| # | ODE | Mathematica | Maple | Sympy |
| \[
{} y^{\prime } = y^{2}+m y \cot \left (x \right )+b^{2} \sin \left (x \right )^{2 m}
\]
|
✓ |
✓ |
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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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✗ |
✗ |
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| \[
{} y^{\prime } = y^{2}+a \lambda +b \lambda +2 a b +a \left (\lambda -a \right ) \tan \left (\lambda x \right )^{2}+b \left (\lambda -b \right ) \cot \left (\lambda x \right )^{2}
\]
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✓ |
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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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✓ |
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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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✓ |
✗ |
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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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✓ |
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| \[
{} y^{\prime } = -\left (1+k \right ) x^{k} y^{2}+\lambda \arcsin \left (x \right )^{n} \left (x^{1+k} y-1\right )
\]
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✓ |
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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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✓ |
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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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✓ |
✓ |
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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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✓ |
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| \[
{} y^{\prime } = -\left (1+k \right ) x^{k} y^{2}+\lambda \arccos \left (x \right )^{n} \left (x^{1+k} y-1\right )
\]
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✓ |
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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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✓ |
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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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✓ |
✓ |
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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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| \[
{} y^{\prime } = -\left (1+k \right ) x^{k} y^{2}+\lambda \arctan \left (x \right )^{n} \left (x^{1+k} y-1\right )
\]
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✓ |
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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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| \[
{} y^{\prime } = \lambda \arctan \left (x \right )^{n} y^{2}-b \lambda \,x^{m} \arctan \left (x \right )^{n} y+b m \,x^{m -1}
\]
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| \[
{} y^{\prime } = \lambda \arctan \left (x \right )^{n} \left (y-a \,x^{m}-b \right )^{2}+a m \,x^{m -1}
\]
|
✓ |
✓ |
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| \[
{} x y^{\prime } = \lambda \arctan \left (x \right )^{n} y^{2}+k y+\lambda \,b^{2} x^{2 k} \arctan \left (x \right )^{n}
\]
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✓ |
✓ |
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| \[
{} y^{\prime } = y^{2}+\lambda \operatorname {arccot}\left (x \right )^{n} y-a^{2}+a \lambda \operatorname {arccot}\left (x \right )^{n}
\]
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✓ |
✓ |
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| \[
{} y^{\prime } = y^{2}+\lambda x \operatorname {arccot}\left (x \right )^{n} y+\lambda \operatorname {arccot}\left (x \right )^{n}
\]
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✓ |
✓ |
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| \[
{} y^{\prime } = -\left (1+k \right ) x^{k} y^{2}+\lambda \operatorname {arccot}\left (x \right )^{n} \left (x^{1+k} y-1\right )
\]
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✓ |
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| \[
{} y^{\prime } = \lambda \operatorname {arccot}\left (x \right )^{n} y^{2}+a y+a b -b^{2} \lambda \operatorname {arccot}\left (x \right )^{n}
\]
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✓ |
✓ |
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| \[
{} y^{\prime } = \lambda \operatorname {arccot}\left (x \right )^{n} y^{2}-b \lambda \,x^{m} \operatorname {arccot}\left (x \right )^{n} y+b m \,x^{m -1}
