| # | ODE | Mathematica | Maple | Sympy |
| \[
{} y y^{\prime \prime }-{y^{\prime }}^{2}-\left (-1+a y\right ) y^{\prime }+2 a^{2} y^{2}-2 y^{3} b^{2}+a y = 0
\]
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| \[
{} y y^{\prime \prime }-{y^{\prime }}^{2}+\left (-1+a y\right ) y^{\prime }-y \left (1+y\right ) \left (b^{2} y^{2}-a^{2}\right ) = 0
\]
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| \[
{} y y^{\prime \prime }-{y^{\prime }}^{2}+\left (\tan \left (x \right )+\cot \left (x \right )\right ) y y^{\prime }+\left (\cos \left (x \right )^{2}-n^{2} \cot \left (x \right )^{2}\right ) y^{2} \ln \left (y\right ) = 0
\]
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| \[
{} y y^{\prime \prime }-{y^{\prime }}^{2}-f \left (x \right ) y y^{\prime }-g \left (x \right ) y^{2} = 0
\]
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| \[
{} y y^{\prime \prime }-{y^{\prime }}^{2}+\left (g \left (x \right )+f \left (x \right ) y^{2}\right ) y^{\prime }-y \left (g^{\prime }\left (x \right )-f^{\prime }\left (x \right ) y^{2}\right ) = 0
\]
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| \[
{} y y^{\prime \prime }-3 {y^{\prime }}^{2}+3 y y^{\prime }-y^{2} = 0
\]
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| \[
{} y y^{\prime \prime }-a {y^{\prime }}^{2} = 0
\]
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| \[
{} y y^{\prime \prime }+a \left (1+{y^{\prime }}^{2}\right ) = 0
\]
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| \[
{} y y^{\prime \prime }+a {y^{\prime }}^{2}+b y^{3} = 0
\]
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| \[
{} y y^{\prime \prime }+a {y^{\prime }}^{2}+b y y^{\prime }+c y^{2}+d y^{1-a} = 0
\]
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| \[
{} y y^{\prime \prime }+a {y^{\prime }}^{2}+b y^{2} y^{\prime }+c y^{4} = 0
\]
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| \[
{} y y^{\prime \prime }-\frac {\left (a -1\right ) {y^{\prime }}^{2}}{a}-f \left (x \right ) y^{2} y^{\prime }+\frac {a f \left (x \right )^{2} y^{4}}{\left (2+a \right )^{2}}-\frac {a f^{\prime }\left (x \right ) y^{3}}{2+a} = 0
\]
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| \[
{} y y^{\prime \prime }-{y^{\prime }}^{2}-1-2 a y \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} = 0
\]
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| \[
{} -y^{\prime }+{y^{\prime }}^{2}+\left (x +y\right ) y^{\prime \prime } = 0
\]
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| \[
{} 2 y^{\prime } \left (1+y^{\prime }\right )+\left (x -y\right ) y^{\prime \prime } = 0
\]
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| \[
{} \left (x -y\right ) y^{\prime \prime }-\left (1+y^{\prime }\right ) \left (1+{y^{\prime }}^{2}\right ) = 0
\]
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| \[
{} \left (x -y\right ) y^{\prime \prime }-h \left (y^{\prime }\right ) = 0
\]
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| \[
{} 1+{y^{\prime }}^{2}+2 y y^{\prime \prime } = 0
\]
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| \[
{} 2 y y^{\prime \prime }-{y^{\prime }}^{2}+a = 0
\]
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| \[
{} 2 y y^{\prime \prime }-{y^{\prime }}^{2}+f \left (x \right ) y^{2}+a = 0
\]
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| \[
{} 2 y y^{\prime \prime }-{y^{\prime }}^{2}-8 y^{3} = 0
\]
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| \[
{} 2 y y^{\prime \prime }-{y^{\prime }}^{2}-8 y^{3}-4 y^{2} = 0
\]
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| \[
{} 2 y y^{\prime \prime }-{y^{\prime }}^{2}-4 y^{2} \left (2 y+x \right ) = 0
\]
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| \[
{} 2 y y^{\prime \prime }-{y^{\prime }}^{2}+\left (a y+b \right ) y^{2} = 0
\]
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| \[
{} 2 y y^{\prime \prime }-{y^{\prime }}^{2}+1+2 x y^{2}+a y^{3} = 0
\]
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| \[
{} 2 y y^{\prime \prime }-{y^{\prime }}^{2}+\left (b x +a y\right ) y^{2} = 0
\]
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| \[
{} 2 y y^{\prime \prime }-{y^{\prime }}^{2}-3 y^{4} = 0
\]
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| \[
