\[ {}x y^{\prime } = a \,x^{2 n} {\mathrm e}^{\lambda x} y^{2}+\left (b \,x^{n} {\mathrm e}^{\lambda x}-n \right ) y+c \,{\mathrm e}^{\lambda x} \]

\[ {}y^{\prime } = y^{2}+2 a \lambda x \,{\mathrm e}^{\lambda \,x^{2}}-a^{2} {\mathrm e}^{2 \lambda \,x^{2}} \]

\[ {}y^{\prime } = a \,{\mathrm e}^{-\lambda \,x^{2}} y^{2}+\lambda x y+a \,b^{2} \]

\[ {}y^{\prime } = a \,x^{n} y^{2}+\lambda x y+a \,b^{2} x^{n} {\mathrm e}^{\lambda \,x^{2}} \]

\[ {}x^{4} \left (y^{\prime }-y^{2}\right ) = a +b \,{\mathrm e}^{\frac {k}{x}}+c \,{\mathrm e}^{\frac {2 k}{x}} \]

\[ {}y^{\prime } = y^{2}-a^{2}+a \lambda \sinh \left (\lambda x \right )-a^{2} \left (\sinh ^{2}\left (\lambda x \right )\right ) \]

\[ {}y^{\prime } = y^{2}+a \sinh \left (\beta x \right ) y+a b \sinh \left (\beta x \right )-b^{2} \]

\[ {}y^{\prime } = y^{2}+a x \left (\sinh ^{m}\left (b x \right )\right ) y+a \left (\sinh ^{m}\left (b x \right )\right ) \]

\[ {}y^{\prime } = \lambda \sinh \left (\lambda x \right ) y^{2}-\lambda \left (\sinh ^{3}\left (\lambda x \right )\right ) \]

\[ {}y^{\prime } = \left (a \left (\sinh ^{2}\left (\lambda x \right )\right )-\lambda \right ) y^{2}-a \left (\sinh ^{2}\left (\lambda x \right )\right )+\lambda -a \]

\[ {}\left (\sinh \left (\lambda x \right ) a +b \right ) y^{\prime } = y^{2}+c \sinh \left (\mu x \right ) y-d^{2}+c d \sinh \left (\mu x \right ) \]

\[ {}\left (\sinh \left (\lambda x \right ) a +b \right ) \left (y^{\prime }-y^{2}\right )+a \,\lambda ^{2} \sinh \left (\lambda x \right ) = 0 \]

\[ {}y^{\prime } = \alpha y^{2}+\beta +\gamma \cosh \relax (x ) \]

\[ {}y^{\prime } = y^{2}+a \cosh \left (\beta x \right ) y+a b \cosh \left (\beta x \right )-b^{2} \]

\[ {}y^{\prime } = y^{2}+a x \left (\cosh ^{m}\left (b x \right )\right ) y+a \left (\cosh ^{m}\left (b x \right )\right ) \]

\[ {}y^{\prime } = \left (\left (\cosh ^{2}\left (\lambda x \right )\right ) a -\lambda \right ) y^{2}+a +\lambda -\left (\cosh ^{2}\left (\lambda x \right )\right ) a \]

\[ {}2 y^{\prime } = \left (a -\lambda +a \cosh \left (\lambda x \right )\right ) y^{2}+a +\lambda -a \cosh \left (\lambda x \right ) \]

\[ {}y^{\prime } = y^{2}-\lambda ^{2}+a \left (\cosh ^{n}\left (\lambda x \right )\right ) \left (\sinh ^{-n -4}\left (\lambda x \right )\right ) \]

\[ {}y^{\prime } = a \sinh \left (\lambda x \right ) y^{2}+b \sinh \left (\lambda x \right ) \left (\cosh ^{n}\left (\lambda x \right )\right ) \]

\[ {}y^{\prime } = a \cosh \left (\lambda x \right ) y^{2}+b \cosh \left (\lambda x \right ) \left (\sinh ^{n}\left (\lambda x \right )\right ) \]

\[ {}\left (a \cosh \left (\lambda x \right )+b \right ) y^{\prime } = y^{2}+c \cosh \left (\mu x \right ) y-d^{2}+c d \cosh \left (\mu x \right ) \]

\[ {}\left (a \cosh \left (\lambda x \right )+b \right ) \left (y^{\prime }-y^{2}\right )+a \,\lambda ^{2} \cosh \left (\lambda x \right ) = 0 \]

\[ {}y^{\prime } = y^{2}+a \lambda -a \left (a +\lambda \right ) \left (\tanh ^{2}\left (\lambda x \right )\right ) \]

\[ {}y^{\prime } = y^{2}+3 a \lambda -\lambda ^{2}-a \left (a +\lambda \right ) \left (\tanh ^{2}\left (\lambda x \right )\right ) \]

