| # | ODE | Mathematica | Maple | Sympy |
| \[
{} \left (a \,x^{n}+b \,x^{m}+c \right ) y^{\prime } = c y^{2}-b \,x^{m -1} y+a \,x^{n -2}
\]
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✗ |
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| \[
{} \left (a \,x^{n}+b \,x^{m}+c \right ) y^{\prime } = a \,x^{n -2} y^{2}+b \,x^{m -1} y+c
\]
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✗ |
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✗ |
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| \[
{} \left (a \,x^{n}+b \,x^{m}+c \right ) y^{\prime } = \alpha \,x^{k} y^{2}+\beta \,x^{s} y-\alpha \,\lambda ^{2} x^{k}+\beta \lambda \,x^{s}
\]
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✓ |
✓ |
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| \[
{} \left (a \,x^{n}+b \,x^{m}+c \right ) \left (x y^{\prime }-y\right )+s \,x^{k} \left (y^{2}-\lambda \,x^{2}\right ) = 0
\]
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✓ |
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| \[
{} y^{\prime } = a y^{2}+b \,{\mathrm e}^{\lambda x}
\]
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✓ |
✓ |
✗ |
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| \[
{} y^{\prime } = y^{2}+a \lambda \,{\mathrm e}^{\lambda x}-a^{2} {\mathrm e}^{2 \lambda x}
\]
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✓ |
✓ |
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| \[
{} y^{\prime } = \sigma y^{2}+a +b \,{\mathrm e}^{\lambda x}+c \,{\mathrm e}^{2 \lambda x}
\]
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✓ |
✓ |
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| \[
{} y^{\prime } = \sigma y^{2}+a y+b \,{\mathrm e}^{x}+c
\]
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✓ |
✓ |
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| \[
{} y^{\prime } = y^{2}+b y+a \left (\lambda -b \right ) {\mathrm e}^{\lambda x}-a^{2} {\mathrm e}^{2 \lambda x}
\]
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✓ |
✓ |
✗ |
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| \[
{} y^{\prime } = y^{2}+a \,{\mathrm e}^{\lambda x} y-a b \,{\mathrm e}^{\lambda x}-b^{2}
\]
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✓ |
✓ |
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| \[
{} y^{\prime } = y^{2}+a \,{\mathrm e}^{2 \lambda x} \left ({\mathrm e}^{\lambda x}+b \right )^{n}-\frac {\lambda ^{2}}{4}
\]
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✗ |
✓ |
✗ |
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| \[
{} y^{\prime } = y^{2}+a \,{\mathrm e}^{8 \lambda x}+b \,{\mathrm e}^{6 \lambda x}+c \,{\mathrm e}^{4 \lambda x}-\lambda ^{2}
\]
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✓ |
✓ |
✗ |
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| \[
{} y^{\prime } = a \,{\mathrm e}^{k x} y^{2}+b \,{\mathrm e}^{s x}
\]
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✓ |
✓ |
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| \[
{} y^{\prime } = b \,{\mathrm e}^{x \mu } y^{2}+a \lambda \,{\mathrm e}^{\lambda x}-a^{2} b \,{\mathrm e}^{\left (\mu +2 \lambda \right ) x}
\]
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✓ |
✗ |
✗ |
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| \[
{} y^{\prime } = a \,{\mathrm e}^{\lambda x} y^{2}+b y+c \,{\mathrm e}^{-\lambda x}
\]
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✓ |
✓ |
✓ |
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| \[
{} y^{\prime } = a \,{\mathrm e}^{x \mu } y^{2}+\lambda y-a \,b^{2} {\mathrm e}^{\left (\mu +2 \lambda \right ) x}
\]
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✓ |
✓ |
✗ |
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| \[
