| # | ODE | Mathematica | Maple | Sympy |
| \[
{} x y y^{\prime \prime }-2 x {y^{\prime }}^{2}+\left (1+y\right ) y^{\prime } = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} a y y^{\prime }-2 x {y^{\prime }}^{2}+x y y^{\prime \prime } = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} 4 y y^{\prime }-4 x {y^{\prime }}^{2}+x y y^{\prime \prime } = 0
\]
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✓ |
✓ |
✗ |
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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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✓ |
✓ |
✗ |
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| \[
{} 2 x y y^{\prime \prime }-x {y^{\prime }}^{2}+y y^{\prime } = 0
\]
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✓ |
✓ |
✗ |
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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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✗ |
✓ |
✗ |
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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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✓ |
✓ |
✗ |
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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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✓ |
✓ |
✗ |
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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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✓ |
✓ |
✗ |
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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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✓ |
✓ |
✗ |
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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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✓ |
✓ |
✗ |
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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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✓ |
✓ |
✗ |
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| \[
{} y^{2} y^{\prime \prime }-a = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} a x +y {y^{\prime }}^{2}+y^{2} y^{\prime \prime } = 0
\]
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✗ |
✓ |
✗ |
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| \[
{} y^{2} y^{\prime \prime }+y {y^{\prime }}^{2}-a x -b = 0
\]
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✗ |
✓ |
✗ |
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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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✓ |
✓ |
✗ |
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| \[
{} \left (1+y^{2}\right ) y^{\prime \prime }-3 y {y^{\prime }}^{2} = 0
\]
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✓ |
✓ |
✗ |
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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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✗ |
✓ |
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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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✓ |
✓ |
✗ |
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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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✓ |
✓ |
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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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✓ |
✓ |
✗ |
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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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✓ |
✓ |
✗ |
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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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✓ |
✓ |
✗ |
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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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✓ |
✓ |
✗ |
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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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✓ |
✓ |
✗ |
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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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✓ |
✓ |
✗ |
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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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✓ |
✓ |
✗ |
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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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✗ |
✗ |
✗ |
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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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✓ |
✗ |
✗ |
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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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✓ |
✓ |
✗ |
|
| \[
{} \sqrt {y}\, y^{\prime \prime }-a = 0
\]
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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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✓ |
✓ |
✗ |
|
| \[
{} \left (b +a \sin \left (y\right )^{2}\right ) y^{\prime \prime }+a {y^{\prime }}^{2} \cos \left (y\right ) \sin \left (y\right )+A y \left (c +a \sin \left (y\right )^{2}\right ) = 0
\]
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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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✗ |
✓ |
✗ |
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| \[
{} y+3 x y^{\prime }+2 {y^{\prime }}^{3} y+\left (x^{2}+2 y^{2} y^{\prime }\right ) y^{\prime \prime } = 0
\]
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✗ |
✗ |
✗ |
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| \[
{} y^{3}+\left ({y^{\prime }}^{2}+y^{2}\right ) y^{\prime \prime } = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} \left ({y^{\prime }}^{2}+a \left (x y^{\prime }-y\right )\right ) y^{\prime \prime }-b = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} \left (a \sqrt {1+{y^{\prime }}^{2}}-x y^{\prime }\right ) y^{\prime \prime }-{y^{\prime }}^{2}-1 = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} {y^{\prime \prime }}^{2}-a y-b = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} a^{2} {y^{\prime \prime }}^{2}-2 a x y^{\prime \prime }+y^{\prime } = 0