\[ {}y^{\prime } = y^{2}+a x \left (\tanh ^{m}\left (b x \right )\right ) y+a \left (\tanh ^{m}\left (b x \right )\right ) \]

\[ {}\left (a \tanh \left (\lambda x \right )+b \right ) y^{\prime } = y^{2}+c \tanh \left (\mu x \right ) y-d^{2}+c d \tanh \left (\mu x \right ) \]

\[ {}y^{\prime } = y^{2}+a \lambda -a \left (a +\lambda \right ) \left (\coth ^{2}\left (\lambda x \right )\right ) \]

\[ {}y^{\prime } = y^{2}-\lambda ^{2}+3 a \lambda -a \left (a +\lambda \right ) \left (\coth ^{2}\left (\lambda x \right )\right ) \]

\[ {}y^{\prime } = y^{2}+a x \left (\coth ^{m}\left (b x \right )\right ) y+a \left (\coth ^{m}\left (b x \right )\right ) \]

\[ {}\left (a \coth \left (\lambda x \right )+b \right ) y^{\prime } = y^{2}+c \coth \left (\mu x \right ) y-d^{2}+c d \coth \left (\mu x \right ) \]

\[ {}y^{\prime } = y^{2}-2 \lambda ^{2} \left (\tanh ^{2}\left (\lambda x \right )\right )-2 \lambda ^{2} \left (\coth ^{2}\left (\lambda x \right )\right ) \]

\[ {}y^{\prime } = y^{2}+a \lambda +b \lambda -2 a b -a \left (a +\lambda \right ) \left (\tanh ^{2}\left (\lambda x \right )\right )-b \left (b +\lambda \right ) \left (\coth ^{2}\left (\lambda x \right )\right ) \]

\[ {}y^{\prime } = a \ln \relax (x )^{n} y^{2}+b m \,x^{m -1}-a \,b^{2} x^{2 m} \ln \relax (x )^{n} \]

\[ {}x y^{\prime } = a y^{2}+b \ln \relax (x )+c \]

\[ {}x y^{\prime } = a y^{2}+b \ln \relax (x )^{k}+c \ln \relax (x )^{2 k +2} \]

\[ {}x y^{\prime } = x y^{2}-a^{2} x \ln \left (\beta x \right )^{2}+a \]

\[ {}x y^{\prime } = x y^{2}-a^{2} x \ln \left (\beta x \right )^{2 k}+a k \ln \left (\beta x \right )^{k -1} \]

\[ {}x y^{\prime } = a \,x^{n} y^{2}+b -a \,b^{2} x^{n} \ln \relax (x )^{2} \]

\[ {}x^{2} y^{\prime } = x^{2} y^{2}+a \ln \relax (x )^{2}+b \ln \relax (x )+c \]

\[ {}x^{2} y^{\prime } = x^{2} y^{2}+a \left (b \ln \relax (x )+c \right )^{n}+\frac {1}{4} \]

\[ {}x^{2} \ln \left (a x \right ) \left (y^{\prime }-y^{2}\right ) = 1 \]

\[ {}y^{\prime } = y^{2}+a \ln \left (\beta x \right ) y-a b \ln \left (\beta x \right )-b^{2} \]

\[ {}y^{\prime } = y^{2}+a x \ln \left (b x \right )^{m} y+a \ln \left (b x \right )^{m} \]

\[ {}y^{\prime } = a \,x^{n} y^{2}-a b \,x^{n +1} \ln \relax (x ) y+b \ln \relax (x )+b \]

\[ {}y^{\prime } = -\left (n +1\right ) x^{n} y^{2}+a \,x^{n +1} \ln \relax (x )^{m} y-a \ln \relax (x )^{m} \]

\[ {}y^{\prime } = a \ln \relax (x )^{n} y-a b x \ln \relax (x )^{n +1} y+b \ln \relax (x )+b \]

\[ {}y^{\prime } = a \ln \relax (x )^{k} \left (y-b \,x^{n}-c \right )^{2}+b n \,x^{n -1} \]

\[ {}y^{\prime } = a \ln \relax (x )^{n} y^{2}+b \ln \relax (x )^{m} y+b c \ln \relax (x )^{m}-a \,c^{2} \ln \relax (x )^{n} \]

\[ {}x y^{\prime } = \left (a y+b \ln \relax (x )\right )^{2} \]

\[ {}x y^{\prime } = a \ln \left (\lambda x \right )^{m} y^{2}+k y+a \,b^{2} x^{2 k} \ln \left (\lambda x \right )^{m} \]

\[ {}x y^{\prime } = a \,x^{n} \left (y+b \ln \relax (x )\right )^{2}-b \]

\[ {}x y^{\prime } = a \,x^{2 n} \ln \relax (x ) y^{2}+\left (b \,x^{n} \ln \relax (x )-n \right ) y+c \ln \relax (x ) \]