{} 2 y y^{\prime \prime }-{y^{\prime }}^{2}+b -4 \left (x^{2}+a \right ) y^{2}-8 x y^{3}-3 y^{4} = 0
\]
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| \[
{} 2 y y^{\prime \prime }-3 {y^{\prime }}^{2} = 0
\]
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| \[
{} 2 y y^{\prime \prime }-3 {y^{\prime }}^{2}-4 y^{2} = 0
\]
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| \[
{} 2 y y^{\prime \prime }-3 {y^{\prime }}^{2}+f \left (x \right ) y^{2} = 0
\]
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| \[
{} 2 y y^{\prime \prime }-6 {y^{\prime }}^{2}+y^{2} \left (1+a y^{3}\right ) = 0
\]
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| \[
{} 2 y y^{\prime \prime }-{y^{\prime }}^{2} \left (1+{y^{\prime }}^{2}\right ) = 0
\]
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| \[
{} 2 \left (y-a \right ) y^{\prime \prime }+{y^{\prime }}^{2}+1 = 0
\]
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| \[
{} 3 y y^{\prime \prime }-2 {y^{\prime }}^{2}-x^{2} a -b x -c = 0
\]
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| \[
{} 3 y y^{\prime \prime }-5 {y^{\prime }}^{2} = 0
\]
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| \[
{} 4 y y^{\prime \prime }-3 {y^{\prime }}^{2}+4 y = 0
\]
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| \[
{} 4 y y^{\prime \prime }-3 {y^{\prime }}^{2}-12 y^{3} = 0
\]
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| \[
{} 4 y y^{\prime \prime }-3 {y^{\prime }}^{2}+a y^{3}+b y^{2}+c y = 0
\]
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| \[
{} 4 y y^{\prime \prime }-5 {y^{\prime }}^{2}+a y^{2} = 0
\]
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| \[
{} 12 y y^{\prime \prime }-15 {y^{\prime }}^{2}+8 y^{3} = 0
\]
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| \[
{} n y y^{\prime \prime }-\left (n -1\right ) {y^{\prime }}^{2} = 0
\]
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| \[
{} a y y^{\prime \prime }+b {y^{\prime }}^{2}+\operatorname {c4} y^{4}+\operatorname {c3} y^{3}+\operatorname {c2} y^{2}+\operatorname {c1} y+\operatorname {c0} = 0
\]
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| \[
{} a y y^{\prime \prime }+b {y^{\prime }}^{2}-\frac {y y^{\prime }}{\sqrt {c^{2}+x^{2}}} = 0
\]
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| \[
{} \left (a y+b \right ) y^{\prime \prime }+c {y^{\prime }}^{2} = 0
\]
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| \[
{} x y y^{\prime \prime }+x {y^{\prime }}^{2}-y y^{\prime } = 0
\]
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| \[
{} f \left (x \right )+a y y^{\prime }+x {y^{\prime }}^{2}+x y y^{\prime \prime } = 0
\]
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| \[
{} x y y^{\prime \prime }-x {y^{\prime }}^{2}+y y^{\prime }+x \left (d +a y^{4}\right )+y \left (c +b y^{2}\right ) = 0
\]
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| \[
{} x y y^{\prime \prime }-x {y^{\prime }}^{2}+a y y^{\prime }+b x y^{3} = 0
\]
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| \[
{} a y y^{\prime }+2 x {y^{\prime }}^{2}+x y y^{\prime \prime } = 0
\]
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| \[
{} x y y^{\prime \prime }-2 x {y^{\prime }}^{2}+\left (1+y\right ) y^{\prime } = 0
\]
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| \[
{} a y y^{\prime }-2 x {y^{\prime }}^{2}+x y y^{\prime \prime } = 0
\]
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| \[
{} 4 y y^{\prime }-4 x {y^{\prime }}^{2}+x y y^{\prime \prime } = 0
\]
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| \[
{} x y y^{\prime \prime }+\left (\frac {a x}{\sqrt {b^{2}-x^{2}}}-x \right ) {y^{\prime }}^{2}-y y^{\prime } = 0
\]
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✓ |
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| \[
{} x \left (x +y\right ) y^{\prime \prime }+x {y^{\prime }}^{2}+\left (x -y\right ) y^{\prime }-y = 0
\]
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| \[
{} 2 x y y^{\prime \prime }-x {y^{\prime }}^{2}+y y^{\prime } = 0
\]
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| \[
{} x^{2} \left (y-1\right ) y^{\prime \prime }-2 x^{2} {y^{\prime }}^{2}-2 x \left (y-1\right ) y^{\prime }-2 y \left (y-1\right )^{2} = 0