\]
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✗ |
✓ |
✗ |
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| \[
{} 2 \left (x^{2}+1\right ) {y^{\prime \prime }}^{2}-x \left (x +4 y^{\prime }\right ) y^{\prime \prime }+2 \left (x +y^{\prime }\right ) y^{\prime }-2 y = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} 4 {y^{\prime }}^{2}-2 \left (3 x y^{\prime }+y\right ) y^{\prime \prime }+3 x^{2} {y^{\prime \prime }}^{2} = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} \left (2-9 x \right ) x^{2} {y^{\prime \prime }}^{2}-6 \left (1-6 x \right ) x y^{\prime } y^{\prime \prime }+6 y y^{\prime \prime }-36 x {y^{\prime }}^{2} = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} y {y^{\prime \prime }}^{2}-a \,{\mathrm e}^{2 x} = 0
\]
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✗ |
✗ |
✗ |
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| \[
{} \left (a^{2} y^{2}-b^{2}\right ) {y^{\prime \prime }}^{2}-2 a^{2} y {y^{\prime }}^{2} y^{\prime \prime }+\left (a^{2} {y^{\prime }}^{2}-1\right ) {y^{\prime }}^{2} = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} \left (y^{2}-x^{2} {y^{\prime }}^{2}+x^{2} y y^{\prime \prime }\right )^{2}-4 x y \left (x y^{\prime }-y\right )^{3} = 0
\]
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✓ |
✗ |
✗ |
|
| \[
{} 32 y^{\prime \prime } \left (x y^{\prime \prime }-y^{\prime }\right )^{3}+\left (2 y y^{\prime \prime }-{y^{\prime }}^{2}\right )^{3} = 0
\]
|
✓ |
✗ |
✗ |
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| \[
{} \sqrt {a {y^{\prime \prime }}^{2}+b {y^{\prime }}^{2}}+c y y^{\prime \prime }+d {y^{\prime }}^{2} = 0
\]
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✗ |
✗ |
✗ |
|
| \[
{} y^{\prime \prime }-f \left (y\right ) = 0
\]
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✓ |
✓ |
✗ |
|
| \[
{} y^{\prime } = y^{2}-\frac {f^{\prime \prime }\left (x \right )}{f \left (x \right )}
\]
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✓ |
✓ |
✗ |
|
| \[
{} y y^{\prime }-y = a^{2} f^{\prime }\left (x \right ) f^{\prime \prime }\left (x \right )-\frac {\left (f \left (x \right )+b \right )^{2} f^{\prime \prime }\left (x \right )}{{f^{\prime }\left (x \right )}^{3}}
\]
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✗ |
✗ |
✗ |
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| \[
{} y^{\prime \prime }+a y = 0
\]
|
✓ |
✓ |
✓ |
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| \[
{} y^{\prime \prime }-\left (a x +b \right ) y = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} y^{\prime \prime }-\left (a^{2} x^{2}+a \right ) y = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} y^{\prime \prime }-\left (x^{2} a +b \right ) y = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} y^{\prime \prime }+a^{3} x \left (-a x +2\right ) y = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} y^{\prime \prime }-\left (x^{2} a +b c x \right ) y = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} y^{\prime \prime }-a \,x^{n} y = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} y^{\prime \prime }-a \left (a \,x^{2 n}+n \,x^{n -1}\right ) y = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} y^{\prime \prime }-a \,x^{n -2} \left (a \,x^{n}+n +1\right ) y = 0
\]
|
✗ |
✓ |
✗ |
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| \[
{} y^{\prime \prime }+\left (a \,x^{2 n}+b \,x^{n -1}\right ) y = 0
\]
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✓ |
✓ |
✗ |
|
| \[
{} b y+a y^{\prime }+y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✓ |
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| \[
{} y^{\prime \prime }+a y^{\prime }+\left (b x +c \right ) y = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} y^{\prime \prime }+a y^{\prime }-\left (b \,x^{2}+c \right ) y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }+a y^{\prime }+b \left (-b \,x^{2}+a x +1\right ) y = 0
\]
|
✓ |
✓ |
✗ |
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| \[
{} y^{\prime \prime }+a y^{\prime }+b x \left (-b \,x^{3}+a x +2\right ) y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }+a y^{\prime }+b \left (-b \,x^{2 n}+a \,x^{n}+n \,x^{n -1}\right ) y = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }+a y^{\prime }+b \left (-b \,x^{2 n}-a \,x^{n}+n \,x^{n -1}\right ) y = 0
\]
|
✗ |
✓ |
✗ |
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| \[
{} y^{\prime \prime }+x y^{\prime }+\left (n -1\right ) y = 0
\]
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✓ |
✓ |
✗ |
|
| \[
{} 2 n y-2 x y^{\prime }+y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} b y+a x y^{\prime }+y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
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| \[
{} y^{\prime \prime }+a x y^{\prime }+b x y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }+a x y^{\prime }+\left (b x +c \right ) y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }+2 a x y^{\prime }+\left (x^{4} b +a^{2} x^{2}+c x +a \right ) y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }+\left (a x +b \right ) y^{\prime }-a y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+a y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+c \left (a x +b -c \right ) y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }+\left (a x +2 b \right ) y^{\prime }+\left (a b x +b^{2}-a \right ) y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+\left (c x +d \right ) y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+c \left (\left (a -c \right ) x^{2}+b x +1\right ) y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }+2 \left (a x +b \right ) y^{\prime }+\left (a^{2} x^{2}+2 a b x +c \right ) y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+\left (\alpha \,x^{2}+\beta x +\gamma \right ) y = 0
\]
|
✓ |
✓ |
✗ |
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| \[
{} y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+c \left (-c \,x^{2 n}+a \,x^{n +1}+b \,x^{n}+n \,x^{n -1}\right ) y = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y^{\prime \prime }+a \left (-b^{2}+x^{2}\right ) y^{\prime }-a \left (x +b \right ) y = 0
\]
|
✓ |
✓ |
✗ |
|