\text{a0}+x) y''(x)+(\text{a1}+\text{b1} x) y'(x)+\text{a2} y(x)=0\)
 4.1602   \(-4 (a+x) y'(x)+(\text{a0}+x)^2 y''(x)+6 y(x)=0\)
 4.1603   \(2 x^2 y''(x)-x y'(x)+y(x)=x^2\)
 4.1604   \(2 x^2 y''(x)+x y'(x)-3 y(x)=0\)
 4.1605   \(2 x^2 y''(x)-(2 x+7) x y'(x)+2 (x+5) y(x)=0\)
 4.1606   \(2 x^2 y''(x)-(1-4 x) x y'(x)-2 (1-3 x) y(x)=0\)
 4.1607   \(2 x^2 y''(x)-(1-4 x) x y'(x)-2 (1-3 x) y(x)=x^3 (x+1)\)
 4.1608   \(\left (2 x^2+1\right ) y''(x)+3 x y'(x)-3 y(x)=0\)
 4.1609   \(2 a^2 y(x)+2 \left (1-x^2\right ) y''(x)-x y'(x)=0\)
 4.1610   \(2 x (x+1) y''(x)+y'(x)-4 y(x)=0\)
 4.1611   \(2 (1-x) x y''(x)+(x+1) y'(x)-y(x)=0\)
 4.1612   \(2 (1-x) x y''(x)+(1-x) y'(x)+y(x)=0\)
 4.1613   \(2 (1-x) x y''(x)+(1-2 x) y'(x)-2 y(x)=0\)
 4.1614   \(2 (1-x) x y''(x)+(1-2 x) y'(x)+8 y(x)=0\)
 4.1615   \(a y(x)+2 (1-x) x y''(x)-(1-2 x) y'(x)=0\)
 4.1616   \(y(x) (a+b x)+2 (1-x) x y''(x)+(1-2 x) y'(x)=0\)
 4.1617   \(2 a (a+1) y(x)+2 (1-x) x y''(x)-(3 x+1) y'(x)=0\)
 4.1618   \((1-2 x) (1-x) y''(x)+2 (1-2 x) y'(x)+4 y(x)=0\)
 4.1619   \((1-2 x) (1-x) y''(x)+2 (3-4 x) y'(x)+12 y(x)=0\)
 4.1620   \(2 (x+1)^2 y''(x)-(x+1) y'(x)+y(x)=0\)
 4.1621   \(2 (x+1)^2 y''(x)-(x+1) y'(x)+y(x)=x\)
 4.1622   \(4 x^2 y''(x)+y(x)=0\)
 4.1623   \(4 x^2 y''(x)+y(x)=\sqrt{x}\)
 4.1624   \(y(x) \left (4 k x-4 p^2-x^2+1\right )+4 x^2 y''(x)=0\)
 4.1625   \(\left (4 a^2 x^2+1\right ) y(x)+4 x^2 y''(x)=0\)
 4.1626   \(-\left (a^2-x\right ) y(x)+4 x^2 y''(x)+4 x y'(x)=0\)
 4.1627   \(4 x^2 y''(x)-\left (4 x^2+1\right ) y(x)+4 x y'(x)=4 e^x x^{3/2}\)
 4.1628   \(-\left ((2 n+1)^2-4 x^2\right ) y(x)+4 x^2 y''(x)+4 x y'(x)=0\)
 4.1629   \(-\left (a^2 x^2+1\right ) y(x)+4 x^2 y''(x)+4 x y'(x)=0\)
 4.1630   \(4 x^2 y''(x)-8 x y'(x)+5 y(x)=0\)
 4.1631   \(4 x^2 y''(x)-2 (x+2) x y'(x)+(x+3) y(x)=0\)
 4.1632   \(4 x^2 y''(x)-\left (-4 x^2+4 x+1\right ) y(x)+4 (1-2 x) x y'(x)=0\)
 4.1633   \(4 x^3 y'(x)+4 x^2 y''(x)-\left (3-2 x^2\right ) y(x)=0\)
 4.1634   \(4 x^3 y'(x)+4 x^2 y''(x)+\left (x^4+2 x^2+1\right ) y(x)=0\)
 4.1635   \(\left (a+x^4+2 x^2\right ) y(x)+4 x^3 y'(x)+4 x^2 y''(x)=0\)
 4.1636   \(4 \left (1-x^2\right ) y''(x)-8 x y'(x)-y(x)=0\)
 4.1637   \(-\left (4 p^2+1\right ) y(x)+4 \left (1-x^2\right ) y''(x)-8 x y'(x)=0\)
 4.1638   \(4 \left (x^2+1\right ) y''(x)=x^2+4 x y'(x)\)
 4.1639   \(4 a x y'(x)-a (a+2) y(x)+4 \left (1-x^2\right ) y''(x)=0\)
 4.1640   \(4 (1-x) x y''(x)+2 (1-x) y'(x)+y(x)=0\)
 4.1641   \(y(x) (a+b x)+4 (1-x) x y''(x)+2 (1-2 x) y'(x)=0\)
 4.1642   \(y(x) \left (a+b x+c x^2\right )+4 (1-x) x y''(x)+2 (1-2 x) y'(x)=0\)
 4.1643   \(y(x) \left (\DOTSB \sum@ \slimits@ _{m=0}^n a(m) x^m\right )+4 (1-x) x y''(x)+2 (1-2 x) y'(x)=0\)
 4.1644   \(-(k-p) (k+p+1) y(x)+2 (1-(3-2 k) x) y'(x)+4 (1-x) x y''(x)=0\)
 4.1645   \(2 (a x+1) y'(x)+y(x) \left (b+k^2 x\right )+4 (1-x) x y''(x)=0\)
 4.1646   \((2 x+1)^2 y''(x)-2 (2 x+1) y'(x)-12 y(x)=0\)
 4.1647   \((2 x+1)^2 y''(x)-2 (2 x+1) y'(x)-12 y(x)=3 x+1\)
 4.1648   \((1-3 x)^2 y''(x)-3 (1-3 x) y'(x)-9 y(x)=0\)
 4.1649   \(16 x^2 y''(x)+(4 x+3) y(x)=0\)
 4.1650   \(16 x^2 y''(x)+32 x y'(x)-(4 x+5) y(x)=0\)
 4.1651   \(\left (a x^2+1\right ) y''(x)+a x y'(x)+b^2 y(x)=0\)
 4.1652   \(\left (a x^2+1\right ) y''(x)+b x y'(x)+c y(x)=0\)
 4.1653   \(\left (1-a^2 x^2\right ) y''(x)-2 a^2 x y'(x)=0\)
 4.1654   \(\left (1-a^2 x^2\right ) y''(x)-2 a^2 x y'(x)+2 a^2 y(x)=0\)
 4.1655   \(x (a+b x) y''(x)+2 a y'(x)-2 b y(x)=0\)
 4.1656   \(y''(x) \left (\text{a0}+\text{b0} x+\text{c0} x^2\right )+(\text{a1}+\text{b1} x) y'(x)+2 \text{a2} y(x)=0\)
 4.1657   \(\text{a1} (a+b x) y'(x)+(a+b x)^2 y''(x)+\text{a2} y(x)=0\)
 4.1658   \(x^3 y''(x)=a+b x\)
 4.1659   \(x^3 y''(x)+x y'(x)-y(x)=0\)
 4.1660   \(x^3 y''(x)+x y'(x)-2 y(x)=0\)
 4.1661   \(x^3 y''(x)+2 x y'(x)-y(x)=0\)
 4.1662   \(\text{a1} x y'(x)+y(x) (\text{a2}+\text{b2} x)+x^3 y''(x)=0\)
 4.1663   \(y(x) \left (a+b x+c x^2\right )+x^3 y''(x)+x^2 y'(x)=0\)
 4.1664   \(x^3 y''(x)+3 x^2 y'(x)+x y(x)=0\)
 4.1665   \(x^3 y''(x)+3 x^2 y'(x)+x y(x)=1\)
 4.1666   \(a x^2 y'(x)+y(x) (b+c x)+x^3 y''(x)=0\)
 4.1667   \(\left (\text{a1}+\text{b1} x^2\right ) y'(x)+\text{a2} x y(x)+x^3 y''(x)=0\)
 4.1668   \(x (\text{a1}+\text{b1} x) y'(x)+\text{a2} y(x)+x^3 y''(x)=0\)
 4.1669   \(x (\text{a1}+\text{b1} x) y'(x)+y(x) (\text{a2}+\text{b2} x)+x^3 y''(x)=0\)
 4.1670   \(\left (1-x^3\right ) y''(x)+6 x y(x)=0\)
 4.1671   \(x \left (1-x^2\right ) y''(x)-y'(x)=0\)
 4.1672   \(x^3+\left (1-x^2\right ) x y''(x)-y'(x)=0\)
 4.1673   \(a x^3 y(x)+\left (1-x^2\right ) x y''(x)-y'(x)=0\)
 4.1674   \(x \left (1-x^2\right ) y''(x)-\left (x^2+7\right ) y'(x)+4 x y(x)=0\)
 4.1675   \(x \left (x^2+1\right ) y''(x)-2 \left (x^2+1\right ) y'(x)+2 x y(x)=0\)
 4.1676   \(x \left (x^2+1\right ) y''(x)-2 \left (1-x^2\right ) y'(x)-2 x y(x)=0\)
 4.1677   \(x \left (1-x^2\right ) y''(x)-2 \left (1-x^2\right ) y'(x)-2 x y(x)=0\)
 4.1678   \(\left (a+b x^2\right ) y'(x)+c x y(x)+x \left (x^2+1\right ) y''(x)=0\)
 4.1679   \(\left (a+b x^2\right ) y'(x)+(a-1) x (a+b) y(x)+x \left (1-x^2\right ) y''(x)=0\)
 4.1680   \(\left (a+b x^2\right ) y'(x)+2 (1-b) x y(x)+x \left (1-x^2\right ) y''(x)=0\)
 4.1681   \(\left (a-(a+1) x^2\right ) y'(x)+c x y(x)+x \left (1-x^2\right ) y''(x)=0\)
 4.1682   \(\left (a+b x^2\right ) y'(x)+c x y(x)+x \left (1-x^2\right ) y''(x)=0\)
 4.1683   \(x \left (x^2+2\right ) y''(x)-y'(x)-6 x y(x)=0\)
 4.1684   \(x \left (2-x^2\right ) y''(x)-\left (x^2+4 x+2\right ) y(x)-\left (-x^3-3 x^2+2 x+2\right ) y'(x)=0\)
 4.1685   \(x \left (\text{a0}+x^2\right ) y''(x)+\left (\text{a1}+\text{b1} x^2\right ) y'(x)+\text{a2} x y(x)=0\)
 4.1686   \(x^2 (x+1) y''(x)+x y'(x)+(x+1)^3 (-y(x))=0\)
 4.1687   \((1-x) x^2 y''(x)-(x+1) x y'(x)+y(x)=0\)
 4.1688   \((x+1) x^2 y''(x)-(2 x+1) x y'(x)+(2 x+1) y(x)=0\)
 4.1689   \((1-x) x^2 y''(x)+2 (2-x) x y'(x)+2 (x+1) y(x)=0\)