{} y^{\prime } = {\mathrm e}^{\lambda x} y^{2}+a \,{\mathrm e}^{x \mu } y+a \lambda \,{\mathrm e}^{\left (\mu -\lambda \right ) x}
\]
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✓ |
✓ |
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| \[
{} y^{\prime } = -\lambda \,{\mathrm e}^{\lambda x} y^{2}+a \,{\mathrm e}^{x \mu } y-a \,{\mathrm e}^{\left (\mu -\lambda \right ) x}
\]
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✓ |
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| \[
{} y^{\prime } = a \,{\mathrm e}^{x \mu } y^{2}+a b \,{\mathrm e}^{\left (\lambda +\mu \right ) x} y-b \lambda \,{\mathrm e}^{\lambda x}
\]
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✓ |
✓ |
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| \[
{} y^{\prime } = a \,{\mathrm e}^{k x} y^{2}+b y+c \,{\mathrm e}^{s x}+d \,{\mathrm e}^{-k x}
\]
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✓ |
✓ |
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| \[
{} y^{\prime } = a \,{\mathrm e}^{\left (\mu +2 \lambda \right ) x} y^{2}+\left (b \,{\mathrm e}^{\left (\lambda +\mu \right ) x}-\lambda \right ) y+c \,{\mathrm e}^{x \mu }
\]
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✓ |
✓ |
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| \[
{} y^{\prime } = a \,{\mathrm e}^{k x} y^{2}+b y+c \,{\mathrm e}^{k n x}+d \,{\mathrm e}^{k \left (2 n +1\right ) x}
\]
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✓ |
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| \[
{} y^{\prime } = {\mathrm e}^{x \mu } \left (y-b \,{\mathrm e}^{\lambda x}\right )^{2}+b \lambda \,{\mathrm e}^{\lambda x}
\]
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✓ |
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|
| \[
{} \left ({\mathrm e}^{\lambda x} a +b \,{\mathrm e}^{x \mu }+c \right ) y^{\prime } = y^{2}+k \,{\mathrm e}^{\nu x} y-m^{2}+k m \,{\mathrm e}^{\nu x}
\]
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✓ |
✓ |
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| \[
{} \left ({\mathrm e}^{\lambda x} a +b \,{\mathrm e}^{x \mu }+c \right ) \left (y^{\prime }-y^{2}\right )+a \,\lambda ^{2} {\mathrm e}^{\lambda x}+b \,\mu ^{2} {\mathrm e}^{x \mu } = 0
\]
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✓ |
✓ |
✗ |
|
| \[
{} y^{\prime } = y^{2}+a x \,{\mathrm e}^{\lambda x} y+{\mathrm e}^{\lambda x} a
\]
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✓ |
✓ |
✗ |
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| \[
{} y^{\prime } = a \,{\mathrm e}^{\lambda x} y^{2}+b \,{\mathrm e}^{-\lambda x}
\]
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✓ |
✓ |
✓ |
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| \[
{} y^{\prime } = a \,{\mathrm e}^{\lambda x} y^{2}+b n \,x^{n -1}-a \,b^{2} {\mathrm e}^{\lambda x} x^{2 n}
\]
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✗ |
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| \[
{} y^{\prime } = {\mathrm e}^{\lambda x} y^{2}+a \,x^{n} y+a \lambda \,x^{n} {\mathrm e}^{-\lambda x}
\]
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✓ |
✓ |
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| \[
{} y^{\prime } = -\lambda \,{\mathrm e}^{\lambda x} y^{2}+a \,x^{n} {\mathrm e}^{\lambda x} y-a \,x^{n}
\]
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✓ |
✓ |
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| \[
{} y^{\prime } = a \,{\mathrm e}^{\lambda x} y^{2}-a b \,x^{n} {\mathrm e}^{\lambda x} y+b n \,x^{n -1}
\]
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✓ |
✓ |
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| \[
{} y^{\prime } = a \,x^{n} y^{2}+b \lambda \,{\mathrm e}^{\lambda x}-a \,b^{2} x^{n} {\mathrm e}^{2 \lambda x}
\]
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✗ |
✗ |
✗ |
