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ODE |
Mathematica |
Maple |
Sympy |
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\[
{} y^{\prime } = y^{2}+a x \coth \left (b x \right )^{m} y+a \coth \left (b x \right )^{m}
\]
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\[
{} \left (a \coth \left (\lambda x \right )+b \right ) y^{\prime } = y^{2}+c \coth \left (x \mu \right ) y-d^{2}+c d \coth \left (x \mu \right )
\]
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\[
{} y^{\prime } = y^{2}-2 \lambda ^{2} \tanh \left (\lambda x \right )^{2}-2 \lambda ^{2} \coth \left (\lambda x \right )^{2}
\]
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\[
{} y^{\prime } = y^{2}+a \lambda +\lambda b -2 a b -a \left (a +\lambda \right ) \tanh \left (\lambda x \right )^{2}-b \left (b +\lambda \right ) \coth \left (\lambda x \right )^{2}
\]
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\[
{} y^{\prime } = a \ln \left (x \right )^{n} y^{2}+b m \,x^{m -1}-a \,b^{2} x^{2 m} \ln \left (x \right )^{n}
\]
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\[
{} x y^{\prime } = a y^{2}+b \ln \left (x \right )+c
\]
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\[
{} x y^{\prime } = a y^{2}+b \ln \left (x \right )^{k}+c \ln \left (x \right )^{2 k +2}
\]
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\[
{} x y^{\prime } = x y^{2}-a^{2} x \ln \left (\beta x \right )^{2}+a
\]
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\[
{} x y^{\prime } = x y^{2}-a^{2} x \ln \left (\beta x \right )^{2 k}+a k \ln \left (\beta x \right )^{k -1}
\]
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\[
{} x y^{\prime } = a \,x^{n} y^{2}+b -a \,b^{2} x^{n} \ln \left (x \right )^{2}
\]
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\[
{} y^{\prime } x^{2} = x^{2} y^{2}+a \ln \left (x \right )^{2}+b \ln \left (x \right )+c
\]
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\[
{} y^{\prime } x^{2} = x^{2} y^{2}+a \left (b \ln \left (x \right )+c \right )^{n}+\frac {1}{4}
\]
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\[
{} x^{2} \ln \left (a x \right ) \left (y^{\prime }-y^{2}\right ) = 1
\]
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\[
{} y^{\prime } = y^{2}+a x \ln \left (b x \right )^{m} y+a \ln \left (b x \right )^{m}
\]
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\[
{} y^{\prime } = a \,x^{n} y^{2}-a b \,x^{n +1} \ln \left (x \right ) y+b \ln \left (x \right )+b
\]
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\[
{} y^{\prime } = -\left (n +1\right ) x^{n} y^{2}+a \,x^{n +1} \ln \left (x \right )^{m} y-a \ln \left (x \right )^{m}
\]
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\[
{} y^{\prime } = a \ln \left (x \right )^{n} y-a b x \ln \left (x \right )^{n +1} y+b \ln \left (x \right )+b
\]
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\[
{} y^{\prime } = a \ln \left (x \right )^{k} \left (y-b \,x^{n}-c \right )^{2}+b n \,x^{n -1}
\]
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\[
{} y^{\prime } = a \ln \left (x \right )^{n} y^{2}+b \ln \left (x \right )^{m} y+b c \ln \left (x \right )^{m}-a \,c^{2} \ln \left (x \right )^{n}
\]
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\[
{} x y^{\prime } = a \ln \left (\lambda x \right )^{m} y^{2}+k y+a \,b^{2} x^{2 k} \ln \left (\lambda x \right )^{m}
\]
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\[
{} x y^{\prime } = a \,x^{n} \left (y+b \ln \left (x \right )\right )^{2}-b
\]
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\[
{} x y^{\prime } = a \,x^{2 n} \ln \left (x \right ) y^{2}+\left (b \,x^{n} \ln \left (x \right )-n \right ) y+c \ln \left (x \right )
\]
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\[
{} y^{\prime } x^{2} = y^{2} a^{2} x^{2}-x y+b^{2} \ln \left (x \right )^{n}
\]
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\[
{} \left (a \ln \left (x \right )+b \right ) y^{\prime } = y^{2}+c \ln \left (x \right )^{n} y-\lambda ^{2}+\lambda c \ln \left (x \right )^{n}
\]
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\[
{} \left (a \ln \left (x \right )+b \right ) y^{\prime } = \ln \left (x \right )^{n} y^{2}+c y-\lambda ^{2} \ln \left (x \right )^{n}+\lambda c
\]
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\[
{} y^{\prime } = \alpha y^{2}+\beta +\gamma \sin \left (\lambda x \right )
