| # | ODE | Mathematica | Maple | Sympy |
| \[
{} 2 y y^{\prime \prime } = y^{2} \left (a x +b y\right )+{y^{\prime }}^{2}
\]
|
✗ |
✗ |
✗ |
|
| \[
{} 2 y y^{\prime \prime } = 3 y^{4}+{y^{\prime }}^{2}
\]
|
✓ |
✓ |
✗ |
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| \[
{} 2 y y^{\prime \prime } = 8 y^{3}-2 y^{2} \left (f \left (x \right )^{2}+f^{\prime }\left (x \right )\right )-3 f \left (x \right ) y y^{\prime }+{y^{\prime }}^{2}
\]
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✗ |
✗ |
✗ |
|
| \[
{} 2 y y^{\prime \prime } = 3 {y^{\prime }}^{2}
\]
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✓ |
✓ |
✗ |
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| \[
{} 2 y y^{\prime \prime } = 4 y^{2}+3 {y^{\prime }}^{2}
\]
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✓ |
✓ |
✗ |
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| \[
{} 2 y y^{\prime \prime } = f \left (x \right ) y^{2}+3 {y^{\prime }}^{2}
\]
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✗ |
✗ |
✗ |
|
| \[
{} 2 y y^{\prime \prime } = y^{2} \left (1-3 y^{2}\right )+6 {y^{\prime }}^{2}
\]
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✓ |
✓ |
✗ |
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| \[
{} 2 y y^{\prime \prime } = -y^{2} \left (1+a y^{3}\right )+6 {y^{\prime }}^{2}
\]
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✓ |
✓ |
✗ |
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| \[
{} 2 y y^{\prime \prime } = {y^{\prime }}^{2} \left (1+{y^{\prime }}^{2}\right )
\]
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✓ |
✓ |
✗ |
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| \[
{} 3 y y^{\prime \prime } = 36 y^{2}+2 {y^{\prime }}^{2}
\]
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✓ |
✓ |
✗ |
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| \[
{} 3 y y^{\prime \prime } = 5 {y^{\prime }}^{2}
\]
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✓ |
✓ |
✗ |
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| \[
{} 4 y y^{\prime \prime } = -4 y+3 {y^{\prime }}^{2}
\]
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✓ |
✓ |
✗ |
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| \[
{} 4 y y^{\prime \prime } = 12 y^{2}+3 {y^{\prime }}^{2}
\]
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✓ |
✓ |
✗ |
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| \[
{} 4 y y^{\prime \prime } = a y+b y^{2}+c y^{3}+3 {y^{\prime }}^{2}
\]
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✓ |
✓ |
✗ |
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| \[
{} 5 y y^{\prime \prime } = {y^{\prime }}^{2}
\]
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✓ |
✓ |
✗ |
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| \[
{} 12 y y^{\prime \prime } = -8 y^{3}+15 {y^{\prime }}^{2}
\]
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✓ |
✓ |
✗ |
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| \[
{} a y y^{\prime \prime } = \left (a -1\right ) {y^{\prime }}^{2}
\]
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✓ |
✓ |
✗ |
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| \[
{} a \left (2+a \right )^{2} y y^{\prime \prime } = -a^{2} f \left (x \right )^{2} y^{4}+a^{2} \left (2+a \right ) y^{3} f^{\prime }\left (x \right )+a \left (2+a \right )^{2} f \left (x \right ) y^{2} y^{\prime }+\left (a -1\right ) \left (2+a \right )^{2} {y^{\prime }}^{2}
\]
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✓ |
✗ |
✗ |
|
| \[
{} y y^{\prime }+x {y^{\prime }}^{2}+x y y^{\prime \prime } = 0
\]
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✓ |
✓ |
✗ |
|
| \[
{} x {y^{\prime }}^{2}+x y y^{\prime \prime } = y y^{\prime }
\]
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✓ |
✓ |
✗ |
|
| \[