 4.1690   \((1-x) x^2 y''(x)-(4-5 x) x y'(x)+(6-9 x) y(x)=0\)
 4.1691   \((x+1) x^2 y''(x)+2 (3 x+2) x y'(x)+2 (3 x+1) y(x)=0\)
 4.1692   \(x (\text{a1}+\text{b1} x) y'(x)+y(x) (\text{a2}+\text{b2} x)+(1-x) x^2 y''(x)=0\)
 4.1693   \(x^2 (\text{a0}+x) y''(x)+x (\text{a1}+\text{b1} x) y'(x)+y(x) (\text{a2}+\text{b2} x)=0\)
 4.1694   \((1-x)^2 x y''(x)-2 y(x)=0\)
 4.1695   \(x \left (x^2+1\right ) y''(x)+x (x+1) y'(x)+y(x)=0\)
 4.1696   \(x (2-x)^2 y''(x)+2 (2-x) y'(x)+2 y(x)=0\)
 4.1697   \((1-x) x (a-x) y''(x)+y'(x) \left (x^2 (\text{a0}+\text{a1}+1)+\text{a0} \text{a2}-\text{a0}+\text{a1}+x (\text{a2}+\text{a3})-\text{a3}+1\right )+\text{a0} \text{a1} (x-k) y(x)=0\)
 4.1698   \((\text{a1}-x) (\text{a2}-x) (\text{a3}-x) y''(x)+y'(x) \left (\text{b0}+\text{b1} x+\text{b2} x^2\right )+y(x) (\text{c0}+\text{c1} x)=0\)
 4.1699   \(\left (1-2 x^3\right ) y''(x)+6 x^2 y'(x)-6 x y(x)=0\)
 4.1700   \(2 (1-x) x^2 y''(x)+(3-5 x) x y'(x)-(x+1) y(x)=0\)
 4.1701   \(2 (2-x) x^2 y''(x)-(4-x) x y'(x)+(3-x) y(x)=0\)
 4.1702   \(x \left (3 x^2+1\right ) y''(x)+2 y'(x)-6 x y(x)=0\)
 4.1703   \(4 (x+1) x^2 y''(x)-4 x^2 y'(x)+(3 x+1) y(x)=0\)
 4.1704   \(x^2 (a+b x) y''(x)-2 x (2 a+b x) y'(x)+2 y(x) (3 a+b x)=0\)
 4.1705   \(y(x) (a+b x)+4 (1-x) x y''(x)+2 (1-3 x) (1-x) y'(x)=0\)
 4.1706   \(4 (1-x) x (1-a x) y''(x)+y'(x) \left (\text{a0}+\text{a1} x+\text{a2} x^2\right )+y(x) \left (\text{b0}+\text{b1} x^2\right )=0\)
 4.1707   \(a^2 y(x)+x^4 y''(x)=0\)
 4.1708   \(x^4 y''(x)+\left (1-2 x^2\right ) y(x)=0\)
 4.1709   \(x^4 y''(x)-\left (2 x^2+1\right ) y(x)=0\)
 4.1710   \(\left (e^{2/x}-a^2\right ) y(x)+x^4 y''(x)=0\)
 4.1711   \(x^4 y''(x)+x y'(x)-2 y(x)=0\)
 4.1712   \(x^4 y''(x)-2 x^2 y'(x)+(2 x+1) y(x)=0\)
 4.1713   \(x^4 y''(x)+x^3 y'(x)+y(x)=0\)
 4.1714   \(x^4 y''(x)+x^3 y'(x)-(x+1) y(x)=0\)
 4.1715   \(y(x) \left (a+b x^2+c x^4\right )+x^4 y''(x)+x^3 y'(x)=0\)
 4.1716   \(x^4 y''(x)+\left (x^2+1\right ) x y'(x)+y(x)=0\)
 4.1717   \(x^4 y''(x)-\left (1-x^2\right ) x y'(x)+\left (1-x^2\right ) y(x)=0\)
 4.1718   \(a^2 y(x)+x^4 y''(x)+2 x^3 y'(x)=0\)
 4.1719   \(x^4 y''(x)+\left (2 x^2+1\right ) x y'(x)-y(x)=0\)
 4.1720   \(2 x^2 (a+x) y'(x)+b y(x)+x^4 y''(x)=0\)
 4.1721   \(\left (x^3+1\right ) x y''(x)-\left (1-x^3\right ) y'(x)+x^2 (-y(x))=0\)
 4.1722   \(x^3 \left (-y'(x)\right )+\left (1-x^2\right ) x^2 y''(x)-2 y(x)=0\)
 4.1723   \(\left (1-x^2\right ) x^2 y''(x)-\left (2-x^2\right ) x y'(x)+\left (2-x^2\right ) y(x)=0\)
 4.1724   \(a (a+1) y(x)-2 x^3 y'(x)+\left (1-x^2\right ) x^2 y''(x)=0\)
 4.1725   \(\left (x^2+1\right )^2 y''(x)+2 x \left (x^2+1\right ) y'(x)+y(x)=0\)
 4.1726   \(\left (x^2+1\right )^2 y''(x)+2 x \left (x^2+1\right ) y'(x)+4 y(x)=0\)
 4.1727   \(a^2 (-y(x))+\left (x^2+1\right )^2 y''(x)-2 x \left (1-x^2\right ) y'(x)=0\)
 4.1728   \(-y(x) \left (m^2-n (n+1) \left (1-x^2\right )\right )+\left (1-x^2\right )^2 y''(x)-2 x \left (1-x^2\right ) y'(x)=0\)
 4.1729   \(-y(x) \left (k^2-p (p+1) \left (1-x^2\right )\right )+\left (1-x^2\right )^2 y''(x)-2 x \left (1-x^2\right ) y'(x)=0\)
 4.1730   \(-y(x) \left (a^2-k \left (1-x^2\right )\right )+\left (1-x^2\right )^2 y''(x)-2 x \left (1-x^2\right ) y'(x)=0\)
 4.1731   \(y(x) \left (\text{a0}+\text{a2} x^2+\text{a4} x^4\right )+\left (1-x^2\right )^2 y''(x)-2 x \left (1-x^2\right ) y'(x)=0\)
 4.1732   \(y(x) \left (\DOTSB \sum@ \slimits@ _{m=0}^n a(m) x^m\right )+\left (1-x^2\right )^2 y''(x)-2 x \left (1-x^2\right ) y'(x)=0\)
 4.1733   \(a x \left (1-x^2\right ) y'(x)+b y(x)+\left (x^2+1\right )^2 y''(x)=0\)
 4.1734   \(\text{a1} x \left (1-x^2\right ) y'(x)+y(x) \left (\text{a2}+\text{b2} x+\text{c2} x^2\right )+\left (1-x^2\right )^2 y''(x)=0\)
 4.1735   \(x^2 \left (a^2+x^2\right )^2 y''(x)+x \left (a^2+2 x^2\right ) y'(x)+b^2 y(x)=0\)
 4.1736   \(\left (a^2+x^2\right )^2 y''(x)+2 x \left (a^2+2 x^2\right ) y'(x)-y(x) \left (\text{a0}+\text{a2} x^2+\text{a4} x^4\right )=0\)
 4.1737   \(\left (a^2-x^2\right )^2 y''(x)-2 x \left (a^2-x^2\right ) y'(x)+y(x) \left (\text{a0}+\text{a2} x^2+\text{a4} x^4\right )=0\)
 4.1738   \(\left (a^2+x^2\right )^2 \left (b^2+x^2\right ) y''(x)+x \left (\text{a0}+\text{b0} x^2\right ) y'(x)+y(x) \left (\text{a1}+\text{b1} x^2\right )=0\)
 4.1739   \(\left (a^2-x^2\right )^2 \left (b^2-x^2\right ) y''(x)+x \left (\text{a0}+\text{b0} x^2\right ) y'(x)+y(x) \left (\text{a1}+\text{b1} x^2+\text{c1} x^4\right )=0\)
 4.1740   \((1-x) x (x+1)^2 y''(x)+2 (3-x) x (x+1) y'(x)-2 (1-x) y(x)=0\)
 4.1741   \(y(x) \left (a+b x+c x^2\right )+(1-x)^2 x^2 y''(x)=0\)
 4.1742   \((1-x)^2 x^2 y''(x)+(1-2 x) (1-x) x y'(x)-y(x)=0\)
 4.1743   \((1-x) x (\text{a1}+\text{b2} x) y'(x)+y(x) \left (\text{a2}+\text{b2} x+\text{c2} x^2\right )+(1-x)^2 x^2 y''(x)=0\)
 4.1744   \(y(x) \left (\DOTSB \sum@ \slimits@ _{m=0}^n a(m) x^m\right )+(1-x)^2 x^2 y''(x)+(1-2 x) (1-x) x y'(x)=0\)
 4.1745   \(x^2 (a-x)^2 y''(x)+b y(x)=0\)
 4.1746   \((a-x)^2 (b-x)^2 y''(x)=k^2 y(x)\)
 4.1747   \((a-x) (A+2 x) (b-x) y'(x)+(a-x)^2 (b-x)^2 y''(x)+B y(x)=0\)
 4.1748   \((a-x)^4 y''(x)-2 (a-x)^3 y'(x)-y(x)=0\)
 4.1749   \((1-2 x) (1-x) x^2 y''(x)+2 (2-3 x) x y'(x)+2 (3 x+1) y(x)=0\)
 4.1750   \((1-2 x) (1-x) x^2 y''(x)+2 (1-2 x) (2-x) x y'(x)+2 (1-x) y(x)=0\)
 4.1751   \(-y(x) \left (4 k^2+\left (4 p^2+1\right ) \left (1-x^2\right )\right )+4 \left (1-x^2\right )^2 y''(x)-8 x \left (1-x^2\right ) y'(x)=0\)
 4.1752   \(-y(x) \left (4 k^2+\left (1-4 p^2\right ) \left (1-x^2\right )\right )+4 \left (1-x^2\right )^2 y''(x)-8 x \left (1-x^2\right ) y'(x)=0\)
 4.1753   \(-y(x) \left (a (a+1) (1-x)+b^2 x\right )+4 \left (1-x^2\right ) x^2 y''(x)+2 (1-3 x) (1-x) x y'(x)=0\)
 4.1754   \((a+b x)^4 y''(x)+y(x)=0\)
 4.1755   \(y''(x) \left (a+b x+c x^2\right )^2+A y(x)=0\)
 4.1756   \(x^5 y''(x)+x y'(x)-y(x)=0\)
