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

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

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

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

\[ {}y^{\prime } = y^{2}-m y \tan \relax (x )+b^{2} \cos \relax (x )^{2 m} \]

\[ {}y^{\prime } = y^{2}+m y \cot \relax (x )+b^{2} \sin \relax (x )^{2 m} \]

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

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

\[ {}y^{\prime } = y^{2}-\frac {\lambda ^{2}}{2}-\frac {3 \lambda ^{2} \tan \left (\lambda x \right )^{2}}{4}+a \cos \left (\lambda x \right )^{2} \sin \left (\lambda x \right )^{n} \]

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

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

\[ {}y^{\prime } = y^{2}+\lambda x \arcsin \relax (x )^{n} y+\arcsin \relax (x )^{n} \lambda \]

\[ {}y^{\prime } = -\left (1+k \right ) x^{k} y^{2}+\lambda \arcsin \relax (x )^{n} \left (x^{1+k} y-1\right ) \]

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

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

\[ {}y^{\prime } = \lambda \arcsin \relax (x )^{n} y^{2}+\beta m \,x^{m -1}-\lambda \,\beta ^{2} x^{2 m} \arcsin \relax (x )^{n} \]

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

\[ {}x y^{\prime } = \lambda \arcsin \relax (x )^{n} y^{2}+k y+\lambda \,b^{2} x^{2 k} \arcsin \relax (x )^{n} \]

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

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

\[ {}y^{\prime } = y^{2}+\lambda x \arccos \relax (x )^{n} y+\lambda \arccos \relax (x )^{n} \]

\[ {}y^{\prime } = -\left (1+k \right ) x^{k} y^{2}+\lambda \arccos \relax (x )^{n} \left (x^{1+k} y-1\right ) \]

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

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

\[ {}y^{\prime } = \lambda \arccos \relax (x )^{n} y^{2}+\beta m \,x^{m -1}-\lambda \,\beta ^{2} x^{2 m} \arccos \relax (x )^{n} \]

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

\[ {}x y^{\prime } = \lambda \arccos \relax (x )^{n} y^{2}+k y+\lambda \,b^{2} x^{2 k} \arccos \relax (x )^{n} \]

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

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

\[ {}y^{\prime } = y^{2}+\lambda x \arctan \relax (x )^{n} y+\arctan \relax (x )^{n} \lambda \]

\[ {}y^{\prime } = -\left (1+k \right ) x^{k} y^{2}+\lambda \arctan \relax (x )^{n} \left (x^{1+k} y-1\right ) \]

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

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

\[ {}y^{\prime } = \lambda \arctan \relax (x )^{n} y^{2}+\beta m \,x^{m -1}-\lambda \,\beta ^{2} x^{2 m} \arctan \relax (x )^{n} \]

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

\[ {}x y^{\prime } = \lambda \arctan \relax (x )^{n} y^{2}+k y+\lambda \,b^{2} x^{2 k} \arctan \relax (x )^{n} \]

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

\[ {}y^{\prime } = y^{2}+\lambda \operatorname {arccot}\relax (x )^{n} y-a^{2}+a \lambda \operatorname {arccot}\relax (x )^{n} \]

\[ {}y^{\prime } = y^{2}+\lambda x \operatorname {arccot}\relax (x )^{n} y+\operatorname {arccot}\relax (x )^{n} \lambda \]

\[ {}y^{\prime } = -\left (1+k \right ) x^{k} y^{2}+\lambda \operatorname {arccot}\relax (x )^{n} \left (x^{1+k} y-1\right ) \]

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

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

\[ {}y^{\prime } = \lambda \operatorname {arccot}\relax (x )^{n} y^{2}+\beta m \,x^{m -1}-\lambda \,\beta ^{2} x^{2 m} \operatorname {arccot}\relax (x )^{n} \]

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

\[ {}x y^{\prime } = \lambda \operatorname {arccot}\relax (x )^{n} y^{2}+k y+\lambda \,b^{2} x^{2 k} \operatorname {arccot}\relax (x )^{n} \]

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

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

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

\[ {}y^{\prime } = y^{2}+x f \relax (x ) y+f \relax (x ) \]

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

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

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

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

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

\[ {}y^{\prime } = y^{2} f \relax (x )+g \relax (x ) y-a^{2} f \relax (x )-a g \relax (x ) \]