\]
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| \[
{} y^{\prime } = \lambda \operatorname {arccot}\left (x \right )^{n} \left (y-a \,x^{m}-b \right )^{2}+a m \,x^{m -1}
\]
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✓ |
✓ |
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| \[
{} x y^{\prime } = \lambda \operatorname {arccot}\left (x \right )^{n} y^{2}+k y+\lambda \,b^{2} x^{2 k} \operatorname {arccot}\left (x \right )^{n}
\]
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✓ |
✓ |
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| \[
{} y^{\prime } = y^{2}+f \left (x \right ) y-a^{2}-f \left (x \right ) a
\]
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✓ |
✓ |
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| \[
{} y^{\prime } = f \left (x \right )+x f \left (x \right ) y+y^{2}
\]
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✓ |
✓ |
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| \[
{} y^{\prime } = f \left (x \right ) y^{2}-a \,x^{n} f \left (x \right ) y+a n \,x^{n -1}
\]
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✗ |
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| \[
{} y^{\prime } = f \left (x \right ) y^{2}+a n \,x^{n -1}-a^{2} x^{2 n} f \left (x \right )
\]
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| \[
{} y^{\prime } = -\left (n +1\right ) x^{n} y^{2}+x^{n +1} f \left (x \right ) y-f \left (x \right )
\]
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✓ |
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| \[
{} x y^{\prime } = f \left (x \right ) y^{2}+n y+a \,x^{2 n} f \left (x \right )
\]
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✓ |
✓ |
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| \[
{} x y^{\prime } = x^{2 n} f \left (x \right ) y^{2}+\left (a \,x^{n} f \left (x \right )-n \right ) y+b f \left (x \right )
\]
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✓ |
✓ |
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| \[
{} y^{\prime } = f \left (x \right ) y^{2}+g \left (x \right ) y-a^{2} f \left (x \right )-a g \left (x \right )
\]
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✓ |
✓ |
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| \[
{} y^{\prime } = f \left (x \right ) y^{2}+g \left (x \right ) y+a n \,x^{n -1}-a \,x^{n} g \left (x \right )-a^{2} x^{2 n} f \left (x \right )
\]
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| \[
{} y^{\prime } = f \left (x \right ) y^{2}-a \,x^{n} g \left (x \right ) y+a n \,x^{n -1}+a^{2} x^{2 n} \left (g \left (x \right )-f \left (x \right )\right )
\]
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✗ |
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|
| \[
{} y^{\prime } = a \,{\mathrm e}^{\lambda x} y^{2}+a \,{\mathrm e}^{\lambda x} f \left (x \right ) y+\lambda f \left (x \right )
\]
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✓ |
✓ |
✗ |
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| \[
{} y^{\prime } = f \left (x \right ) y^{2}-a \,{\mathrm e}^{\lambda x} f \left (x \right ) y+a \lambda \,{\mathrm e}^{\lambda x}
\]
|
✓ |
✗ |
✗ |
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| \[
{} y^{\prime } = f \left (x \right ) y^{2}+a \lambda \,{\mathrm e}^{\lambda x}-a^{2} {\mathrm e}^{2 \lambda x} f \left (x \right )
\]
|
✗ |
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| \[
{} y^{\prime } = f \left (x \right ) y^{2}+\lambda y+a^{2} {\mathrm e}^{2 \lambda x} f \left (x \right )
\]
|
✓ |
✓ |
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| \[
{} y^{\prime } = f \left (x \right ) y^{2}-f \left (x \right ) \left ({\mathrm e}^{\lambda x} a +b \right ) y+a \lambda \,{\mathrm e}^{\lambda x}
\]
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✗ |
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| \[
{} y^{\prime } = {\mathrm e}^{\lambda x} f \left (x \right ) y^{2}+\left (f \left (x \right ) a -\lambda \right ) y+b \,{\mathrm e}^{-\lambda x} f \left (x \right )
\]
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✓ |
✓ |
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| \[
{} y^{\prime } = f \left (x \right ) y^{2}+g \left (x \right ) y+a \lambda \,{\mathrm e}^{\lambda x}-a \,{\mathrm e}^{\lambda x} g \left (x \right )-a^{2} {\mathrm e}^{2 \lambda x} f \left (x \right )
\]
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✗ |
✗ |
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| \[
{} y^{\prime } = f \left (x \right ) y^{2}-a \,{\mathrm e}^{\lambda x} g \left (x \right ) y+a \lambda \,{\mathrm e}^{\lambda x}+a^{2} {\mathrm e}^{2 \lambda x} \left (g \left (x \right )-f \left (x \right )\right )
\]
|
✗ |
✗ |
✗ |