 4.1757   \(x^5 y''(x)-\left (1-2 x^3\right ) x y'(x)+\left (1-2 x^3\right ) y(x)=0\)
 4.1758   \(x \left (a^2-x^2\right ) \left (b^2-x^2\right ) y''(x)+\left (\text{a0}+\text{b0} x^4\right ) y'(x)+x^3 y(x) \left (\text{a1}+\text{b1} x^2+\text{c1} x^4\right )=0\)
 4.1759   \(a y(x)+x^6 y''(x)-x^5 y'(x)=0\)
 4.1760   \(x^6 y''(x)+3 x^5 y'(x)+y(x)=0\)
 4.1761   \(x^3 \left (a+3 x^2\right ) y'(x)+x^6 y''(x)+y(x)=0\)
 4.1762   \((a-x) (b-x) (c-x) y'(x) \left (\text{a1}+\text{b1} x+\text{c1} x^2\right )+(a-x)^2 (b-x)^2 (c-x)^2 y''(x)+y(x) \left (\text{a2}+\text{b2} x+\text{c2} x^2\right )=0\)
 4.1763   \(4 x^6 y''(x)+\left (1-2 x^2\right ) y(x)+4 \left (2 x^2+1\right ) x^3 y'(x)=0\)
 4.1764   \(4 x^6 y''(x)+\left (8 x^4+10 x^2+1\right ) y(x)-4 \left (2 x^2+1\right ) x^3 y'(x)=0\)
 4.1765   \(\left (4 b-a^2\right ) y(x)+4 x^6 y''(x)+12 x^5 y'(x)=0\)
 4.1766   \(x^{2 a} y''(x)+a x^{2 a-1} y'(x)+(1-a)^2 y(x)=0\)
 4.1767   \(a^2 x^{a-1} y(x)+x^{a+1} y''(x)+(1-2 a) x^a y'(x)=0\)
 4.1768   \(x^2 y''(x) \left (\text{a0}+\text{b0} x^k\right )+x y'(x) \left (\text{a1}+\text{b1} x^k\right )+y(x) \left (\text{a2}+\text{b2} x^k\right )=0\)
 4.1769   \(\left (1-a^2 \cos ^2(x)\right ) y''(x)+a^2 \sin (x) \cos (x) y'(x)+y(x) \left (\text{a0}+\text{a1} \cos ^2(x)\right )=0\)
 4.1770   \(-y(x) \left (4 k^2-\left (1-p^2\right ) \sinh ^2(x)\right )+4 \sinh ^2(x) y''(x)+4 \sinh (x) \cosh (x) y'(x)=0\)
 4.1771   \(y''(x)=0\)
 4.1772   \(y''(x)=a y(x)\)
 4.1773   \(y''(x)=6 y(x)^2\)
 4.1774   \(y''(x)=6 y(x)^2+x\)
 4.1775   \(y''(x)=a+b x+c y(x)^2\)
 4.1776   \(y''(x)=2 y(x)^3\)
 4.1777   \(y''(x)=a+b y(x)+2 y(x)^3\)
 4.1778   \(y''(x)=a+2 y(x)^3+x y(x)\)
 4.1779   \(y''(x)=f(x)+g(x) y(x)+2 y(x)^3\)
 4.1780   \(y''(x)=-2 a b x y(x)+a+2 b^2 y(x)^3\)
 4.1781   \(y''(x)=\text{a0}+\text{a1} x y(x)+\text{a2} y(x)+\text{a3} y(x)^3\)
 4.1782   \(y''(x)=\text{a0}+\text{a1} y(x)+\text{a2} y(x)^2+\text{a3} y(x)^3\)
 4.1783   \(a x^r y(x)^s+y''(x)=0\)
 4.1784   \(a \sin (y(x))+y''(x)=0\)
 4.1785   \(a e^{y(x)}+y''(x)=0\)
 4.1786   \(y''(x)=f(y(x))\)
 4.1787   \(y(x) \left (f'(x)+2 f(x)^2\right )+3 f(x) y'(x)+y''(x)=2 y(x)^3\)
 4.1788   \(y''(x)+y(x) y'(x)=0\)
 4.1789   \(y''(x)+y(x) y'(x)=y(x)^3\)
 4.1790   \(a y(x)+y''(x)+y(x) y'(x)=y(x)^3\)
 4.1791   \(y''(x)+y(x) y'(x)=12 f'(x)-12 f(x) y(x)+y(x)^3\)
 4.1792   \(2 a^2 y(x)+(3 a+y(x)) y'(x)+a y(x)^2+y''(x)=y(x)^3\)
 4.1793   \(y''(x)=y(x) \left (f'(x)-2 f(x)^2\right )+(3 f(x)-y(x)) y'(x)+f(x) y(x)^2+y(x)^3\)
 4.1794   \(y''(x)=(3 \text{f1}(x)-y(x)) y'(x)+\text{f1}(x) y(x)^2+\text{f2}(x)+\text{f3}(x) y(x)+y(x)^3\)
 4.1795   \(y''(x)=y'(x) (\text{f0}(x) y(x)+\text{f1}(x))+\text{g0}(x) y(x)^3+\text{g1}(x) y(x)^2+\text{g2}(x) y(x)+\text{g3}(x)\)
 4.1796   \(y''(x)=y(x) f'(x)+(f(x)-2 y(x)) y'(x)\)
 4.1797   \(y''(x)=(f(x)-2 y(x)) y'(x)+f(x) y(x)^2+g(x)\)
 4.1798   \(y''(x)=(\text{f1}(x)-2 y(x)) y'(x)+\text{f2}(x) y(x)^2+\text{f3}(x)\)
 4.1799   \(y''(x)=(\text{f1}(x)-2 y(x)) y'(x)+\text{f2}(x) y(x)^2+\text{f3}(x) y(x)+\text{f4}(x)\)
 4.1800   \(y''(x)=a+4 b^2 y(x)+3 b y(x)^2+3 y(x) y'(x)\)
 4.1801   \(y''(x)+3 y(x) y'(x)=f(x)+g(x) y(x)-y(x)^3\)
 4.1802   \(y''(x)=(f(x)-3 y(x)) y'(x)+f(x) y(x)^2-y(x)^3\)
 4.1803   \(y''(x)=a \left (2 y(x) y'(x)+1\right )\)
 4.1804   \(a \left (y(x)^2-1\right ) y'(x)+b y(x)+y''(x)=0\)
 4.1805   \(y'(x) f(x,y(x))+g(x,y(x))+y''(x)=0\)
 4.1806   \(y''(x)=\left (x^2-y'(x)\right )^2+2 x\)
 4.1807   \(y''(x)+2 y'(x)^2 \tan (y(x))+2 \cot (x) y'(x)=0\)
 4.1808   \(y''(x)=a y'(x)^2\)
 4.1809   \(y''(x)=a^2+b^2 y'(x)^2\)
 4.1810   \(a y'(x)^2+b y(x)+y''(x)=0\)
 4.1811   \(a y'(x)^2+b \sin (y(x))+y''(x)=0\)
 4.1812   \(a y'(x)^2+b y'(x)+c y(x)+y''(x)=0\)
 4.1813   \(y''(x)=e^x y'(x)^2\)
 4.1814   \(f(x) y'(x)+g(x) y'(x)^2+y''(x)=0\)
 4.1815   \(a y(x) y'(x)^2+b y(x)+y''(x)=0\)
 4.1816   \(f(y(x)) y'(x)^2+g(y(x))+y''(x)=0\)
 4.1817   \(f(x) y'(x)+g(y(x)) y'(x)^2+y''(x)=0\)
 4.1818   \(f(y(x)) y'(x)+g(y(x)) y'(x)^2+y''(x)=0\)
 4.1819   \(f(y(x)) y'(x)+g(y(x)) y'(x)^2+h(y(x))+y''(x)=0\)
 4.1820   \(y''(x)+y'(x)^3+y'(x)=0\)
 4.1821   \(y''(x)=(a-x) y'(x)^3\)
 4.1822   \(y''(x)+\left (e^{2 y(x)}+x\right ) y'(x)^3=0\)
 4.1823   \(y''(x)+4 y'(x)^3+2 y'(x)=0\)
 4.1824   \(a y'(x)^3+y''(x)=0\)
 4.1825   \(y''(x)=x y'(x)^3\)
 4.1826   \(y'(x)^3 (a x+b y(x))+y''(x)=0\)
 4.1827   \(a y(x) \left (y'(x)^2+1\right )^2+y''(x)=0\)
 4.1828   \(y''(x)=a \left (x y'(x)-y(x)\right )^k\)
 4.1829   \(f(x) y'(x)^k+g(x) y'(x)+y''(x)=0\)
 4.1830   \(y''(x)=A x^a y(x)^b y'(x)^c\)
 4.1831   \(y''(x)=a \sqrt{y'(x)^2+1}\)
 4.1832   \(y''(x)=a \sqrt{b y(x)^2+y'(x)^2}\)
 4.1833   \(y''(x)=a \left (y'(x)^2+1\right )^{3/2}\)
 4.1834   \(y''(x)=a x \left (y'(x)^2+1\right )^{3/2}\)
 4.1835   \(y''(x)=a y(x) \left (y'(x)^2+1\right )^{3/2}\)
 4.1836   \(y''(x)=a y(x) \left (\left (b-y'(x)\right )^2+1\right )^{3/2}\)
 4.1837   \(y''(x)=a \left (y'(x)^2+1\right )^{3/2} (b+c x+y(x))\)
 4.1838   \(y''(x)+y(x)^3 y'(x)=y(x) y'(x) \sqrt{4 y'(x)+y(x)^4}\)
 4.1839   \(y''(x)=f\left (y'(x)\right )\)
 4.1840   \(y''(x)=f\left (a x+b y(x),y'(x)\right )\)
 4.1841   \(y''(x)=y(x) f\left (x,\frac{y'(x)}{y(x)}\right )\)
 4.1842   \(y''(x)=x^{n-2} f\left (x^{-n} y(x),x^{1-n} y'(x)\right )\)
 4.1843   \(2 y''(x)=12 y(x)^2+1\)
 4.1844   \(2 y''(x)=y(x) \left (a-y(x)^2\right )\)
 4.1845   \(8 y''(x)+9 y'(x)^4=0\)
 4.1846   \(a x e^{y(x)}+x y''(x)+y'(x)=0\)
 4.1847   \(x y''(x)+2 y'(x)+x y(x)^5=0\)
 4.1848   \(x y(x)^n+x y''(x)+2 y'(x)=0\)
 4.1849   \(x^m y(x)^n+x y''(x)+2 y'(x)=0\)
 4.1850   \(a x^m y(x)^n+x y''(x)+2 y'(x)=0\)
 4.1851   \(a y'(x)+b x e^{y(x)}+x y''(x)=0\)
 4.1852   \(\left (2-a x^2\right ) y'(x)+x y''(x)=0\)
 4.1853   \(x y''(x)=(1-y(x)) y'(x)\)
 4.1854   \(x y''(x)+x y'(x)^2=y'(x)\)
 4.1855   \(x y''(x)=x y'(x)^2+y'(x)\)
 4.1856   \(x y''(x)+2 x y'(x)^2-2 y'(x)=0\)