\]
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\[
{} y^{\prime } = y^{2}-a^{2}+a \lambda \sin \left (\lambda x \right )+a^{2} \sin \left (\lambda x \right )^{2}
\]
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\[
{} y^{\prime } = y^{2}+\lambda ^{2}+c \sin \left (\lambda x +a \right )^{n} \sin \left (\lambda x +b \right )^{-n -4}
\]
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\[
{} y^{\prime } = y^{2}+a \sin \left (\beta x \right ) y+a b \sin \left (\beta x \right )-b^{2}
\]
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\[
{} y^{\prime } = y^{2}+a \sin \left (b x \right )^{m} y+a \sin \left (b x \right )^{m}
\]
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\[
{} y^{\prime } = \lambda \sin \left (\lambda x \right ) y^{2}+\lambda \sin \left (\lambda x \right )^{3}
\]
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\[
{} 2 y^{\prime } = \left (\lambda +a -\sin \left (\lambda x \right ) a \right ) y^{2}+\lambda -a -\sin \left (\lambda x \right ) a
\]
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\[
{} y^{\prime } = \left (\lambda +a \sin \left (\lambda x \right )^{2}\right ) y^{2}+\lambda -a +a \sin \left (\lambda x \right )^{2}
\]
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\[
{} y^{\prime } = -\left (k +1\right ) x^{k} y^{2}+a \,x^{k +1} \sin \left (x \right )^{m} y-a \sin \left (x \right )^{m}
\]
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\[
{} y^{\prime } = a \sin \left (\lambda x +\mu \right )^{k} \left (y-b \,x^{n}-c \right )^{2}+b n \,x^{n -1}
\]
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\[
{} x y^{\prime } = a \sin \left (\lambda x \right )^{m} y^{2}+k y+a \,b^{2} x^{2 k} \sin \left (\lambda x \right )^{m}
\]
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\[
{} \left (\sin \left (\lambda x \right ) a +b \right ) y^{\prime } = y^{2}+c \sin \left (x \mu \right ) y-d^{2}+c d \sin \left (x \mu \right )
\]
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\[
{} \left (\sin \left (\lambda x \right ) a +b \right ) \left (y^{\prime }-y^{2}\right )-a \,\lambda ^{2} \sin \left (\lambda x \right ) = 0
\]
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\[
{} y^{\prime } = \alpha y^{2}+\beta +\gamma \cos \left (\lambda x \right )
\]
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\[
{} y^{\prime } = y^{2}-a^{2}+a \lambda \cos \left (\lambda x \right )+a^{2} \cos \left (\lambda x \right )^{2}
\]
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\[
{} y^{\prime } = y^{2}+\lambda ^{2}+c \cos \left (\lambda x +a \right )^{n} \cos \left (\lambda x +b \right )^{-n -4}
\]
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\[
{} y^{\prime } = y^{2}+a \cos \left (\beta x \right ) y+a b \cos \left (\beta x \right )-b^{2}
\]
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\[
{} y^{\prime } = y^{2}+a \cos \left (b x \right )^{m} y+a \cos \left (b x \right )^{m}
\]
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\[
{} y^{\prime } = \lambda \cos \left (\lambda x \right ) y^{2}+\lambda \cos \left (\lambda x \right )^{3}
\]
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\[
{} 2 y^{\prime } = \left (\lambda +a -a \cos \left (\lambda x \right )\right ) y^{2}+\lambda -a -a \cos \left (\lambda x \right )
\]
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\[
{} y^{\prime } = \left (\lambda +a \cos \left (\lambda x \right )^{2}\right ) y^{2}+\lambda -a +a \cos \left (\lambda x \right )^{2}
\]
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\[
{} y^{\prime } = -\left (k +1\right ) x^{k} y^{2}+a \,x^{k +1} \cos \left (x \right )^{m} y-a \cos \left (x \right )^{m}
\]
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\[
{} y^{\prime } = a \cos \left (\lambda x +\mu \right )^{k} \left (y-b \,x^{n}-c \right )^{2}+b n \,x^{n -1}
\]
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\[
{} x y^{\prime } = a \cos \left (\lambda x \right )^{m} y^{2}+k y+a \,b^{2} x^{2 k} \cos \left (\lambda x \right )^{m}
\]
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\[
{} \left (a \cos \left (\lambda x \right )+b \right ) y^{\prime } = y^{2}+c \cos \left (x \mu \right ) y-d^{2}+c d \cos \left (x \mu \right )
\]
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\[