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

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

\[ {}y^{\prime } = a \,{\mathrm e}^{\lambda x} y^{2}+a \,{\mathrm e}^{\lambda x} f \relax (x ) y+\lambda f \relax (x ) \]

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

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

\[ {}y^{\prime } = y^{2} f \relax (x )+\lambda y+a^{2} {\mathrm e}^{2 \lambda x} f \relax (x ) \]

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

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

\[ {}y^{\prime } = y^{2} f \relax (x )+g \relax (x ) y+a \lambda \,{\mathrm e}^{\lambda x}-a \,{\mathrm e}^{\lambda x} g \relax (x )-a^{2} {\mathrm e}^{2 \lambda x} f \relax (x ) \]

\[ {}y^{\prime } = y^{2} f \relax (x )-a \,{\mathrm e}^{\lambda x} g \relax (x ) y+a \lambda \,{\mathrm e}^{\lambda x}+a^{2} {\mathrm e}^{2 \lambda x} \left (g \relax (x )-f \relax (x )\right ) \]

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

\[ {}y^{\prime } = y^{2} f \relax (x )+\lambda x y+a f \relax (x ) {\mathrm e}^{\lambda x} \]

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime } = y^{2}-f \relax (x )^{2}+f^{\prime }\relax (x ) \]

\[ {}y^{\prime } = y^{2} f \relax (x )-f \relax (x ) g \relax (x ) y+g^{\prime }\relax (x ) \]

\[ {}y^{\prime } = -f^{\prime }\relax (x ) y^{2}+f \relax (x ) g \relax (x ) y-g \relax (x ) \]

\[ {}y^{\prime } = g \relax (x ) \left (y-f \relax (x )\right )^{2}+f^{\prime }\relax (x ) \]

\[ {}y^{\prime } = \frac {f^{\prime }\relax (x ) y^{2}}{g \relax (x )}-\frac {g^{\prime }\relax (x )}{f \relax (x )} \]

\[ {}f \relax (x )^{2} y^{\prime }-f^{\prime }\relax (x ) y^{2}+g \relax (x ) \left (y-f \relax (x )\right ) = 0 \]

\[ {}y^{\prime } = f^{\prime }\relax (x ) y^{2}+a \,{\mathrm e}^{\lambda x} f \relax (x ) y+{\mathrm e}^{\lambda x} a \]

\[ {}y^{\prime } = y^{2} f \relax (x )+g^{\prime }\relax (x ) y+a f \relax (x ) {\mathrm e}^{2 g \relax (x )} \]

\[ {}y^{\prime } = y^{2}-\frac {f^{\prime \prime }\relax (x )}{f \relax (x )} \]

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

\[ {}y^{\prime } = y^{2}+\frac {f \left (\frac {1}{x}\right )}{x^{4}} \]

\[ {}y^{\prime } = y^{2}+\frac {f \left (\frac {a x +b}{c x +d}\right )}{\left (c x +d \right )^{4}} \]

\[ {}x^{2} y^{\prime } = x^{4} f \relax (x ) y^{2}+1 \]

\[ {}x^{2} y^{\prime } = x^{4} y^{2}+x^{2 n} f \left (a \,x^{n}+b \right )-\frac {n^{2}}{4}+\frac {1}{4} \]

\[ {}y^{\prime } = y^{2} f \relax (x )+g \relax (x ) y+h \relax (x ) \]

\[ {}y^{\prime } = y^{2}+{\mathrm e}^{2 \lambda x} f \left ({\mathrm e}^{\lambda x}\right )-\frac {\lambda ^{2}}{4} \]

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

\[ {}y^{\prime } = y^{2}-\lambda ^{2}+\frac {f \left (\coth \left (\lambda x \right )\right )}{\sinh \left (\lambda x \right )^{4}} \]

\[ {}y^{\prime } = y^{2}-\lambda ^{2}+\frac {f \left (\tanh \left (\lambda x \right )\right )}{\cosh \left (\lambda x \right )^{4}} \]

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

\[ {}y^{\prime } = y^{2}+\lambda ^{2}+\frac {f \left (\cot \left (\lambda x \right )\right )}{\sin \left (\lambda x \right )^{4}} \]