 4.1857   \(x y''(x)=x^2 y'(x)^2-2 y'(x)-y(x)^2\)
 4.1858   \(a x^2 y'(x)^2+x y''(x)+2 y'(x)=b\)
 4.1859   \(\left (a x y'(x)-y(x)\right )^2+x y''(x)=b\)
 4.1860   \(x y''(x)=y'(x)^3+y'(x)\)
 4.1861   \(x y''(x)+2 y'(x)=a x^{2 k} y'(x)^k\)
 4.1862   \(2 x y''(x)+y'(x)^3+y'(x)=0\)
 4.1863   \(a y(x) \left (1-y(x)^n\right )+x^2 y''(x)=0\)
 4.1864   \(a e^{y(x)-1}+x^2 y''(x)=0\)
 4.1865   \((a+1) x y'(x)+x^2 y''(x)=x^k f\left (x^k y(x),k y(x)+x y'(x)\right )\)
 4.1866   \(x^2 y''(x)+y'(x)^2=0\)
 4.1867   \(x^2 y''(x)=\left (3 x-2 y'(x)\right ) y'(x)\)
 4.1868   \(x^2 y''(x)+x^2 y'(x)^2+4 x y'(x)+2=0\)
 4.1869   \(x^2 y''(x)=x^4 y'(x)^2-4 x^2 y(x)^2+6 y(x)\)
 4.1870   \(a \left (x y'(x)-y(x)\right )^2+x^2 y''(x)=b x^2\)
 4.1871   \(a x^4 y'(x)^2+x^2 y''(x)+2 x y(x)=b\)
 4.1872   \(a y(x) y'(x)^2+b x+x^2 y''(x)=0\)
 4.1873   \(x^2 y''(x)=\sqrt{a x^2 y'(x)^2+b y(x)^2}\)
 4.1874   \(x^2 y''(x)=y(x) f\left (\frac{x y'(x)}{y(x)}\right )\)
 4.1875   \(\left (x^2+1\right ) y''(x)+y'(x)^2+1=0\)
 4.1876   \(a y(x)^3+9 x^2 y''(x)+2 y(x)=0\)
 4.1877   \(x^3 y''(x)-x^2 y'(x)=3-x^2\)
 4.1878   \(x^3 \left (y''(x)+y(x) y'(x)-y(x)^3\right )+12 x y(x)+24=0\)
 4.1879   \(x^3 y''(x)=a \left (x y'(x)-y(x)\right )^2\)
 4.1880   \(2 x^3 y''(x)+x^2 (2 x y(x)+9) y'(x)+x y(x) \left (-2 x^2 y(x)^2+3 x y(x)+12\right )-6=0\)
 4.1881   \(x^4 y''(x)=x \left (x^2+2 y(x)\right ) y'(x)-4 y(x)^2\)
 4.1882   \(x^4 y''(x)=x^2 y'(x) \left (y'(x)+x\right )-4 y(x)^2\)
 4.1883   \(x^4 y''(x)+\left (x y'(x)-y(x)\right )^3=0\)
 4.1884   \(x^a y''(x)+y(x)^b=0\)
 4.1885   \(\left (1-12 x^2\right ) \left (3 y'(x)+y(x)^2\right )+2 x \left (1-4 x^2\right ) \left (y''(x)+y(x) y'(x)-y(x)^3\right )-48 x y(x)+24=0\)
 4.1886   \(a x y(x)+b-\left (k x^{k-1}-12 x^2\right ) \left (3 y'(x)+y(x)^2\right )+2 \left (x^k-4 x^3\right ) \left (y''(x)+y(x) y'(x)-y(x)^3\right )=0\)
 4.1887   \(\sqrt{x} y''(x)=y(x)^{3/2}\)
 4.1888   \(x^{3/2} y''(x)=f\left (\frac{y(x)}{\sqrt{x}}\right )\)
 4.1889   \(y''(x) \left (a+2 b x+c x^2\right )^{3/2}=f\left (\frac{x}{\sqrt{a+2 b x+c x^2}}\right )\)
 4.1890   \(f(x) f'(x) y'(x)+f(x)^2 y''(x)=g\left (y(x),f(x) y'(x)\right )\)
 4.1891   \(f(x)^2 y''(x)=y'(x) \left (3 f(x) f'(x)-f(x)^2 y(x)+3 f(x)^3\right )-24 f(x)^4\)
 4.1892   \(f(x)^2 y''(x)=-a f(x)^5+3 f(x) f'(x)-f(x)^2 y(x)+3 f(x)^3\)
 4.1893   \(2 f(x)^2 y''(x)=f(x) y'(x) \left (3 f'(x)-2 f(x) y(x)\right )+f(x) y(x)^2 f'(x)+y(x) \left (f(x) f''(x)-2 f'(x)^2-2 f(x)^3\right )+2 f(x)^2 y(x)^3\)
 4.1894   \(y(x) y''(x)=a\)
 4.1895   \(y(x) y''(x)=y'(x)^2\)
 4.1896   \(y(x) y''(x)+y'(x)^2=0\)
 4.1897   \(y(x) y''(x)=y'(x)^2-a^2\)
 4.1898   \(y(x) y''(x)+y'(x)^2=a^2\)
 4.1899   \(y(x) y''(x)+y'(x)^2+y(x)^2=0\)
 4.1900   \(2 a^2 y(x)^2+y(x) y''(x)+y'(x)^2=0\)
 4.1901   \(y(x) y''(x)=\text{a0}+\text{a1} y(x)+y(x)^3 (\text{a2}+\text{a3} y(x))+y'(x)^2\)
 4.1902   \(y(x) y''(x)=\text{a0}+\text{a1} y(x)+\text{a2} y(x)^2+\text{a3} y(x)^3+\text{a4} y(x)^4+y'(x)^2\)
 4.1903   \(y(x) y''(x)=y'(x)^2+y(x) y'(x)\)
 4.1904   \(y(x) y''(x)=e^x y(x) \left (\text{a0}+\text{a1} y(x)^2\right )+e^{2 x} \left (\text{a2}+\text{a3} y(x)^4\right )+y'(x)^2\)
 4.1905   \(y(x) y''(x)=y'(x)^2+y(x)^2 \log (y(x))\)
 4.1906   \(y(x) y''(x)=-x^2 y(x)^2+y'(x)^2+y(x)^2 \log (y(x))\)
 4.1907   \(y(x) y''(x)+y'(x)^2=y'(x)\)
 4.1908   \(y(x) y''(x)=y'(x)^2-y'(x)\)
 4.1909   \(y(x) y''(x)=y(x)^2 \left (f(x) y(x)+g'(x)\right )+y'(x)^2+y'(x)\)
 4.1910   \(y(x) y''(x)=y'(x)^2-2 y'(x)\)
 4.1911   \(y(x) y''(x)+y'(x)^2-x y'(x)+y(x)=0\)
 4.1912   \(a x y'(x)+y(x) y''(x)+y'(x)^2=0\)
 4.1913   \(y(x) y''(x)=-y(x) f'(x)+f(x) y'(x)+y'(x)^2+y(x)^3\)
 4.1914   \(y(x) y''(x)=y(x) f''(x)-f(x) y'(x)-f(x) y(x)^3+y'(x)^2+y(x)^4\)
 4.1915   \(y(x) y''(x)=-a y(x) y'(x)-b y(x)^2+y'(x)^2\)
 4.1916   \(y(x) y''(x)=a y(x) y'(x)+b y(x)^2+y'(x)^2+y(x)^3\)
 4.1917   \(y(x) y''(x)=y(x)^2 y'(x)+y'(x)^2\)
 4.1918   \(y(x) y''(x)=f(x) y(x) y'(x)+g(x) y(x)^2+y'(x)^2\)
 4.1919   \(y(x) y''(x)=-y(x) \left (f'(x)-y(x)^2 g'(x)\right )+y'(x) \left (f(x)+g(x) y(x)^2\right )+y'(x)^2\)
 4.1920   \(y(x) y''(x)=2 y'(x)^2+y(x)^2\)
 4.1921   \(y(x) y''(x)=2 \left (y'(x)^2-y(x)^2\right )\)
 4.1922   \(y(x) y''(x)=-3 y(x) y'(x)+3 y'(x)^2+y(x)^2\)
 4.1923   \(y(x) y''(x)=a y'(x)^2\)
 4.1924   \(y(x) y''(x)=a y'(x)^2+b\)
 4.1925   \(y(x) y''(x)=a y'(x)^2+b y(x)^3\)
 4.1926   \(y(x) y''(x)=a y'(x)^2+\text{a0}+\text{a1} y(x)+\text{a2} y(x)^2+\text{a3} y(x)^3+\text{a3} y(x)^2+\text{a4} y(x)^4\)
 4.1927   \(y(x) y''(x)=a y'(x)^2+b y(x) y'(x)+c y(x)^2\)
 4.1928   \(y(x) y''(x)=\text{a3} y(x)^{a+1}+a y'(x)^2+\text{a1} y(x) y'(x)+\text{a2} y(x)^2\)
 4.1929   \(a y'(x)^2+f(x) y(x) y'(x)+g(x) y(x)^2+y(x) y''(x)=0\)
 4.1930   \(y(x) y''(x)+y'(x)^3=0\)
 4.1931   \(y(x) y''(x)+y'(x)^3-y'(x)^2=0\)
 4.1932   \(y(x) y''(x)=y'(x)^2 \left (y'(x) (-\sin (y(x)))-y(x) y'(x) \cos (y(x))+1\right )\)
 4.1933   \((1-y(x)) y''(x)+2 y'(x)^2=0\)
 4.1934   \((a+y(x)) y''(x)=y'(x)^2\)
 4.1935   \((a+y(x)) y''(x)+y'(x)^2=b\)
 4.1936   \((a+y(x)) y''(x)+b y'(x)^2=0\)
 4.1937   \((y(x)+x) y''(x)+y'(x)^2-y'(x)=0\)
 4.1938   \((x-y(x)) y''(x)+2 y'(x) \left (y'(x)+1\right )=0\)
 4.1939   \((x-y(x)) y''(x)=\left (y'(x)+1\right ) \left (y'(x)^2+1\right )\)
 4.1940   \((x-y(x)) y''(x)=f\left (y'(x)\right )\)
 4.1941   \(2 y(x) y''(x)=y'(x)^2\)
 4.1942   \(2 y(x) y''(x)+y'(x)^2+1=0\)
 4.1943   \(2 y(x) y''(x)=a+y'(x)^2\)
 4.1944   \(2 y(x) y''(x)=y'(x)^2+8 y(x)^3\)
 4.1945   \(2 y(x) y''(x)=y'(x)^2+8 y(x)^3+4 y(x)^2\)
 4.1946   \(2 y(x) y''(x)=y'(x)^2+4 (2 y(x)+x) y(x)^2\)
 4.1947   \(2 y(x) y''(x)=y(x)^2 (a+b y(x))+y'(x)^2\)
 4.1948   \(2 y(x) y''(x)=a y(x)^3+y'(x)^2-2 x y(x)^2-1\)
 4.1949   \(2 y(x) y''(x)=y(x)^2 (a x+b y(x))+y'(x)^2\)
 4.1950   \(2 y(x) y''(x)=y'(x)^2+3 y(x)^4\)
 4.1951   \(2 y(x) y''(x)=-a^2-4 \left (b-x^2\right ) y(x)^2+y'(x)^2+3 y(x)^4+8 x y(x)^3\)