{} \left (a \cos \left (\lambda x \right )+b \right ) \left (y^{\prime }-y^{2}\right )-a \,\lambda ^{2} \cos \left (\lambda x \right ) = 0
\]
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\[
{} y^{\prime } = y^{2}+a \lambda +a \left (\lambda -a \right ) \tan \left (\lambda x \right )^{2}
\]
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\[
{} y^{\prime } = y^{2}+\lambda ^{2}+3 a \lambda +a \left (\lambda -a \right ) \tan \left (\lambda x \right )^{2}
\]
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\[
{} y^{\prime } = a y^{2}+b \tan \left (x \right ) y+c
\]
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\[
{} y^{\prime } = y^{2}+a \tan \left (\beta x \right ) y+a b \tan \left (\beta x \right )-b^{2}
\]
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\[
{} y^{\prime } = y^{2}+a x \tan \left (b x \right )^{m} y+a \tan \left (b x \right )^{m}
\]
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\[
{} y^{\prime } = -\left (k +1\right ) x^{k} y^{2}+a \,x^{k +1} \tan \left (x \right )^{m} y-a \tan \left (x \right )^{m}
\]
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\[
{} y^{\prime } = a \tan \left (\lambda x \right )^{n} y^{2}-a \,b^{2} \tan \left (\lambda x \right )^{n +2}+b \lambda \tan \left (\lambda x \right )^{2}+\lambda b
\]
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\[
{} y^{\prime } = a \tan \left (\lambda x +\mu \right )^{k} \left (y-b \,x^{n}-c \right )^{2}+b n \,x^{n -1}
\]
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\[
{} x y^{\prime } = a \tan \left (\lambda x \right )^{m} y^{2}+k y+a \,b^{2} x^{2 k} \tan \left (\lambda x \right )^{m}
\]
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\[
{} \left (a \tan \left (\lambda x \right )+b \right ) y^{\prime } = y^{2}+k \tan \left (x \mu \right ) y-d^{2}+k d \tan \left (x \mu \right )
\]
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\[
{} y^{\prime } = y^{2}+a \lambda +a \left (\lambda -a \right ) \cot \left (\lambda x \right )^{2}
\]
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\[
{} y^{\prime } = y^{2}+\lambda ^{2}+3 a \lambda +a \left (\lambda -a \right ) \cot \left (\lambda x \right )^{2}
\]
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\[
{} y^{\prime } = y^{2}-2 a b \cot \left (a x \right ) y+b^{2}-a^{2}
\]
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\[
{} y^{\prime } = y^{2}+a \cot \left (\beta x \right ) y+a b \cot \left (\beta x \right )-b^{2}
\]
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\[
{} y^{\prime } = y^{2}+a x \cot \left (b x \right )^{m} y+a \cot \left (b x \right )^{m}
\]
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\[
{} y^{\prime } = -\left (k +1\right ) x^{k} y^{2}+a \,x^{k +1} \cot \left (x \right )^{m} y-a \cot \left (x \right )^{m}
\]
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\[
{} y^{\prime } = a \cot \left (\lambda x +\mu \right )^{k} \left (y-b \,x^{n}-c \right )^{2}+b n \,x^{n -1}
\]
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\[
{} x y^{\prime } = a \cot \left (\lambda x \right )^{m} y^{2}+k y+a \,b^{2} x^{2 k} \cot \left (\lambda x \right )^{m}
\]
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\[
{} \left (a \cot \left (\lambda x \right )+b \right ) y^{\prime } = y^{2}+c \cot \left (x \mu \right ) y-d^{2}+c d \cot \left (x \mu \right )
\]
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\[
{} y^{\prime } = y^{2}+\lambda ^{2}+c \sin \left (\lambda x \right )^{n} \cos \left (\lambda x \right )^{-n -4}
\]
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\[
{} y^{\prime } = a \sin \left (\lambda x \right ) y^{2}+b \sin \left (\lambda x \right ) \cos \left (\lambda x \right )^{n}
\]
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\[
{} y^{\prime } = \lambda \sin \left (\lambda x \right ) y^{2}+a \cos \left (\lambda x \right )^{n} y-a \cos \left (\lambda x \right )^{n -1}
\]
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\[
{} y^{\prime } = a \cos \left (\lambda x \right ) y^{2}+b \cos \left (\lambda x \right ) \sin \left (\lambda x \right )^{n}
\]
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\[
{} y^{\prime } = \lambda \sin \left (\lambda x \right ) y^{2}+a \,x^{n} \cos \left (\lambda x \right ) y-a \,x^{n}
\]
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\[
{} \sin \left (2 x \right )^{n +1} y^{\prime } = a y^{2} \sin \left (x \right )^{2 n}+b \cos \left (x \right )^{2 n}