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| \[
{} y^{\prime } = f \left (x \right ) y^{2}+2 a \lambda x \,{\mathrm e}^{\lambda \,x^{2}}-a^{2} f \left (x \right ) {\mathrm e}^{2 \lambda \,x^{2}}
\]
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✗ |
✗ |
✗ |
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| \[
{} y^{\prime } = f \left (x \right ) y^{2}+\lambda x y+a f \left (x \right ) {\mathrm e}^{\lambda x}
\]
|
✗ |
✗ |
✗ |
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| \[
{} y^{\prime } = f \left (x \right ) y^{2}-a \tanh \left (\lambda x \right )^{2} \left (f \left (x \right ) a +\lambda \right )+a \lambda
\]
|
✗ |
✗ |
✗ |
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| \[
{} y^{\prime } = f \left (x \right ) y^{2}-a \coth \left (\lambda x \right )^{2} \left (f \left (x \right ) a +\lambda \right )+a \lambda
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y^{\prime } = f \left (x \right ) y^{2}-a^{2} f \left (x \right )+a \lambda \sinh \left (\lambda x \right )-a^{2} f \left (x \right ) \sinh \left (\lambda x \right )^{2}
\]
|
✗ |
✗ |
✗ |
|
| \[
{} x y^{\prime } = f \left (x \right ) y^{2}+a -a^{2} f \left (x \right ) \ln \left (x \right )^{2}
\]
|
✗ |
✗ |
✗ |
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| \[
{} x y^{\prime } = f \left (x \right ) \left (y+a \ln \left (x \right )\right )^{2}-a
\]
|
✓ |
✓ |
✗ |
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| \[
{} y^{\prime } = f \left (x \right ) y^{2}-a x \ln \left (x \right ) f \left (x \right ) y+a \ln \left (x \right )+a
\]
|
✗ |
✗ |
✗ |
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| \[
{} y^{\prime } = -a \ln \left (x \right ) y^{2}+a f \left (x \right ) \left (x \ln \left (x \right )-x \right ) y-f \left (x \right )
\]
|
✗ |
✓ |
✗ |
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| \[
{} y^{\prime } = \lambda \sin \left (\lambda x \right ) y^{2}+f \left (x \right ) \cos \left (\lambda x \right ) y-f \left (x \right )
\]
|
✗ |
✓ |
✗ |
|
| \[
{} y^{\prime } = f \left (x \right ) y^{2}-a^{2} f \left (x \right )+a \lambda \sin \left (\lambda x \right )+a^{2} f \left (x \right ) \sin \left (\lambda x \right )^{2}
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y^{\prime } = f \left (x \right ) y^{2}-a^{2} f \left (x \right )+a \lambda \cos \left (\lambda x \right )+a^{2} f \left (x \right ) \cos \left (\lambda x \right )^{2}
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y^{\prime } = f \left (x \right ) y^{2}-a \tan \left (\lambda x \right )^{2} \left (f \left (x \right ) a -\lambda \right )+a \lambda
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y^{\prime } = f \left (x \right ) y^{2}-a \cot \left (\lambda x \right )^{2} \left (f \left (x \right ) a -\lambda \right )+a \lambda
\]
|
✗ |
✗ |
✗ |
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| \[
{} y^{\prime } = y^{2}-f \left (x \right )^{2}+f^{\prime }\left (x \right )
\]
|
✗ |
✓ |
✗ |
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| \[
{} y^{\prime } = f \left (x \right ) y^{2}-f \left (x \right ) g \left (x \right ) y+g^{\prime }\left (x \right )
\]
|
✗ |
✗ |
✗ |
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| \[
{} y^{\prime } = -f^{\prime }\left (x \right ) y^{2}+f \left (x \right ) g \left (x \right ) y-g \left (x \right )
\]
|
✗ |
✓ |
✗ |
|
| \[
{} y^{\prime } = g \left (x \right ) \left (y-f \left (x \right )\right )^{2}+f^{\prime }\left (x \right )
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime } = \frac {y^{2} f^{\prime }\left (x \right )}{g \left (x \right )}-\frac {g^{\prime }\left (x \right )}{f \left (x \right )}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} f \left (x \right )^{2} y^{\prime }-f^{\prime }\left (x \right ) y^{2}+g \left (x \right ) \left (y-f \left (x \right )\right ) = 0
\]
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✗ |
✗ |
✗ |
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| \[
{} y^{\prime } = f^{\prime }\left (x \right ) y^{2}+a \,{\mathrm e}^{\lambda x} f \left (x \right ) y+{\mathrm e}^{\lambda x} a
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime } = f \left (x \right ) y^{2}+g^{\prime }\left (x \right ) y+a f \left (x \right ) {\mathrm e}^{2 g \left (x \right )}
\]
|
✓ |
✓ |
✗ |
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| \[
{} y^{\prime } = y^{2}-\frac {f^{\prime \prime }\left (x \right )}{f \left (x \right )}
\]
|
✓ |
✓ |
✗ |
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| \[
{} y^{\prime } = y^{2}+a^{2} f \left (a x +b \right )
\]
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✗ |
✗ |
✗ |
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| \[
{} y^{\prime } = y^{2}+\frac {f \left (\frac {1}{x}\right )}{x^{4}}