 4.1952   \(2 y(x) y''(x)=-2 y(x)^2 \left (f'(x)+f(x)^2\right )-3 f(x) y(x) y'(x)+y'(x)^2+8 y(x)^3\)
 4.1953   \(2 y(x) y''(x)=2 x f(x) y(x)^2-4 y(x)^2 y'(x)+y'(x)^2-y(x)^4-1\)
 4.1954   \(2 y(x) y''(x)=3 y'(x)^2\)
 4.1955   \(2 y(x) y''(x)=3 y'(x)^2+4 y(x)^2\)
 4.1956   \(2 y(x) y''(x)=f(x) y(x)^2+3 y'(x)^2\)
 4.1957   \(2 y(x) y''(x)=6 y'(x)^2+\left (1-3 y(x)^2\right ) y(x)^2\)
 4.1958   \(2 y(x) y''(x)=6 y'(x)^2-y(x)^2 \left (a y(x)^3+1\right )\)
 4.1959   \(2 y(x) y''(x)=y'(x)^2 \left (y'(x)^2+1\right )\)
 4.1960   \(3 y(x) y''(x)=2 y'(x)^2+36 y(x)^2\)
 4.1961   \(3 y(x) y''(x)=5 y'(x)^2\)
 4.1962   \(4 y(x) y''(x)=3 y'(x)^2-4 y(x)\)
 4.1963   \(4 y(x) y''(x)=3 y'(x)^2+12 y(x)^2\)
 4.1964   \(4 y(x) y''(x)=a y(x)+b y(x)^2+c y(x)^3+3 y'(x)^2\)
 4.1965   \(5 y(x) y''(x)=y'(x)^2\)
 4.1966   \(12 y(x) y''(x)=15 y'(x)^2-8 y(x)^3\)
 4.1967   \(a y(x) y''(x)=(a-1) y'(x)^2\)
 4.1968   \(a (a+2)^2 y(x) y''(x)=a^2 (a+2) y(x)^3 f'(x)-a^2 f(x)^2 y(x)^4+a (a+2)^2 f(x) y(x)^2 y'(x)+(a-1) (a+2)^2 y'(x)^2\)
 4.1969   \(x y(x) y''(x)+x y'(x)^2+y(x) y'(x)=0\)
 4.1970   \(x y(x) y''(x)+x y'(x)^2=y(x) y'(x)\)
 4.1971   \(x y(x) y''(x)=x y'(x)^2-y(x) y'(x)\)
 4.1972   \(x y(x) y''(x)=x \left (\text{a0}+\text{a1} y(x)^4\right )+y(x) \left (\text{a2}+\text{a3} y(x)^2\right )+x y'(x)^2-y(x) y'(x)\)
 4.1973   \(x y(x) y''(x)+x y'(x)^2+2 y(x) y'(x)=0\)
 4.1974   \(x y(x) y''(x)+x y'(x)^2=3 y(x) y'(x)\)
 4.1975   \(a y(x) y'(x)+f(x)+x y(x) y''(x)+x y'(x)^2=0\)
 4.1976   \(x y(x) y''(x)=a y(x) y'(x)+x y'(x)^2+x y(x)^3\)
 4.1977   \(x y(x) y''(x)=a y(x) y'(x)+b^2 x y(x)^3+x y'(x)^2\)
 4.1978   \(x y(x) y''(x)+2 x y'(x)^2+y(x) y'(x)=0\)
 4.1979   \(x y(x) y''(x)-2 x y'(x)^2+y(x) y'(x)=0\)
 4.1980   \(x y(x) y''(x)-2 x y'(x)^2-y(x) y'(x)=0\)
 4.1981   \(x y(x) y''(x)=2 x y'(x)^2-(y(x)+1) y'(x)\)
 4.1982   \(a y(x) y'(x)+x y(x) y''(x)+2 x y'(x)^2=0\)
 4.1983   \(a y(x) y'(x)+x y(x) y''(x)-2 x y'(x)^2=0\)
 4.1984   \(x y(x) y''(x)-4 x y'(x)^2+4 y(x) y'(x)=0\)
 4.1985   \(a y'(x) \left (x y'(x)-y(x)\right )+x y(x) y''(x)=0\)
 4.1986   \(x (y(x)+x) y''(x)+x y'(x)^2+(x-y(x)) y'(x)=y(x)\)
 4.1987   \(2 x y(x) y''(x)=x y'(x)^2-y(x) y'(x)\)
 4.1988   \(x^2+x (2 y(x)+x) y''(x)+2 x y'(x)^2+4 (y(x)+x) y'(x)+2 y(x)=0\)
 4.1989   \(x^2 y(x) y''(x)+\left (x y'(x)-y(x)\right )^2=0\)
 4.1990   \(x^2 y(x) y''(x)+\left (x y'(x)-y(x)\right )^2=3 y(x)^2\)
 4.1991   \(x^2 y(x) y''(x)=a x y(x) y'(x)+a y(x)^2+2 x^2 y'(x)^2\)
 4.1992   \(a x^2 y'(x)^2+b x y(x) y'(x)+c y(x)^2+x^2 y(x) y''(x)\)
 4.1993   \(x^2 (1-y(x)) y''(x)+2 x^2 y'(x)^2-2 x (1-y(x)) y'(x)+2 (1-y(x))^2 y(x)=0\)
 4.1994   \(x^2 (x-y(x)) y''(x)=\left (x y'(x)-y(x)\right )^2\)
 4.1995   \(x^2 (x-y(x)) y''(x)+\left (x y'(x)-y(x)\right )^2=0\)
 4.1996   \(x^2 (x-y(x)) y''(x)=a \left (x y'(x)-y(x)\right )^2\)
 4.1997   \(2 x^2 y(x) y''(x)=x^2 y'(x)^2-y(x)^2\)
 4.1998   \(2 x^2 y(x) y''(x)=x^2 y'(x)^2+2 x y(x) y'(x)-4 y(x)^2\)
 4.1999   \(x^3 y(x) y''(x)+x^3 y'(x)^2+6 x^2 y(x) y'(x)+3 x y(x)^2=a\)
 4.2000   \(x (x+1)^2 y(x) y''(x)=a (x+2) y(x)^2-2 \left (x^2+1\right ) y(x) y'(x)+x (x+1)^2 y'(x)^2\)
 4.2001   \(8 \left (1-x^3\right ) y(x) y''(x)+4 \left (1-x^3\right ) y'(x)^2-12 x^2 y(x) y'(x)+3 x y(x)^2=0\)
 4.2002   \(\sqrt{a^2+x^2} \left (b y'(x)^2+y(x) y''(x)\right )=y(x) y'(x)\)
 4.2003   \(\sqrt{a^2-x^2} \left (x y(x) y''(x)-x y'(x)^2-y(x) y'(x)\right )=b x y'(x)^2\)
 4.2004   \(\text{f0}(x) y(x) y''(x)+\text{f1}(x) y'(x)^2+\text{f2}(x) y(x) y'(x)+\text{f3}(x) y(x)^2=0\)
 4.2005   \(4 f(x) y(x) y''(x)=y'(x) \left (2 f'(x)-6 f(x) y(x)^2\right )+2 y(x)^3 f'(x)+3 f(x) g(x) y(x)^2+3 f(x) y'(x)^2-f(x) y(x)^4+4 f(x)^2 y(x)\)
 4.2006   \(y(x)^2 y''(x)=a\)
 4.2007   \(a x+y(x)^2 y''(x)+y(x) y'(x)^2=0\)
 4.2008   \(y(x)^2 y''(x)+y(x) y'(x)^2=a+b x\)
 4.2009   \(\left (y(x)^2+1\right ) y''(x)+(1-2 y(x)) y'(x)^2=0\)
 4.2010   \(\left (y(x)^2+1\right ) y''(x)=3 y(x) y'(x)^2\)
 4.2011   \(\left (y(x)^2+1\right ) y''(x)=(a+3 y(x)) y'(x)^2\)
 4.2012   \(\left (y(x)^2+1\right ) y''(x)+y'(x) \left (y'(x)^2+1\right )=0\)
 4.2013   \(\left (y(x)^2+x\right ) y''(x)+2 y(x) y'(x)^2+2 y'(x)=a\)
 4.2014   \(\left (y(x)^2+x\right ) y''(x)=2 \left (x-y(x)^2\right ) y'(x)^3-y'(x) \left (4 y(x) y'(x)+1\right )\)
 4.2015   \(\left (x^2+y(x)^2\right ) y''(x)=\left (y(x)^2+1\right ) \left (x y'(x)-y(x)\right )\)
 4.2016   \(\left (x^2+y(x)^2\right ) y''(x)=2 \left (y(x)^2+1\right ) \left (x y'(x)-y(x)\right )\)
 4.2017   \(2 (1-y(x)) y(x) y''(x)=(1-2 y(x)) y'(x)^2\)
 4.2018   \(2 (1-y(x)) y(x) y''(x)=f(x) (1-y(x)) y(x) y'(x)+(1-2 y(x)) y'(x)^2\)
 4.2019   \(2 (1-y(x)) y(x) y''(x)=(1-3 y(x)) y'(x)^2\)
 4.2020   \(2 (1-y(x)) y(x) y''(x)=4 y(x) y'(x) (f(x)+g(x) y(x))+(1-3 y(x)) y'(x)^2\)
 4.2021   \(2 (1-y(x)) y(x) y''(x)=-4 y(x)^2 (1-y(x)) \left (f'(x)+f(x)^2+g'(x)-g(x)^2\right )-4 y(x) y'(x) (f(x)+g(x) y(x))+(1-y(x))^3 \left (-\left (\text{F0}(x)^2-\text{G0}(x)^2 y(x)^2\right )\right )+(1-3 y(x)) y'(x)^2\)
 4.2022   \(3 (1-y(x)) y(x) y''(x)=2 (1-2 y(x)) y'(x)^2\)
 4.2023   \(4 (1-y(x)) y(x) y''(x)=3 (1-2 y(x)) y'(x)^2\)
 4.2024   \(x y(x)^2 y''(x)=a\)
 4.2025   \(x y(x)^2 y''(x)=\left (a-y(x)^2\right ) y'(x)+x y(x) y'(x)^2\)
 4.2026   \(x^2 y(x)^2 y''(x)=\left (x^2+y(x)^2\right ) \left (x y'(x)-y(x)\right )\)
 4.2027   \(\left (a^2-x^2\right ) \left (a^2-y(x)^2\right ) y''(x)+\left (a^2-x^2\right ) y(x) y'(x)^2=x \left (a^2-y(x)^2\right ) y'(x)\)
 4.2028   \((1-y(x))^3 \left (\text{a0}+\text{a1} y(x)^2\right )+\text{a2} x (1-y(x)) y(x)^2+\text{a3} x^3 y(x)^2 (y(x)+1)+2 x^2 (1-y(x)) y(x) y''(x)-x^2 (1-3 y(x)) y'(x)^2+2 x (1-y(x)) y(x) y'(x)=0\)
 4.2029   \(x^3 y(x)^2 y''(x)+(y(x)+x) \left (x y'(x)-y(x)\right )^3=0\)
 4.2030   \(y(x)^3 y''(x)=a^2\)
 4.2031   \(y(x) \left (y(x)^2+1\right ) y''(x)+\left (1-3 y(x)^2\right ) y'(x)^2=0\)
 4.2032   \(2 y(x)^3 y''(x)+y(x)^2 y'(x)^2=2\)