\]
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\[
{} y^{\prime } = y^{2}-y \tan \left (x \right )+a \left (1-a \right ) \cot \left (x \right )^{2}
\]
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\[
{} y^{\prime } = y^{2}-m y \tan \left (x \right )+b^{2} \cos \left (x \right )^{2 m}
\]
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\[
{} y^{\prime } = y^{2}+m y \cot \left (x \right )+b^{2} \sin \left (x \right )^{2 m}
\]
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\[
{} y^{\prime } = y^{2}-2 \lambda ^{2} \tan \left (x \right )^{2}-2 \lambda ^{2} \cot \left (\lambda x \right )^{2}
\]
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\[
{} y^{\prime } = y^{2}+a \lambda +\lambda b +2 a b +a \left (\lambda -a \right ) \tan \left (\lambda x \right )^{2}+b \left (\lambda -b \right ) \cot \left (\lambda x \right )^{2}
\]
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\[
{} y^{\prime } = y^{2}-\frac {\lambda ^{2}}{2}-\frac {3 \lambda ^{2} \tan \left (\lambda x \right )^{2}}{4}+a \cos \left (\lambda x \right )^{2} \sin \left (\lambda x \right )^{n}
\]
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\[
{} y^{\prime } = \lambda \sin \left (\lambda x \right ) y^{2}+a \sin \left (\lambda x \right ) y-a \tan \left (\lambda x \right )
\]
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\[
{} y^{\prime } = y^{2}+\lambda x \arcsin \left (x \right )^{n} y+\lambda \arcsin \left (x \right )^{n}
\]
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\[
{} y^{\prime } = -\left (k +1\right ) x^{k} y^{2}+\lambda \arcsin \left (x \right )^{n} \left (x^{k +1} y-1\right )
\]
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\[
{} y^{\prime } = \lambda \arcsin \left (x \right )^{n} y^{2}-b \lambda \,x^{m} \arcsin \left (x \right )^{n} y+b m \,x^{m -1}
\]
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\[
{} y^{\prime } = \lambda \arcsin \left (x \right )^{n} y^{2}+\beta m \,x^{m -1}-\lambda \,\beta ^{2} x^{2 m} \arcsin \left (x \right )^{n}
\]
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\[
{} y^{\prime } = \lambda \arcsin \left (x \right )^{n} \left (y-a \,x^{m}-b \right )^{2}+a m \,x^{m -1}
\]
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\[
{} x y^{\prime } = \lambda \arcsin \left (x \right )^{n} y^{2}+k y+\lambda \,b^{2} x^{2 k} \arcsin \left (x \right )^{n}
\]
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\[
{} x y^{\prime } = \left (a \,x^{2 m} y^{2}+b \,x^{n} y+c \right ) \arcsin \left (x \right )^{m}-n y
\]
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\[
{} y^{\prime } = y^{2}+\lambda x \arccos \left (x \right )^{n} y+\lambda \arccos \left (x \right )^{n}
\]
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\[
{} y^{\prime } = -\left (k +1\right ) x^{k} y^{2}+\lambda \arccos \left (x \right )^{n} \left (x^{k +1} y-1\right )
\]
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\[
{} y^{\prime } = \lambda \arccos \left (x \right )^{n} y^{2}-b \lambda \,x^{m} \arccos \left (x \right )^{n} y+b m \,x^{m -1}
\]
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\[
{} y^{\prime } = \lambda \arccos \left (x \right )^{n} y^{2}+\beta m \,x^{m -1}-\lambda \,\beta ^{2} x^{2 m} \arccos \left (x \right )^{n}
\]
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\[
{} y^{\prime } = \lambda \arccos \left (x \right )^{n} \left (y-a \,x^{m}-b \right )^{2}+a m \,x^{m -1}
\]
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\[
{} x y^{\prime } = \lambda \arccos \left (x \right )^{n} y^{2}+k y+\lambda \,b^{2} x^{2 k} \arccos \left (x \right )^{n}
\]
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\[
{} x y^{\prime } = \left (a \,x^{2 m} y^{2}+b \,x^{n} y+c \right ) \arccos \left (x \right )^{m}-n y
\]
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\[
{} y^{\prime } = y^{2}+\lambda x \arctan \left (x \right )^{n} y+\lambda \arctan \left (x \right )^{n}
\]
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\[
{} y^{\prime } = -\left (k +1\right ) x^{k} y^{2}+\lambda \arctan \left (x \right )^{n} \left (x^{k +1} y-1\right )
\]
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\[
{} y^{\prime } = \lambda \arctan \left (x \right )^{n} y^{2}+a y+a b -b^{2} \lambda \arctan \left (x \right )^{n}
\]
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