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| \[
{} y^{\prime } = a \,x^{n} y^{2}+\lambda y-a \,b^{2} x^{n} {\mathrm e}^{2 \lambda x}
\]
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✓ |
✓ |
✗ |
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| \[
{} y^{\prime } = a \,x^{n} y^{2}-a b \,x^{n} {\mathrm e}^{\lambda x} y+b \lambda \,{\mathrm e}^{\lambda x}
\]
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✓ |
✗ |
✗ |
|
| \[
{} y^{\prime } = -\left (1+k \right ) x^{k} y^{2}+a \,x^{1+k} {\mathrm e}^{\lambda x} y-{\mathrm e}^{\lambda x} a
\]
|
✓ |
✓ |
✗ |
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| \[
{} y^{\prime } = a \,x^{n} y^{2}-a \,x^{n} \left (b \,{\mathrm e}^{\lambda x}+c \right ) y+c \,x^{n}
\]
|
✗ |
✗ |
✗ |
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| \[
{} y^{\prime } = a \,x^{n} {\mathrm e}^{2 \lambda x} y^{2}+\left (b \,x^{n} {\mathrm e}^{\lambda x}-\lambda \right ) y+c \,x^{n}
\]
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✓ |
✓ |
✗ |
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| \[
{} y^{\prime } = a \,{\mathrm e}^{\lambda x} \left (y-b \,x^{n}-c \right )^{2}+b n \,x^{n -1}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x y^{\prime } = a \,{\mathrm e}^{\lambda x} y^{2}+k y+a \,b^{2} x^{2 k} {\mathrm e}^{\lambda x}
\]
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✓ |
✓ |
✗ |
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| \[
{} x y^{\prime } = a \,x^{2 n} {\mathrm e}^{\lambda x} y^{2}+\left (b \,x^{n} {\mathrm e}^{\lambda x}-n \right ) y+c \,{\mathrm e}^{\lambda x}
\]
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✓ |
✓ |
✗ |
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| \[
{} y^{\prime } = y^{2}+2 a \lambda x \,{\mathrm e}^{\lambda \,x^{2}}-a^{2} {\mathrm e}^{2 \lambda \,x^{2}}
\]
|
✗ |
✗ |
✗ |
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| \[
{} y^{\prime } = a \,{\mathrm e}^{-\lambda \,x^{2}} y^{2}+\lambda x y+a \,b^{2}
\]
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✓ |
✓ |
✗ |
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| \[
{} y^{\prime } = a \,x^{n} y^{2}+\lambda x y+a \,b^{2} x^{n} {\mathrm e}^{\lambda \,x^{2}}
\]
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✓ |
✓ |
✗ |
|
| \[
{} x^{4} \left (y^{\prime }-y^{2}\right ) = a +b \,{\mathrm e}^{\frac {k}{x}}+c \,{\mathrm e}^{\frac {2 k}{x}}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime } = y^{2}-a^{2}+a \lambda \sinh \left (\lambda x \right )-a^{2} \sinh \left (\lambda x \right )^{2}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime } = y^{2}+a \sinh \left (\beta x \right ) y+a b \sinh \left (\beta x \right )-b^{2}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime } = y^{2}+a x \sinh \left (b x \right )^{m} y+a \sinh \left (b x \right )^{m}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime } = \lambda \sinh \left (\lambda x \right ) y^{2}-\lambda \sinh \left (\lambda x \right )^{3}
\]
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✗ |
✓ |
✗ |
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| \[
{} y^{\prime } = \left (a \sinh \left (\lambda x \right )^{2}-\lambda \right ) y^{2}-a \sinh \left (\lambda x \right )^{2}+\lambda -a
\]
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✓ |
✓ |
✗ |
|
| \[
{} \left (\sinh \left (\lambda x \right ) a +b \right ) y^{\prime } = y^{2}+c \sinh \left (x \mu \right ) y-d^{2}+c d \sinh \left (x \mu \right )
\]
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✓ |
✓ |
✗ |
|
| \[
{} \left (\sinh \left (\lambda x \right ) a +b \right ) \left (y^{\prime }-y^{2}\right )+a \,\lambda ^{2} \sinh \left (\lambda x \right ) = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime } = \alpha y^{2}+\beta +\gamma \cosh \left (x \right )