 4.2033   \(2 (1-y(x)) y(x) (a-y(x)) y''(x)+(-(1-y(x)) (a-y(x))+y(x) (a-y(x))+(1-y(x)) y(x)) y'(x)^2=\text{a0} y(x)^2 \left (1-y(x)^2\right ) (a-y(x))^2+\text{a2} y(x)^2 (a-y(x))^2+\text{a3} (1-y(x))^2 (a-y(x))^2+\text{a1} (1-y(x))^2 y(x)^2\)
 4.2034   \(2 (a-y(x)) (b-y(x)) (c-y(x)) y''(x)+y'(x)^2 ((a-y(x)) (b-y(x))+(a-y(x)) (c-y(x))+(b-y(x)) (c-y(x)))=\text{a0} (a-y(x))^2 (b-y(x))^2 (c-y(x))^2+2 \text{a2} (a-y(x))^2 (c-y(x))^2+\text{a3} (a-y(x))^2 (b-y(x))^2+\text{a1} (b-y(x))^2 (c-y(x))^2\)
 4.2035   \(2 (1-x) x (1-y(x)) (x-y(x)) y(x) y''(x)=2 (1-y(x)) \left (x^2-2 x y(x)+y(x)\right ) y(x) y'(x)+(1-x) x \left (3 y(x)^2-2 x y(x)-2 y(x)+x\right ) y'(x)^2-\left (1-y(x)^2\right ) y(x)^2\)
 4.2036   \(2 (1-x) x (1-y(x)) (x-y(x)) y(x) y''(x)=f(x) ((1-y(x)) (x-y(x)) y(x))^{3/2}+2 (1-y(x)) \left (x^2-2 x y(x)+y(x)\right ) y(x) y'(x)+(1-x) x \left (3 y(x)^2-2 x y(x)-2 y(x)+x\right ) y'(x)^2-\left (1-y(x)^2\right ) y(x)^2\)
 4.2037   \(2 (1-x)^2 x^2 (1-y(x)) (x-y(x)) y(x) y''(x)=\text{a0} x (x-y(x))^2 (1-y(x))^2+\text{a1} (1-x) (x-y(x))^2 y(x)^2+(\text{a2}-1) (1-x) x y(x)^2 (1-y(x))^2+\text{a3} (x-y(x))^2 y(x)^2 (1-y(x))^2+2 (1-x) x y(x) \left (x^2-2 x y(x)+y(x)\right ) (1-y(x))^2 y'(x)+(1-x)^2 x^2 \left (3 y(x)^2-2 x y(x)-2 y(x)+x\right ) y'(x)^2\)
 4.2038   \(b \sqrt{\left (1-y(x)^2\right ) \left (1-a^2 y(x)^2\right )} y'(x)^2+\left (1-y(x)^2\right ) \left (1-a^2 y(x)^2\right ) y''(x)+y(x) \left (-2 a^2 y(x)^2+a^2+1\right )=0\)
 4.2039   \(a^2 y(x)+\left (x^2+y(x)^2\right )^2 y''(x)=0\)
 4.2040   \(y''(x) \left (a+2 b x+c x^2+y(x)^2\right )^2+A y(x)=0\)
 4.2041   \(\text{f0}(y(x)) y''(x)+\text{f1}(y(x)) y'(x)^2+\text{f2}(y(x)) y'(x)+\text{f3}(y(x))=0\)
 4.2042   \(\sqrt{y(x)} y''(x)=a\)
 4.2043   \(\sqrt{y(x)} y''(x)=2 (a+b x)\)
 4.2044   \(y''(x) X(x,y(x))^3=1\)
 4.2045   \(y''(x) \left (\text{a0}+\text{a1} \sin ^2(y(x))\right )+\text{a2} y(x) \left (\text{a1} \sin ^2(y(x))+\text{a3}\right )+\text{a1} y'(x)^2+\text{a1} y'(x)^2 \sin (y(x)) \cos (y(x))=0\)
 4.2046   \(y(x) y''(x) (1-\log (y(x)))+y'(x)^2 (\log (y(x))+1)=0\)
 4.2047   \(f(y(x)) y''(x)=y'(x)^2 f'(y(x))-g(x) f(y(x)) y'(x)-h(x) f(y(x))^2\)
 4.2048   \(f(y(x)) y''(x)=f(y(x))^2 \text{F0}\left (x,\frac{y'(x)}{f(y(x))}\right )+y'(x)^2 f'(y(x))\)
 4.2049   \(a y'(x)^2 f'(y(x))+f(y(x)) y''(x)+g(y(x))=0\)
 4.2050   \(y'(x) y''(x)=a^2 x\)
 4.2051   \(y'(x) y''(x)=x^2 y(x) y'(x)+x y(x)^2\)
 4.2052   \(\left (2 x^2 y'(x)+y(x)^2\right ) y''(x)+2 (y(x)+x) y'(x)^2+x y'(x)+y(x)=0\)
 4.2053   \(a y(x)^2+x^3 y'(x) y''(x)=0\)
 4.2054   \(\text{f1} y'(x) y''(x)+\text{f2} y(x) y''(x)+\text{f3} y'(x)^2+\text{f4} y(x) y'(x)+\text{f5} y(x)^2=0\)
 4.2055   \(3 y(x) y'(x) y''(x)=y'(x)^3-1\)
 4.2056   \(\left (x^2+2 y(x)^2 y'(x)\right ) y''(x)+2 y(x) y'(x)^3+3 x y'(x)+y(x)=0\)
 4.2057   \(\left (x-y'(x)^2\right ) y''(x)=x^2-y'(x)\)
 4.2058   \(\left (y'(x)^2+y(x)^2\right ) y''(x)+y(x)^3=0\)
 4.2059   \(y''(x) \left (a \left (x y'(x)-y(x)\right )+y'(x)^2\right )=b\)
 4.2060   \(4 y(x) y'(x)^2 y''(x)=y'(x)^4+3\)
 4.2061   \(y''(x) f\left (y'(x)\right )+g(y(x)) y'(x)+h(x)=0\)
 4.2062   \(y''(x)^2=a+b y(x)\)
 4.2063   \(y''(x)^2=a+b y'(x)^2\)
 4.2064   \(y''(x)^2-x y''(x)+y'(x)=0\)
 4.2065   \(a^2 y''(x)^2=\left (y'(x)^2+1\right )^3\)
 4.2066   \(a x+x y''(x)^2-2 y'(x) y''(x)=0\)
 4.2067   \(\left (x y''(x)-y'(x)\right )^2=y''(x)^2+1\)
 4.2068   \(2 \left (x^2+1\right ) y''(x)^2+2 \left (x-y'(x)\right ) y'(x)-x \left (4 y'(x)+x\right ) y''(x)=2 y(x)\)
 4.2069   \(3 x^2 y''(x)^2+4 y'(x)^2-2 \left (3 x y'(x)+y(x)\right ) y''(x)=0\)
 4.2070   \((2-9 x) x^2 y''(x)^2+6 y(x) y''(x)-6 (1-6 x) x y'(x) y''(x)=36 x y'(x)^2\)
 4.2071   \(\text{f0} y''(x)^2+\text{f1} y'(x) y''(x)+\text{f2} y(x) y''(x)+\text{g0} y'(x)^2+\text{g1} y(x) y'(x)+h y(x)^2=0\)
 4.2072   \(y(x) y''(x)+4 y(x) y'(x)^3-y'(x)^2=0\)
 4.2073   \(\left (y(x) y''(x)+y'(x)^2+1\right )^2=\left (y'(x)^2+1\right )^3\)
 4.2074   \(y''(x)^2 \left (a^2-b^2 y(x)^2\right )+y'(x)^2 \left (1-b^2 y'(x)^2\right )+2 b^2 y(x) y'(x)^2 y''(x)=0\)
 4.2075   \(\left (x^2 y(x) y''(x)+x^2 \left (-y'(x)^2\right )+y(x)^2\right )^2=4 x y(x) \left (x y'(x)-y(x)\right )^3\)
 4.2076   \(y''(x)^3=12 y'(x) \left (x y''(x)-2 y'(x)\right )\)
 4.2077   \(32 y''(x) \left (x y''(x)-y'(x)\right )^3+\left (2 y(x) y''(x)-y'(x)^2\right )^3=0\)
 4.2078   \(f\left (y''(x)\right )+x y''(x)=y'(x)\)
 4.2079   \(y'(x) f\left (\frac{y''(x)}{y'(x)}\right )=y'(x)^2-y(x) y''(x)\)
 4.2080   \(f\left (y''(x),y'(x)-x y''(x),\frac{1}{2} x^2 y''(x)-x y'(x)+y(x)\right )=0\)
 4.2081   \(f\left (x,y''(x)\right )=0\)
 4.2082   \(f\left (y(x),y''(x)\right )=0\)
 4.2083   \(f\left (y'(x),y''(x)\right )=0\)
 4.2084   \(f\left (x,y'(x),y''(x)\right )=0\)
 4.2085   \(f\left (y(x),y'(x),y''(x)\right )=0\)
 4.2086   \(y'''(x)=0\)
 4.2087   \(y'''(x)=\cos (x)+1\)
 4.2088   \(y'''(x)+\sin (x)=0\)
 4.2089   \(y'''(x)=\sin ^3(x)\)
 4.2090   \(y'''(x)=y(x)\)
 4.2091   \(y'''(x)=x^2+y(x)\)
 4.2092   \(y'''(x)=y(x)+e^x x+\cos ^2(x)\)
 4.2093   \(y'''(x)+a y(x)=0\)
 4.2094   \(y'''(x)=x y(x)\)
 4.2095   \(y'''(x)+y'(x)=0\)
 4.2096   \(y'''(x)=y'(x)\)
 4.2097   \(y'''(x)+y'(x)=x^3+\cos (x)\)
 4.2098   \(y'''(x)-2 y'(x)+4 y(x)=0\)
 4.2099   \(y'''(x)-2 y'(x)+4 y(x)=e^x \cos (x)\)
 4.2100   \(y'''(x)-3 y'(x)+2 y(x)=0\)
 4.2101   \(y'''(x)-3 y'(x)+2 y(x)=3 e^x\)
 4.2102   \(y'''(x)-3 y'(x)+2 y(x)=e^x x^2\)
 4.2103   \(y'''(x)-4 y'(x)=x^2-3 e^{2 x}\)
 4.2104   \(y'''(x)-7 y'(x)+6 y(x)=0\)
 4.2105   \(y'''(x)=a^2 y(x)\)
 4.2106   \(y'''(x)+2 x y'(x)+y(x)=0\)
 4.2107   \(y'''(x)+2 a x y'(x)+a y(x)=0\)
 4.2108   \(y'''(x)+y(x) f'(x)+2 f(x) y'(x)=0\)
 4.2109   \(y'''(x)-y''(x)+y'(x)=0\)
 4.2110   \(y'''(x)-y''(x)+y'(x)+y(x)=0\)
 4.2111   \(y'''(x)+y''(x)+y'(x)-3 y(x)=0\)
 4.2112   \(y'''(x)-y''(x)-2 y'(x)=0\)
 4.2113   \(y'''(x)-y''(x)-2 y'(x)=e^{-x}\)