\[ {}x^{2} y^{\prime } = a^{2} x^{2} y^{2}-x y+b^{2} \ln \relax (x )^{n} \]

\[ {}\left (a \ln \relax (x )+b \right ) y^{\prime } = y^{2}+c \ln \relax (x )^{n} y-\lambda ^{2}+\lambda c \ln \relax (x )^{n} \]

\[ {}\left (a \ln \relax (x )+b \right ) y^{\prime } = \ln \relax (x )^{n} y^{2}+c y-\lambda ^{2} \ln \relax (x )^{n}+c \lambda \]

\[ {}y^{\prime } = \alpha y^{2}+\beta +\gamma \sin \left (\lambda x \right ) \]

\[ {}y^{\prime } = y^{2}-a^{2}+a \lambda \sin \left (\lambda x \right )+a^{2} \left (\sin ^{2}\left (\lambda x \right )\right ) \]

\[ {}y^{\prime } = y^{2}+\lambda ^{2}+c \left (\sin ^{n}\left (\lambda x +a \right )\right ) \left (\sin ^{-n -4}\left (\lambda x +b \right )\right ) \]

\[ {}y^{\prime } = y^{2}+a \sin \left (\beta x \right ) y+a b \sin \left (\beta x \right )-b^{2} \]

\[ {}y^{\prime } = y^{2}+a \left (\sin ^{m}\left (b x \right )\right ) y+a \left (\sin ^{m}\left (b x \right )\right ) \]

\[ {}y^{\prime } = \lambda \sin \left (\lambda x \right ) y^{2}+\lambda \left (\sin ^{3}\left (\lambda x \right )\right ) \]

\[ {}2 y^{\prime } = \left (\lambda +a -\sin \left (\lambda x \right ) a \right ) y^{2}+\lambda -a -\sin \left (\lambda x \right ) a \]

\[ {}y^{\prime } = \left (\lambda +a \left (\sin ^{2}\left (\lambda x \right )\right )\right ) y^{2}+\lambda -a +a \left (\sin ^{2}\left (\lambda x \right )\right ) \]

\[ {}y^{\prime } = -\left (k +1\right ) x^{k} y^{2}+a \,x^{k +1} \left (\sin ^{m}\relax (x )\right ) y-a \left (\sin ^{m}\relax (x )\right ) \]

\[ {}y^{\prime } = a \left (\sin ^{k}\left (\lambda x +\mu \right )\right ) \left (y-b \,x^{n}-c \right )^{2}+b n \,x^{n -1} \]

\[ {}x y^{\prime } = a \left (\sin ^{m}\left (\lambda x \right )\right ) y^{2}+k y+a \,b^{2} x^{2 k} \left (\sin ^{m}\left (\lambda x \right )\right ) \]

\[ {}\left (\sin \left (\lambda x \right ) a +b \right ) y^{\prime } = y^{2}+c \sin \left (\mu x \right ) y-d^{2}+c d \sin \left (\mu x \right ) \]

\[ {}\left (\sin \left (\lambda x \right ) a +b \right ) \left (y^{\prime }-y^{2}\right )-a \,\lambda ^{2} \sin \left (\lambda x \right ) = 0 \]

\[ {}y^{\prime } = \alpha y^{2}+\beta +\gamma \cos \left (\lambda x \right ) \]

\[ {}y^{\prime } = y^{2}-a^{2}+a \lambda \cos \left (\lambda x \right )+a^{2} \left (\cos ^{2}\left (\lambda x \right )\right ) \]

\[ {}y^{\prime } = y^{2}+\lambda ^{2}+c \left (\cos ^{n}\left (\lambda x +a \right )\right ) \left (\cos ^{-n -4}\left (\lambda x +b \right )\right ) \]

\[ {}y^{\prime } = y^{2}+a \cos \left (\beta x \right ) y+a b \cos \left (\beta x \right )-b^{2} \]

\[ {}y^{\prime } = y^{2}+a \left (\cos ^{m}\left (b x \right )\right ) y+a \left (\cos ^{m}\left (b x \right )\right ) \]

\[ {}y^{\prime } = \lambda \cos \left (\lambda x \right ) y^{2}+\lambda \left (\cos ^{3}\left (\lambda x \right )\right ) \]

\[ {}2 y^{\prime } = \left (\lambda +a -\cos \left (\lambda x \right ) a \right ) y^{2}+\lambda -a -\cos \left (\lambda x \right ) a \]

\[ {}y^{\prime } = \left (\lambda +\left (\cos ^{2}\left (\lambda x \right )\right ) a \right ) y^{2}+\lambda -a +\left (\cos ^{2}\left (\lambda x \right )\right ) a \]