\]
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| \[
{} x^{2} \left (x +y\right ) y^{\prime \prime }-\left (x y^{\prime }-y\right )^{2} = 0
\]
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| \[
{} x^{2} \left (x -y\right ) y^{\prime \prime }+a \left (x y^{\prime }-y\right )^{2} = 0
\]
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| \[
{} 2 x^{2} y y^{\prime \prime }-x^{2} \left (1+{y^{\prime }}^{2}\right )+y^{2} = 0
\]
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| \[
{} a \,x^{2} y y^{\prime \prime }+b \,x^{2} {y^{\prime }}^{2}+c x y y^{\prime }+d y^{2} = 0
\]
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| \[
{} x \left (1+x \right )^{2} y y^{\prime \prime }-x \left (1+x \right )^{2} {y^{\prime }}^{2}+2 \left (1+x \right )^{2} y y^{\prime }-a \left (x +2\right ) y^{2} = 0
\]
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| \[
{} 8 \left (-x^{3}+1\right ) y y^{\prime \prime }-4 \left (-x^{3}+1\right ) {y^{\prime }}^{2}-12 x^{2} y y^{\prime }+3 x y^{2} = 0
\]
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| \[
{} y^{2} y^{\prime \prime }-a = 0
\]
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| \[
{} a x +y {y^{\prime }}^{2}+y^{2} y^{\prime \prime } = 0
\]
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| \[
{} y^{2} y^{\prime \prime }+y {y^{\prime }}^{2}-a x -b = 0
\]
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| \[
{} \left (1-2 y\right ) {y^{\prime }}^{2}+\left (1+y^{2}\right ) y^{\prime \prime } = 0
\]
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| \[
{} \left (1+y^{2}\right ) y^{\prime \prime }-3 y {y^{\prime }}^{2} = 0
\]
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| \[
{} \left (x +y^{2}\right ) y^{\prime \prime }-2 \left (x -y^{2}\right ) {y^{\prime }}^{3}+y^{\prime } \left (1+4 y y^{\prime }\right ) = 0
\]
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| \[
{} \left (x^{2}+y^{2}\right ) y^{\prime \prime }-\left (1+{y^{\prime }}^{2}\right ) \left (x y^{\prime }-y\right ) = 0
\]
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| \[
{} \left (x^{2}+y^{2}\right ) y^{\prime \prime }-2 \left (1+{y^{\prime }}^{2}\right ) \left (x y^{\prime }-y\right ) = 0
\]
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| \[
{} 2 \left (1-y\right ) y y^{\prime \prime }-\left (1-2 y\right ) {y^{\prime }}^{2}+f \left (x \right ) \left (1-y\right ) y y^{\prime } = 0
\]
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| \[
{} 2 \left (1-y\right ) y y^{\prime \prime }-\left (1-3 y\right ) {y^{\prime }}^{2}+h \left (y\right ) = 0
\]
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| \[
{} 3 \left (1-y\right ) y y^{\prime \prime }-2 \left (1-2 y\right ) {y^{\prime }}^{2}-h \left (y\right ) = 0
\]
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| \[
{} \left (1-y\right ) y^{\prime \prime }-3 \left (1-2 y\right ) {y^{\prime }}^{2}-h \left (y\right ) = 0
\]
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| \[
{} a y \left (y-1\right ) y^{\prime \prime }+\left (b y+c \right ) {y^{\prime }}^{2}+h \left (y\right ) = 0
\]
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| \[
{} a y \left (y-1\right ) y^{\prime \prime }-\left (a -1\right ) \left (2 y-1\right ) {y^{\prime }}^{2}+f y \left (y-1\right ) y^{\prime } = 0
\]
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| \[
{} a b y \left (y-1\right ) y^{\prime \prime }-\left (\left (2 a b -a -b \right ) y+\left (1-a \right ) b \right ) {y^{\prime }}^{2}+f y \left (y-1\right ) y^{\prime } = 0
\]
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✓ |
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| \[
{} x y^{2} y^{\prime \prime }-a = 0
\]
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✓ |
✓ |
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| \[
{} \left (a^{2}-x^{2}\right ) \left (a^{2}-y^{2}\right ) y^{\prime \prime }+\left (a^{2}-x^{2}\right ) y {y^{\prime }}^{2}-x \left (a^{2}-y^{2}\right ) y^{\prime } = 0
\]
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| \[
{} 2 x^{2} y \left (y-1\right ) y^{\prime \prime }-x^{2} \left (3 y-1\right ) {y^{\prime }}^{2}+2 x y \left (y-1\right ) y^{\prime }+\left (a y^{2}+b \right ) \left (y-1\right )^{3}+c x y^{2} \left (y-1\right )+d \,x^{2} y^{2} \left (1+y\right ) = 0