 4.2114   \(y'''(x)+y''(x)+4 y'(x)+4 y(x)=0\)
 4.2115   \(y'''(x)+y''(x)+2 y'(x)+4 y(x)=\sin (2 x)\)
 4.2116   \(y'''(x)+y''(x)-7 y'(x)-15 y(x)=0\)
 4.2117   \(y'''(x)+2 y''(x)+y'(x)=0\)
 4.2118   \(y'''(x)+2 y''(x)+y'(x)=(x-1) x\)
 4.2119   \(y'''(x)-2 y''(x)+y'(x)=e^x\)
 4.2120   \(y'''(x)-2 y''(x)-y'(x)+2 y(x)=\sinh (x)\)
 4.2121   \(y'''(x)-2 y''(x)-3 y'(x)=0\)
 4.2122   \(y'''(x)-2 y''(x)-3 y'(x)=3 x^2+\sin (x)\)
 4.2123   \(y'''(x)-2 y''(x)-3 y'(x)=3 x^2+e^{-x}\)
 4.2124   \(y'''(x)-2 y''(x)+3 y'(x)+10 y(x)=0\)
 4.2125   \(y'''(x)-a^2 y'(x)+2 a^2 y(x)-2 y''(x)=0\)
 4.2126   \(y'''(x)-a^2 y'(x)+2 a^2 y(x)-2 y''(x)=\sinh (x)\)
 4.2127   \(y'''(x)-3 y''(x)+4 y(x)=0\)
 4.2128   \(y'''(x)+3 y''(x)-y'(x)-3 y(x)=0\)
 4.2129   \(y'''(x)-3 y''(x)-y'(x)+3 y(x)=x^2\)
 4.2130   \(y'''(x)+3 y''(x)-y'(x)-3 y(x)=\cosh (x)\)
 4.2131   \(y'''(x)+3 y''(x)+3 y'(x)+y(x)=0\)
 4.2132   \(y'''(x)+3 y''(x)+3 y'(x)+y(x)=e^{-x} x\)
 4.2133   \(y'''(x)-3 y''(x)+3 y'(x)-y(x)=x \left (1-e^x x^2\right )\)
 4.2134   \(y'''(x)+3 y''(x)+3 y'(x)+y(x)=e^{-x} \left (2-x^2\right )\)
 4.2135   \(y'''(x)-3 y''(x)+4 y'(x)-2 y(x)=0\)
 4.2136   \(y'''(x)-3 y''(x)+4 y'(x)-2 y(x)=e^x+\cos (x)\)
 4.2137   \(y'''(x)-4 y''(x)+5 y'(x)-2 y(x)=0\)
 4.2138   \(y'''(x)-4 y''(x)+5 y'(x)-2 y(x)=x\)
 4.2139   \(y'''(x)-4 y''(x)+6 y'(x)-4 y(x)=0\)
 4.2140   \(y'''(x)-6 y''(x)+9 y'(x)=0\)
 4.2141   \(y'''(x)-6 y''(x)+12 y'(x)-8 y(x)=e^{2 x} x^2\)
 4.2142   \(y'''(x)+a^3 (-y(x))+3 a^2 y'(x)-3 a y''(x)=0\)
 4.2143   \(y'''(x)+a^3 (-y(x))+3 a^2 y'(x)-3 a y''(x)=e^{a x}\)
 4.2144   \(y'''(x)=a y''(x)\)
 4.2145   \(y'''(x)+\text{a1} y''(x)+\text{a2} y'(x)+\text{a3} y(x)=0\)
 4.2146   \(y'''(x)-2 \left (-2 a-4 x^2+1\right ) y'(x)-8 a x y(x)-6 x y''(x)=0\)
 4.2147   \(y'''(x)+a^3 x^3 y(x)+3 a^2 x^2 y'(x)+3 a x y''(x)=0\)
 4.2148   \(y'''(x)+x^2 \left (-y''(x)\right )+2 x y'(x)-2 y(x)=0\)
 4.2149   \(y'''(x)+y''(x) (2 \cot (x)+\csc (x))-y'(x)=\cot (x)\)
 4.2150   \(y'''(x)-\sin (x) y''(x)-2 \cos (x) y'(x)+y(x) \sin (x)=\log (x)\)
 4.2151   \(y'''(x)+y'(x) \left (2 f'(x)^2+f'(x)+4 g(x)\right )+2 y(x) \left (2 f(x) g(x)+g'(x)\right )+3 f(x) y''(x)=0\)
 4.2152   \(y'''(x)+f(x) y''(x)+f(x) y(x)+y'(x)=0\)
 4.2153   \(4 y'''(x)-3 y'(x)+y(x)=0\)
 4.2154   \(4 y'''(x)-8 y''(x)-11 y'(x)-3 y(x)=0\)
 4.2155   \(4 y'''(x)-8 y''(x)-11 y'(x)-3 y(x)+18 e^x=0\)
 4.2156   \(x y'''(x)=2\)
 4.2157   \(x y'''(x)+3 y'(x)+x y(x)=0\)
 4.2158   \(x y'''(x)-y''(x)+x y'(x)-y(x)=0\)
 4.2159   \(x y'''(x)-y''(x)-x y'(x)+y(x)=0\)
 4.2160   \(x y'''(x)-y''(x)-x y'(x)+y(x)=1-x^2\)
 4.2161   \(x y'''(x)+x^2 (-y(x))+3 y''(x)=0\)
 4.2162   \(x y'''(x)-\left (3-x^2\right ) y''(x)+4 x y'(x)+2 y(x)=0\)
 4.2163   \((1-2 x) y'''(x)-(x+4) y''(x)-2 y'(x)=0\)
 4.2164   \(x^2 y'''(x)+a x^2 y(x)-6 y'(x)=0\)
 4.2165   \(x^2 y'''(x)+2 x y''(x)=a\)
 4.2166   \(x^2 y'''(x)+\left (x^2+2\right ) y'(x)+4 x y''(x)+3 x y(x)=f(x)\)
 4.2167   \(x^2 y'''(x)+5 x y''(x)+4 y'(x)=\log (x)\)
 4.2168   \(x^2 y'''(x)+6 x y''(x)+6 y'(x)=0\)
 4.2169   \(x^2 y'''(x)+a x^2 y(x)+6 x y''(x)+6 y'(x)=0\)
 4.2170   \(x^2 y'''(x)-2 (n+1) x y''(x)+6 n y'(x)=0\)
 4.2171   \(x^2 y'''(x)+\left (6-2 x^3\right ) y'(x)+2 x^3 y(x)+\left (6-x^2\right ) x y''(x)=0\)
 4.2172   \(\left (x^2+1\right ) y'''(x)+8 x y'(x)+10 y'(x)=0\)
 4.2173   \(\left (x^2+2\right ) y'''(x)+\left (x^2+2\right ) y'(x)-2 x y''(x)-2 x y(x)=0\)
 4.2174   \(\left (x^2-2 x+2\right ) y'''(x)+x^2 \left (-y''(x)\right )+2 x y'(x)-2 y(x)=0\)
 4.2175   \((x+2)^2 y'''(x)+(x+2) y''(x)+y'(x)=0\)
 4.2176   \(4 x^2 y'''(x)+8 x y''(x)+y'(x)=0\)
 4.2177   \(x (\text{a0}+\text{b0} x) y'''(x)+(\text{a1}+\text{b1} x) y''(x)+x y'(x)+y(x)=f(x)\)
 4.2178   \(x^3 y'''(x)=a\)
 4.2179   \(x^3 y'''(x)+x y'(x)-y(x)=0\)
 4.2180   \(x^3 y'''(x)+x y'(x)-y(x)=x \log (x)\)
 4.2181   \(x^3 y'''(x)-x^2 y''(x)+2 x y'(x)-2 y(x)=0\)
 4.2182   \(x^3 y'''(x)-x^2 y''(x)+2 x y'(x)-2 y(x)=x \left (x^2+3\right )\)
 4.2183   \(x^3 y'''(x)+x^2 y''(x)+3 x y'(x)-8 y(x)=0\)
 4.2184   \(x^3 y'''(x)-x^2 y''(x)+x y'(x)=0\)
 4.2185   \(x^3 y'''(x)+2 x^2 y''(x)+2 y(x)=0\)
 4.2186   \(x^3 y'''(x)+2 x^2 y''(x)-x y'(x)+y(x)=0\)
 4.2187   \(x^3 y'''(x)+3 x^2 y''(x)=a\)
 4.2188   \(x^3 y'''(x)+3 x^2 y''(x)-2 x y'(x)+2 y(x)=0\)
 4.2189   \(x^3 y'''(x)-3 x^2 y''(x)+7 x y'(x)-8 y(x)=0\)
 4.2190   \(x^3 y'''(x)+\left (1-a^2\right ) x y'(x)+3 x^2 y''(x)=0\)
 4.2191   \(x^3 y'''(x)+4 x^2 y''(x)-8 x y'(x)+8 y(x)=0\)
 4.2192   \(x^3 y'''(x)-4 x^2 y''(x)+\left (x^2+8\right ) x y'(x)-2 \left (x^2+4\right ) y(x)=0\)
 4.2193   \(x^3 y'''(x)-\left (12-a x^3\right ) y(x)+6 x^2 y''(x)=0\)
 4.2194   \(x^3 y'''(x)+x^2 \log (x) y''(x)+2 x y'(x)-y(x)=2 x^3\)
 4.2195   \(\left (x^3+1\right ) y'''(x)+9 x^2 y''(x)+18 x y'(x)+6 y(x)=0\)
 4.2196   \(x \left (x^2+1\right ) y'''(x)+3 \left (2 x^2+1\right ) y''(x)-12 y(x)=0\)
 4.2197   \(x \left (1-x^2\right ) y'''(x)+\left (3-8 x^2\right ) y''(x)-14 x y'(x)-4 y(x)=0\)
 4.2198   \(x \left (x^2-2 x+2\right ) y'''(x)+\left (-x^3+3 x^2-6 x+6\right ) y''(x)=0\)
 4.2199   \((x+1)^3 y'''(x)+(x+1)^2 y''(x)+3 (x+1) y'(x)-8 y(x)=0\)
 4.2200   \(x^2 (y(x)+3) y'''(x)-3 (x+2) x y''(x)+6 (x+1) y'(x)-6 y(x)=0\)
 4.2201   \(4 x^3 y'''(x)+x y'(x)-y(x)=0\)
 4.2202   \((1-2 x)^3 y'''(x)+(1-2 x) y'(x)+2 y(x)=0\)
 4.2203   \(x^4 y'''(x)+2 x^3 y''(x)+2 x y(x)=10 \left (x^2+1\right )\)
 4.2204   \(x^4 y'''(x)+2 x^3 y''(x)-x^2 y'(x)+x y(x)=1\)
 4.2205   \(\left (x^2+1\right ) x^2 y'''(x)+8 x^3 y''(x)+10 x^2 y'(x)=3 x^2+2 x^2 \log (x)-1\)
 4.2206   \((x+1) x^3 y'''(x)-2 (2 x+1) x^2 y''(x)+2 (5 x+2) x y'(x)-4 (3 x+1) y(x)=0\)
 4.2207   \(4 x^4 y'''(x)-4 x^3 y''(x)+4 x^2 y'(x)=1\)
 4.2208   \(\left (x^2+1\right ) x^3 y'''(x)-2 \left (2 x^2+1\right ) x^2 y''(x)+2 \left (5 x^2+2\right ) x y'(x)-4 \left (3 x^2+1\right ) y(x)=0\)
 4.2209   \((a-x)^3 (b-x)^3 y'''(x)=c y(x)\)