\]
|
✓ |
✓ |
✗ |
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| \[
{} y^{\prime } = y^{2}+a \cosh \left (\beta x \right ) y+a b \cosh \left (\beta x \right )-b^{2}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime } = y^{2}+a x \cosh \left (b x \right )^{m} y+a \cosh \left (b x \right )^{m}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime } = \left (a \cosh \left (\lambda x \right )^{2}-\lambda \right ) y^{2}+a +\lambda -a \cosh \left (\lambda x \right )^{2}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 2 y^{\prime } = \left (a -\lambda +a \cosh \left (\lambda x \right )\right ) y^{2}+a +\lambda -a \cosh \left (\lambda x \right )
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime } = y^{2}-\lambda ^{2}+a \cosh \left (\lambda x \right )^{n} \sinh \left (\lambda x \right )^{-n -4}
\]
|
✗ |
✗ |
✗ |
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| \[
{} y^{\prime } = a \sinh \left (\lambda x \right ) y^{2}+b \sinh \left (\lambda x \right ) \cosh \left (\lambda x \right )^{n}
\]
|
✓ |
✓ |
✗ |
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| \[
{} y^{\prime } = a \cosh \left (\lambda x \right ) y^{2}+b \cosh \left (\lambda x \right ) \sinh \left (\lambda x \right )^{n}
\]
|
✓ |
✓ |
✗ |
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| \[
{} \left (a \cosh \left (\lambda x \right )+b \right ) y^{\prime } = y^{2}+c \cosh \left (x \mu \right ) y-d^{2}+c d \cosh \left (x \mu \right )
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (a \cosh \left (\lambda x \right )+b \right ) \left (y^{\prime }-y^{2}\right )+a \,\lambda ^{2} \cosh \left (\lambda x \right ) = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime } = y^{2}+a \lambda -a \left (a +\lambda \right ) \tanh \left (\lambda x \right )^{2}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime } = y^{2}+3 a \lambda -\lambda ^{2}-a \left (a +\lambda \right ) \tanh \left (\lambda x \right )^{2}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime } = y^{2}+a x \tanh \left (b x \right )^{m} y+a \tanh \left (b x \right )^{m}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (a \tanh \left (\lambda x \right )+b \right ) y^{\prime } = y^{2}+c \tanh \left (x \mu \right ) y-d^{2}+c d \tanh \left (x \mu \right )
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime } = y^{2}+a \lambda -a \left (a +\lambda \right ) \coth \left (\lambda x \right )^{2}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime } = y^{2}-\lambda ^{2}+3 a \lambda -a \left (a +\lambda \right ) \coth \left (\lambda x \right )^{2}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime } = y^{2}+a x \coth \left (b x \right )^{m} y+a \coth \left (b x \right )^{m}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (a \coth \left (\lambda x \right )+b \right ) y^{\prime } = y^{2}+c \coth \left (x \mu \right ) y-d^{2}+c d \coth \left (x \mu \right )
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime } = y^{2}-2 \lambda ^{2} \tanh \left (\lambda x \right )^{2}-2 \lambda ^{2} \coth \left (\lambda x \right )^{2}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime } = y^{2}+a \lambda +b \lambda -2 a b -a \left (a +\lambda \right ) \tanh \left (\lambda x \right )^{2}-b \left (b +\lambda \right ) \coth \left (\lambda x \right )^{2}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime } = a \ln \left (x \right )^{n} y^{2}+b m \,x^{m -1}-a \,b^{2} x^{2 m} \ln \left (x \right )^{n}
\]
|
✗ |
✗ |
✗ |
|
| \[
{} x y^{\prime } = a y^{2}+b \ln \left (x \right )+c
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x y^{\prime } = a y^{2}+b \ln \left (x \right )^{k}+c \ln \left (x \right )^{2+2 k}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x y^{\prime } = x y^{2}-a^{2} x \ln \left (\beta x \right )^{2}+a