\]
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| \[
{} \left (x +y\right ) \left (x y^{\prime }-y\right )^{3}+x^{3} y^{2} y^{\prime \prime } = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} y^{3} y^{\prime \prime }-a = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} \left (1-3 y^{2}\right ) {y^{\prime }}^{2}+y \left (1+y^{2}\right ) y^{\prime \prime } = 0
\]
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✓ |
✓ |
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| \[
{} 2 y^{3} y^{\prime \prime }+y^{4}-a^{2} x y^{2}-1 = 0
\]
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✗ |
✗ |
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| \[
{} 2 y^{3} y^{\prime \prime }+y^{2} {y^{\prime }}^{2}-x^{2} a -b x -c = 0
\]
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| \[
{} 2 \left (y-a \right ) \left (y-b \right ) \left (y-c \right ) y^{\prime \prime }-\left (\left (y-a \right )^{2} \left (y-b \right ) \left (y-c \right )+\left (y-b \right ) \left (y-c \right )\right ) {y^{\prime }}^{2}+\left (y-a \right )^{2} \left (y-b \right )^{2} \left (y-c \right )^{2} \left (A_{0} +\frac {B_{0}}{\left (y-a \right )^{2}}+\frac {C_{1}}{\left (y-b \right )^{2}}+\frac {D_{0}}{\left (y-c \right )^{2}}\right ) = 0
\]
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| \[
{} \left (4 y^{3}-a y-b \right ) y^{\prime \prime }-\left (6 y^{2}-\frac {a}{2}\right ) {y^{\prime }}^{2} = 0
\]
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✓ |
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| \[
{} \left (4 y^{3}-a y-b \right ) \left (y^{\prime \prime }+f y^{\prime }\right )-\left (6 y^{2}-\frac {a}{2}\right ) {y^{\prime }}^{2} = 0
\]
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✓ |
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| \[
{} \left (y^{2}-1\right ) \left (a^{2} y^{2}-1\right ) y^{\prime \prime }+b \sqrt {\left (1-y^{2}\right ) \left (1-a^{2} y^{2}\right )}\, {y^{\prime }}^{2}+\left (1+a^{2}-2 a^{2} y^{2}\right ) y {y^{\prime }}^{2} = 0
\]
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| \[
{} \left (c +2 b x +x^{2} a +y^{2}\right )^{2} y^{\prime \prime }+y d = 0
\]
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✓ |
✓ |
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| \[
{} \sqrt {y}\, y^{\prime \prime }-a = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} \sqrt {x^{2}+y^{2}}\, y^{\prime \prime }-a \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} = 0
\]
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✗ |
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| \[
{} \left (1+\ln \left (y\right )\right ) {y^{\prime }}^{2}+\left (1-\ln \left (y\right )\right ) y y^{\prime \prime } = 0
\]
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✓ |
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| \[
{} \left (b +a \sin \left (y\right )^{2}\right ) y^{\prime \prime }+a {y^{\prime }}^{2} \cos \left (y\right ) \sin \left (y\right )+A y \left (c +a \sin \left (y\right )^{2}\right ) = 0
\]
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✓ |
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| \[
{} h \left (y\right ) y^{\prime \prime }+a h \left (y\right ) {y^{\prime }}^{2}+j \left (y\right ) = 0
\]
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✓ |
✓ |
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| \[
{} y^{\prime } y^{\prime \prime }-x^{2} y y^{\prime }-x y^{2} = 0
\]
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✗ |
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| \[
{} \left (x y^{\prime }-y\right ) y^{\prime \prime }+4 {y^{\prime }}^{2} = 0
\]
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✓ |
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| \[
{} \left (x y^{\prime }-y\right ) y^{\prime \prime }-\left (1+{y^{\prime }}^{2}\right )^{2} = 0
\]
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✓ |
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| \[
{} a \,x^{3} y^{\prime } y^{\prime \prime }+b y^{2} = 0
\]
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