\[ {}y^{\prime } = -\left (k +1\right ) x^{k} y^{2}+a \,x^{k +1} \left (\cos ^{m}\relax (x )\right ) y-a \left (\cos ^{m}\relax (x )\right ) \]

\[ {}y^{\prime } = a \left (\cos ^{k}\left (\lambda x +\mu \right )\right ) \left (y-b \,x^{n}-c \right )^{2}+b n \,x^{n -1} \]

\[ {}x y^{\prime } = a \left (\cos ^{m}\left (\lambda x \right )\right ) y^{2}+k y+a \,b^{2} x^{2 k} \left (\cos ^{m}\left (\lambda x \right )\right ) \]

\[ {}\left (\cos \left (\lambda x \right ) a +b \right ) y^{\prime } = y^{2}+c \cos \left (\mu x \right ) y-d^{2}+c d \cos \left (\mu x \right ) \]

\[ {}\left (\cos \left (\lambda x \right ) a +b \right ) \left (y^{\prime }-y^{2}\right )-a \,\lambda ^{2} \cos \left (\lambda x \right ) = 0 \]

\[ {}y^{\prime } = y^{2}+a \lambda +a \left (\lambda -a \right ) \left (\tan ^{2}\left (\lambda x \right )\right ) \]

\[ {}y^{\prime } = y^{2}+\lambda ^{2}+3 a \lambda +a \left (\lambda -a \right ) \left (\tan ^{2}\left (\lambda x \right )\right ) \]

\[ {}y^{\prime } = a y^{2}+b \tan \relax (x ) y+c \]

\[ {}y^{\prime } = a y^{2}+2 a b \tan \relax (x ) y+b \left (a b -1\right ) \left (\tan ^{2}\relax (x )\right ) \]

\[ {}y^{\prime } = y^{2}+a \tan \left (\beta x \right ) y+a b \tan \left (\beta x \right )-b^{2} \]

\[ {}y^{\prime } = y^{2}+a x \left (\tan ^{m}\left (b x \right )\right ) y+a \left (\tan ^{m}\left (b x \right )\right ) \]

\[ {}y^{\prime } = -\left (k +1\right ) x^{k} y^{2}+a \,x^{k +1} \left (\tan ^{m}\relax (x )\right ) y-a \left (\tan ^{m}\relax (x )\right ) \]

\[ {}y^{\prime } = a \left (\tan ^{n}\left (\lambda x \right )\right ) y^{2}-a \,b^{2} \left (\tan ^{2+n}\left (\lambda x \right )\right )+b \lambda \left (\tan ^{2}\left (\lambda x \right )\right )+b \lambda \]

\[ {}y^{\prime } = a \left (\tan ^{k}\left (\lambda x +\mu \right )\right ) \left (y-b \,x^{n}-c \right )^{2}+b n \,x^{n -1} \]

\[ {}x y^{\prime } = a \left (\tan ^{m}\left (\lambda x \right )\right ) y^{2}+k y+a \,b^{2} x^{2 k} \left (\tan ^{m}\left (\lambda x \right )\right ) \]

\[ {}\left (a \tan \left (\lambda x \right )+b \right ) y^{\prime } = y^{2}+k \tan \left (\mu x \right ) y-d^{2}+k d \tan \left (\mu x \right ) \]

\[ {}y^{\prime } = y^{2}+a \lambda +a \left (\lambda -a \right ) \left (\cot ^{2}\left (\lambda x \right )\right ) \]

\[ {}y^{\prime } = y^{2}+\lambda ^{2}+3 a \lambda +a \left (\lambda -a \right ) \left (\cot ^{2}\left (\lambda x \right )\right ) \]

\[ {}y^{\prime } = y^{2}-2 a b \cot \left (a x \right ) y+b^{2}-a^{2} \]

\[ {}y^{\prime } = y^{2}+a \cot \left (\beta x \right ) y+a b \cot \left (\beta x \right )-b^{2} \]

\[ {}y^{\prime } = y^{2}+a x \left (\cot ^{m}\left (b x \right )\right ) y+a \left (\cot ^{m}\left (b x \right )\right ) \]

\[ {}y^{\prime } = -\left (k +1\right ) x^{k} y^{2}+a \,x^{k +1} \left (\cot ^{m}\relax (x )\right ) y-a \left (\cot ^{m}\relax (x )\right ) \]

\[ {}y^{\prime } = a \left (\cot ^{k}\left (\lambda x +\mu \right )\right ) \left (y-b \,x^{n}-c \right )^{2}+b n \,x^{n -1} \]

\[ {}x y^{\prime } = a \left (\cot ^{m}\left (\lambda x \right )\right ) y^{2}+k y+a \,b^{2} x^{2 k} \left (\cot ^{m}\left (\lambda x \right )\right ) \]