\]
|
✗ |
✗ |
✗ |
|
| \[
{} x y^{\prime } = x y^{2}-a^{2} x \ln \left (\beta x \right )^{2 k}+a k \ln \left (\beta x \right )^{k -1}
\]
|
✗ |
✗ |
✗ |
|
| \[
{} x y^{\prime } = a \,x^{n} y^{2}+b -a \,b^{2} x^{n} \ln \left (x \right )^{2}
\]
|
✗ |
✗ |
✗ |
|
| \[
{} x^{2} y^{\prime } = x^{2} y^{2}+a \ln \left (x \right )^{2}+b \ln \left (x \right )+c
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{2} y^{\prime } = x^{2} y^{2}+a \left (b \ln \left (x \right )+c \right )^{n}+\frac {1}{4}
\]
|
✗ |
✗ |
✗ |
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| \[
{} x^{2} \ln \left (a x \right ) \left (y^{\prime }-y^{2}\right ) = 1
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime } = y^{2}+a \ln \left (\beta x \right ) y-a b \ln \left (\beta x \right )-b^{2}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime } = y^{2}+a x \ln \left (b x \right )^{m} y+a \ln \left (b x \right )^{m}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime } = a \,x^{n} y^{2}-a b \,x^{n +1} \ln \left (x \right ) y+b \ln \left (x \right )+b
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y^{\prime } = -\left (n +1\right ) x^{n} y^{2}+a \,x^{n +1} \ln \left (x \right )^{m} y-a \ln \left (x \right )^{m}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime } = a \ln \left (x \right )^{n} y-a b x \ln \left (x \right )^{n +1} y+b \ln \left (x \right )+b
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime } = a \ln \left (x \right )^{k} \left (y-b \,x^{n}-c \right )^{2}+b n \,x^{n -1}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime } = a \ln \left (x \right )^{n} y^{2}+b \ln \left (x \right )^{m} y+b c \ln \left (x \right )^{m}-a \,c^{2} \ln \left (x \right )^{n}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x y^{\prime } = \left (a y+b \ln \left (x \right )\right )^{2}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x y^{\prime } = a \ln \left (\lambda x \right )^{m} y^{2}+k y+a \,b^{2} x^{2 k} \ln \left (\lambda x \right )^{m}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x y^{\prime } = a \,x^{n} \left (y+b \ln \left (x \right )\right )^{2}-b
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x y^{\prime } = a \,x^{2 n} \ln \left (x \right ) y^{2}+\left (b \,x^{n} \ln \left (x \right )-n \right ) y+c \ln \left (x \right )
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{2} y^{\prime } = y^{2} a^{2} x^{2}-x y+b^{2} \ln \left (x \right )^{n}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (a \ln \left (x \right )+b \right ) y^{\prime } = y^{2}+c \ln \left (x \right )^{n} y-\lambda ^{2}+\lambda c \ln \left (x \right )^{n}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (a \ln \left (x \right )+b \right ) y^{\prime } = \ln \left (x \right )^{n} y^{2}+c y-\lambda ^{2} \ln \left (x \right )^{n}+\lambda c
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime } = \alpha y^{2}+\beta +\gamma \sin \left (\lambda x \right )
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime } = y^{2}-a^{2}+a \lambda \sin \left (\lambda x \right )+a^{2} \sin \left (\lambda x \right )^{2}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime } = y^{2}+\lambda ^{2}+c \sin \left (\lambda x +a \right )^{n} \sin \left (\lambda x +b \right )^{-n -4}
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y^{\prime } = y^{2}+a \sin \left (\beta x \right ) y+a b \sin \left (\beta x \right )-b^{2}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime } = y^{2}+a \sin \left (b x \right )^{m} y+a \sin \left (b x \right )^{m}
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y^{\prime } = \lambda \sin \left (\lambda x \right ) y^{2}+\lambda \sin \left (\lambda x \right )^{3}
\]
|
✗ |
✓ |
✗ |
|