{} x y y^{\prime \prime } = -y y^{\prime }+x {y^{\prime }}^{2}
\]
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✓ |
✓ |
✗ |
|
| \[
{} x y y^{\prime \prime } = y \left (\operatorname {a2} +\operatorname {a3} y^{2}\right )+x \left (\operatorname {a0} +\operatorname {a1} y^{4}\right )-y y^{\prime }+x {y^{\prime }}^{2}
\]
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✗ |
✗ |
✗ |
|
| \[
{} 2 y y^{\prime }+x {y^{\prime }}^{2}+x y y^{\prime \prime } = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} x {y^{\prime }}^{2}+x y y^{\prime \prime } = 3 y y^{\prime }
\]
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✓ |
✓ |
✗ |
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| \[
{} x y y^{\prime \prime } = x y^{3}+a y y^{\prime }+x {y^{\prime }}^{2}
\]
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✗ |
✗ |
✗ |
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| \[
{} x y y^{\prime \prime } = b^{2} x y^{3}+a y y^{\prime }+x {y^{\prime }}^{2}
\]
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✗ |
✗ |
✗ |
|
| \[
{} y y^{\prime }+2 x {y^{\prime }}^{2}+x y y^{\prime \prime } = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} y y^{\prime }-2 x {y^{\prime }}^{2}+x y y^{\prime \prime } = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} -y y^{\prime }-2 x {y^{\prime }}^{2}+x y y^{\prime \prime } = 0
\]
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✓ |
✓ |
✗ |
|
| \[
{} x y y^{\prime \prime } = -\left (1+y\right ) y^{\prime }+2 x {y^{\prime }}^{2}
\]
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✓ |
✓ |
✗ |
|
| \[
{} a y y^{\prime }+2 x {y^{\prime }}^{2}+x y y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} a y y^{\prime }-2 x {y^{\prime }}^{2}+x y y^{\prime \prime } = 0
\]
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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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| \[
{} a y^{\prime } \left (x y^{\prime }-y\right )+x y y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
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| \[
{} \left (x -y\right ) y^{\prime }+x {y^{\prime }}^{2}+x \left (x +y\right ) y^{\prime \prime } = y
\]
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✓ |
✓ |
✗ |
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| \[
{} 2 x y y^{\prime \prime } = -y y^{\prime }+x {y^{\prime }}^{2}
\]
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✓ |
✓ |
✗ |
|
| \[
{} \left (x y^{\prime }-y\right )^{2}+x^{2} y y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (x y^{\prime }-y\right )^{2}+x^{2} y y^{\prime \prime } = 3 y^{2}
\]
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✓ |
✓ |
✗ |
|
| \[
{} x^{2} y y^{\prime \prime } = a y^{2}+a x y y^{\prime }+2 x^{2} {y^{\prime }}^{2}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} c y^{2}+b x y y^{\prime }+a \,x^{2} {y^{\prime }}^{2}+x^{2} y y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 2 \left (1-y\right )^{2} y-2 x \left (1-y\right ) y^{\prime }+2 x^{2} {y^{\prime }}^{2}+x^{2} \left (1-y\right ) y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{2} \left (x -y\right ) y^{\prime \prime } = \left (x y^{\prime }-y\right )^{2}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (x y^{\prime }-y\right )^{2}+x^{2} \left (x -y\right ) y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{2} \left (x -y\right ) y^{\prime \prime } = a \left (x y^{\prime }-y\right )^{2}
\]
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✓ |
✓ |
✗ |
|
| \[