\]
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✗ |
✗ |
✗ |
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| \[
{} y^{\prime } = y^{2}+\frac {f \left (\frac {a x +b}{c x +d}\right )}{\left (c x +d \right )^{4}}
\]
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✗ |
✗ |
✗ |
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| \[
{} x^{2} y^{\prime } = x^{4} f \left (x \right ) y^{2}+1
\]
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✗ |
✗ |
✗ |
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| \[
{} x^{2} y^{\prime } = x^{4} y^{2}+x^{2 n} f \left (a \,x^{n}+b \right )-\frac {n^{2}}{4}+\frac {1}{4}
\]
|
✗ |
✗ |
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| \[
{} y^{\prime } = f \left (x \right ) y^{2}+g \left (x \right ) y+h \left (x \right )
\]
|
✗ |
✗ |
✗ |
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| \[
{} y^{\prime } = y^{2}+{\mathrm e}^{2 \lambda x} f \left ({\mathrm e}^{\lambda x}\right )-\frac {\lambda ^{2}}{4}
\]
|
✗ |
✗ |
✗ |
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| \[
{} y^{\prime } = y^{2}-\frac {\lambda ^{2}}{4}+\frac {{\mathrm e}^{2 \lambda x} f \left (\frac {{\mathrm e}^{\lambda x} a +b}{c \,{\mathrm e}^{\lambda x}+d}\right )}{\left (c \,{\mathrm e}^{\lambda x}+d \right )^{4}}
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y^{\prime } = y^{2}-\lambda ^{2}+\frac {f \left (\coth \left (\lambda x \right )\right )}{\sinh \left (\lambda x \right )^{4}}
\]
|
✗ |
✗ |
✗ |
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| \[
{} y^{\prime } = y^{2}-\lambda ^{2}+\frac {f \left (\tanh \left (\lambda x \right )\right )}{\cosh \left (\lambda x \right )^{4}}
\]
|
✗ |
✗ |
✗ |
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| \[
{} x^{2} y^{\prime } = x^{2} y^{2}+f \left (a \ln \left (x \right )+b \right )+\frac {1}{4}
\]
|
✗ |
✗ |
✗ |
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| \[
{} y^{\prime } = y^{2}+\lambda ^{2}+\frac {f \left (\cot \left (\lambda x \right )\right )}{\sin \left (\lambda x \right )^{4}}
\]
|
✗ |
✗ |
✗ |
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| \[
{} y^{\prime } = y^{2}+\lambda ^{2}+\frac {f \left (\tan \left (\lambda x \right )\right )}{\cos \left (\lambda x \right )^{4}}
\]
|
✗ |
✗ |
✗ |
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| \[
{} y^{\prime } = y^{2}+\lambda ^{2}+\frac {f \left (\frac {\sin \left (\lambda x +a \right )}{\sin \left (\lambda x +b \right )}\right )}{\sin \left (\lambda x +b \right )^{4}}
\]
|
✗ |
✗ |
✗ |
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| \[
{} y y^{\prime }-y = A x +B
\]
|
✓ |
✓ |
✗ |
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| \[
{} y y^{\prime }-y = -\frac {2 x}{9}+A +\frac {B}{\sqrt {x}}
\]
|
✓ |
✓ |
✗ |
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| \[
{} y y^{\prime }-y = 2 A \left (\sqrt {x}+4 A +\frac {3 A^{2}}{\sqrt {x}}\right )
\]
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✗ |
✓ |
✗ |
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| \[
{} y y^{\prime }-y = A x +\frac {B}{x}-\frac {B^{2}}{x^{3}}
\]
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✗ |
✓ |
✗ |
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| \[
{} y y^{\prime }-y = A \,x^{k -1}-k B \,x^{k}+k \,B^{2} x^{2 k -1}
\]
|
✗ |
✗ |
✗ |
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| \[
{} y y^{\prime }-y = \frac {A}{x}-\frac {A^{2}}{x^{3}}
\]
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✓ |
✓ |
✗ |
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| \[
{} y y^{\prime }-y = A +B \,{\mathrm e}^{-\frac {2 x}{A}}
\]
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✗ |
✓ |
✗ |
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| \[
{} y y^{\prime }-y = A \left ({\mathrm e}^{\frac {2 x}{A}}-1\right )
\]
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✗ |
✓ |
✗ |
|
| \[
{} y y^{\prime }-y = -\frac {2 \left (1+m \right )}{\left (3+m \right )^{2}}+A \,x^{m}
\]
|
✗ |
✗ |
✗ |
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| \[
{} y y^{\prime }-y = -\frac {2 x}{9}+6 A^{2} \left (1+\frac {2 A}{\sqrt {x}}\right )
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y y^{\prime }-y = \frac {2 m -2}{\left (m -3\right )^{2}}+\frac {2 A \left (m \left (3+m \right ) \sqrt {x}+\left (4 m^{2}+3 m +9\right ) A +\frac {3 m \left (3+m \right ) A^{2}}{\sqrt {x}}\right )}{\left (m -3\right )^{2}}
\]
|
✗ |
✗ |
✗ |
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| \[
{} y y^{\prime }-y = \frac {\left (2 m +1\right ) x}{4 m^{2}}+\frac {A}{x}-\frac {A^{2}}{x^{3}}
\]
|
✗ |
✓ |
✗ |
|
| \[
{} y y^{\prime }-y = \frac {4}{9} x +2 A \,x^{2}+2 A^{2} x^{3}
\]
|
✓ |
✓ |
✗ |
|