 4.2210   \((x+\sin (x)) y'''(x)+3 (\cos (x)+1) y''(x)-3 \sin (x) y'(x)-y(x) \cos (x)+\sin (x)=0\)
 4.2211   \(y''''(x)=0\)
 4.2212   \(y''''(x)=x \cos (x)\)
 4.2213   \(y''''(x)+4 e^{-x} \cos (x)=0\)
 4.2214   \(y''''(x)=y(x)+\cos (x)\)
 4.2215   \(y''''(x)=y(x)+e^x \cos (x)\)
 4.2216   \(y''''(x)+a y(x)=0\)
 4.2217   \(y''''(x)=a^4 y(x)+x^3\)
 4.2218   \(y''''(x)+y''(x)+y(x)=0\)
 4.2219   \(y''''(x)+2 y''(x)+y(x)=0\)
 4.2220   \(y''''(x)-2 y''(x)+y(x)=0\)
 4.2221   \(y''''(x)+2 y''(x)+y(x)=\cos (x)\)
 4.2222   \(y''''(x)-2 y''(x)+y(x)=\cos (x)\)
 4.2223   \(y''''(x)+2 y''(x)+y(x)=24 x \sin (x)\)
 4.2224   \(y''''(x)-2 y''(x)+y(x)=e^x+4\)
 4.2225   \(y''''(x)-2 y''(x)-8 y(x)=0\)
 4.2226   \(y''''(x)+3 y''(x)-4 y(x)=0\)
 4.2227   \(y''''(x)+5 y''(x)+6 y(x)=0\)
 4.2228   \(y''''(x)-12 y''(x)+27 y(x)=0\)
 4.2229   \(y''''(x)+a^2 y''(x)=0\)
 4.2230   \(y''''(x)+a^4 y(x)+2 a^2 y''(x)=0\)
 4.2231   \(y''''(x)+a^4 y(x)+2 a^2 y''(x)=\cosh (a x)\)
 4.2232   \(y''''(x)+\left (a^2+b^2\right ) y''(x)+a^2 b^2 y(x)=0\)
 4.2233   \(y''''(x)+3 y(x) \left (f''(x)+3 f(x)^2\right )+10 f'(x) y'(x)+10 f(x) y''(x)=0\)
 4.2234   \(-y'''(x)+y''''(x)-3 y''(x)+5 y'(x)-2 y(x)=0\)
 4.2235   \(-y'''(x)+y''''(x)-3 y''(x)+5 y'(x)-2 y(x)=e^{3 x}\)
 4.2236   \(-2 y'''(x)+y''''(x)+y(x)^2=0\)
 4.2237   \(-2 y'''(x)+y''''(x)+y(x)^2=x^3\)
 4.2238   \(2 y'''(x)+y''''(x)-2 y'(x)-y(x)=0\)
 4.2239   \(-2 y'''(x)+y''''(x)+2 y''(x)-2 y'(x)+y(x)=0\)
 4.2240   \(2 y'''(x)+y''''(x)+3 y''(x)+2 y'(x)+y(x)=0\)
 4.2241   \(2 y'''(x)+y''''(x)-3 y''(x)-4 y'(x)+4 y(x)=0\)
 4.2242   \(-3 y'''(x)+y''''(x)+y''(x)-y'(x)=0\)
 4.2243   \(-4 y'''(x)+y''''(x)+6 y''(x)-4 y'(x)+y(x)=0\)
 4.2244   \(-4 y'''(x)+y''''(x)+12 y''(x)-16 y'(x)+16 y(x)=0\)
 4.2245   \(4 a x y'''(x)+y''''(x)+a^4 x^4 y(x)+4 a^3 x^3 y'(x)+6 a^2 x^2 y''(x)=0\)
 4.2246   \(2 \left (y''''(x)+\left (a^2+b^2\right ) y''(x)+a^2 b^2 y(x)\right )=\cos (a x)+\cos (b x)\)
 4.2247   \(-12 y'''(x)+4 y''''(x)+11 y''(x)-3 y'(x)=0\)
 4.2248   \(3 y'''(x)+x y''''(x)=0\)
 4.2249   \(5 y'''(x)+x y''''(x)=0\)
 4.2250   \(x^2 y''''(x)=2 y'''(x)\)
 4.2251   \(x^2 y''''(x)=2 y''(x)\)
 4.2252   \(x^2 y''''(x)+4 x y'''(x)+2 y''(x)=0\)
 4.2253   \(x^2 y''''(x)+6 x y'''(x)+6 y''(x)=0\)
 4.2254   \(x^2 y''''(x)+8 x y'''(x)+12 y''(x)=0\)
 4.2255   \(x^2 y''''(x)+8 x y'''(x)+a^2 (-y(x))+12 y''(x)=0\)
 4.2256   \((a+x)^2 y''''(x)=1\)
 4.2257   \(32 x (a-b+2) y'''(x)+16 x^2 y''''(x)+16 (a-b+1) (a-b+2) y''(x)+c^4 (-y(x))=0\)
 4.2258   \(x^3 y''''(x)+2 x^2 y'''(x)+a^4 \left (-x^3\right ) y(x)-x y''(x)=0\)
 4.2259   \(x^3 y''''(x)+6 x^2 y'''(x)+6 x y''(x)=0\)
 4.2260   \(x^2 (a+b+c+3) y'''(x)+x^3 y''''(x)+x (a b+a c+a+b c+b+c+1) y''(x)-y'(x) (x-a b c)-k y(x)=0\)
 4.2261   \(x^4 y''''(x)+6 x^3 y'''(x)+4 x^2 y''(x)-2 x y'(x)-4 y(x)=0\)
 4.2262   \(x^4 y''''(x)+6 x^3 y'''(x)+9 x^2 y''(x)+3 x y'(x)+y(x)=0\)
 4.2263   \(x^4 y''''(x)+8 x^3 y'''(x)+12 x^2 y''(x)=0\)
 4.2264   \(x^4 y''''(x)+8 x^3 y'''(x)+a y(x)+12 x^2 y''(x)=0\)
 4.2265   \(\text{A1} x^3 y'''(x)+x^4 y''''(x)+\text{A2} x^2 y''(x)+\text{A3} x y'(x)+\text{A4} y(x)=0\)
 4.2266   \(16 a^4 x^4 y''''(x)-32 (1-2 a) a^2 x^3 y'''(x)+16 (1-2 a) (1-a) a^2 x^2 y''(x)-b^4 x^{2/a} y(x)=0\)
 4.2267   \(4 \left (e^x+2\right ) y'''(x)+\left (2 x+e^x\right ) y''''(x)+6 e^x y''(x)+4 e^x y'(x)+e^x y(x)=0\)
 4.2268   \(-y'''(x)+y'''''(x)-2 y''(x)+2 y'(x)=0\)
 4.2269   \(2 y'''(x)+y'''''(x)+y'(x)=0\)
 4.2270   \(2 y'''(x)+y'''''(x)+y'(x)=a x+b \cos (x)+c \sin (x)\)
 4.2271   \(y''''''(x)=0\)
 4.2272   \(y''''''(x)+a y(x)=0\)
 4.2273   \(2 y'''(x)+y''''''(x)+y(x)=0\)
 4.2274   \(y''''''''(x)=y(x)\)
 4.2275   \(y''''''''(x)-2 y''''+y(x)=0\)
 4.2276   \(y^{(2 n)}(x)=a^{2 n} y(x)\)
 4.2277   \(x^n y^{(2 n)}(x)=y(x)\)
 4.2278   \(x^{n+\frac{1}{2}} y^{(2 n+1)}(x)=y(x)\)
 4.2279   \(y^{(n)}(x)=e^x x\)
 4.2280   \(a m x^{m-1} y(x)+a x^m y'(x)+y^{(n)}(x)=0\)
 4.2281   \((a-x)^n (b-x)^n y^{(n)}(x)=c y(x)\)
 4.2282   \(y'''(x)=y'(x) \left (y'(x)+1\right )\)
 4.2283   \(y'''(x)+y'(x)^2-y(x) y'(x)=0\)
 4.2284   \(y'''(x)+a y(x) y''(x)=0\)
 4.2285   \(x^2 y'''(x)+x y''(x)-(1-2 x y(x)) y'(x)+y(x)^2=f(x)\)
 4.2286   \(x^2 y'''(x)-x (1-y(x)) y''(x)+x y'(x)^2+(1-y(x)) y'(x)=0\)
 4.2287   \(y(x) y'''(x)+y(x)^3 y'(x)-y'(x) y''(x)=0\)
 4.2288   \((a+y(x)) y'''(x)+3 y'(x) y''(x)=0\)
 4.2289   \(x^3 y(x) y'''(x)+3 x^3 y'(x) y''(x)+9 x^2 y(x) y''(x)+9 x^2 y'(x)^2+18 x y(x) y'(x)+3 y(x)^2=0\)
 4.2290   \(\left (y(x)^2+x\right ) y'''(x)+3 y''(x)+2 y'(x)^3+6 y(x) y'(x) y''(x)=0\)
 4.2291   \(4 y(x)^2 y'''(x)+15 y'(x)^3-18 y(x) y'(x) y''(x)=0\)
 4.2292   \(9 y(x)^2 y'''(x)+40 y'(x)^3-45 y(x) y'(x) y''(x)=0\)
 4.2293   \(y'(x) y'''(x)+y'(x)^2=2 y''(x)^2\)
 4.2294   \(y'(x) y''(x)=a x y'(x)^5+3 y''(x)^2\)
 4.2295   \(2 y'(x) y'''(x)=2 y''(x)^2\)
 4.2296   \(\left (y'(x)^2+1\right ) y'''(x)=3 y'(x) y''(x)^2\)
 4.2297   \(\left (y'(x)^2+1\right ) y'''(x)=y''(x)^2 \left (a+3 y'(x)\right )\)
 4.2298   \(y'(x)^3 y'''(x)=1\)
 4.2299   \(y''(x) y'''(x)=2\)
 4.2300   \(y''(x) y'''(x)=a \sqrt{b^2 y''(x)^2+1}\)
 4.2301   \(2 x y''(x) y'''(x)=y''(x)^2-a^2\)
 4.2302   \(\left (1-x^2\right ) \left (y'''(x)\right )^2+2 x y''(x) y'''(x)-y''(x)^2+1=0\)
 4.2303   \(\sqrt{y''(x)^2+1} \left (1-y'''(x)\right )=y''(x) y'''(x)\)
 4.2304   \(3 y''(x) y''''(x)=5 \left (y'''(x)\right )^2\)
 4.2305   \(-4 y'(x) \left (y'''(x)\right )^2+3 y'(x) y''(x) y''''(x)-3 y''(x)^3=0\)
 4.2306   \(-45 y''(x) y'''(x) y''''(x)+9 y''(x)^2 y'''''(x)+40 \left (y'''(x)\right )^3=0\)
 4.2307   \(y^{(n)}(x)=f(x)\)
 4.2308   \(y^{(n)}(x)=f\left (y^{(n-2)}(x)\right )\)
 4.2309   \(y^{(n)}(x)=f\left (y^{(n-1)}(x)\right )\)
 4.2310   \(y^{(n-2)}(x) y^{(n)}(x)=y^{(n-1)}(x)^2\)
 4.2311   \(f\left (x,y^{(n)}(x)\right )=0\)
 4.2312   \(f\left (x,y^{(n-1)}(x),y^{(n)}(x)\right )=0\)
 4.2313   \(f\left (y^{(n-2)}(x),y^{(n-1)}(x),y^{(n)}(x)\right )=0\)