{} 2 x^{2} y y^{\prime \prime } = x^{2} {y^{\prime }}^{2}-y^{2}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 2 x^{2} y y^{\prime \prime } = -4 y^{2}+2 y y^{\prime } x +x^{2} {y^{\prime }}^{2}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x \left (1+x \right )^{2} y y^{\prime \prime } = a \left (x +2\right ) y^{2}-2 \left (x^{2}+1\right ) y y^{\prime }+x \left (1+x \right )^{2} {y^{\prime }}^{2}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 3 x y^{2}-12 x^{2} y y^{\prime }+4 \left (-x^{3}+1\right ) {y^{\prime }}^{2}+8 \left (-x^{3}+1\right ) y y^{\prime \prime } = 0
\]
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✓ |
✓ |
✗ |
|
| \[
{} \sqrt {a^{2}+x^{2}}\, \left (b {y^{\prime }}^{2}+y y^{\prime \prime }\right ) = y y^{\prime }
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \sqrt {a^{2}-x^{2}}\, \left (-y y^{\prime }-x {y^{\prime }}^{2}+x y y^{\prime \prime }\right ) = b x {y^{\prime }}^{2}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \operatorname {f3} \left (x \right ) y^{2}+\operatorname {f2} \left (x \right ) y y^{\prime }+\operatorname {f1} \left (x \right ) {y^{\prime }}^{2}+\operatorname {f0} \left (x \right ) y y^{\prime \prime } = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} 4 f \left (x \right ) y y^{\prime \prime } = 4 f \left (x \right )^{2} y+3 f \left (x \right ) g \left (x \right ) y^{2}-f \left (x \right ) y^{4}+2 y^{3} f^{\prime }\left (x \right )+\left (-6 f \left (x \right ) y^{2}+2 f^{\prime }\left (x \right )\right ) y^{\prime }+3 f \left (x \right ) {y^{\prime }}^{2}
\]
|
✗ |
✗ |
✗ |
|
| \[
{} \left (1-2 y\right ) {y^{\prime }}^{2}+\left (1+y^{2}\right ) y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (1+y^{2}\right ) y^{\prime \prime } = 3 y {y^{\prime }}^{2}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (1+y^{2}\right ) y^{\prime \prime } = \left (a +3 y\right ) {y^{\prime }}^{2}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime } \left (1+{y^{\prime }}^{2}\right )+\left (1+y^{2}\right ) y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (x +y^{2}\right ) y^{\prime \prime } = 2 \left (x -y^{2}\right ) {y^{\prime }}^{3}-y^{\prime } \left (1+4 y y^{\prime }\right )
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (x^{2}+y^{2}\right ) y^{\prime \prime } = \left (1+y^{2}\right ) \left (x y^{\prime }-y\right )
\]
|
✗ |
✗ |
✗ |
|
| \[
{} \left (x^{2}+y^{2}\right ) y^{\prime \prime } = 2 \left (1+y^{2}\right ) \left (x y^{\prime }-y\right )
\]
|
✗ |
✗ |
✗ |
|
| \[
{} 2 \left (1-y\right ) y y^{\prime \prime } = \left (1-2 y\right ) {y^{\prime }}^{2}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 2 \left (1-y\right ) y y^{\prime \prime } = f \left (x \right ) \left (1-y\right ) y y^{\prime }+\left (1-2 y\right ) {y^{\prime }}^{2}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 2 \left (1-y\right ) y y^{\prime \prime } = \left (1-3 y\right ) {y^{\prime }}^{2}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 2 \left (1-y\right ) y y^{\prime \prime } = 4 y \left (f \left (x \right )+g \left (x \right ) y\right ) y^{\prime }+\left (1-3 y\right ) {y^{\prime }}^{2}
\]
|
✗ |
✗ |
✗ |
|
| \[
{} 2 \left (1-y\right ) y y^{\prime \prime } = -\left (1-y\right )^{3} \left (\operatorname {F0} \left (x \right )^{2}-\operatorname {G0} \left (x \right )^{2} y^{2}\right )-4 \left (1-y\right ) y^{2} \left (f \left (x \right )^{2}-g \left (x \right )^{2}+f^{\prime }\left (x \right )+g^{\prime }\left (x \right )\right )-4 y \left (f \left (x \right )+g \left (x \right ) y\right ) y^{\prime }+\left (1-3 y\right ) {y^{\prime }}^{2}
\]
|
✗ |
✗ |
✗ |
|
| \[
{} 3 \left (1-y\right ) y y^{\prime \prime } = 2 \left (1-2 y\right ) {y^{\prime }}^{2}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 4 \left (1-y\right ) y y^{\prime \prime } = 3 \left (1-2 y\right ) {y^{\prime }}^{2}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x y^{2} y^{\prime \prime } = \left (a -y^{2}\right ) y^{\prime }+x y {y^{\prime }}^{2}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{2} y^{2} y^{\prime \prime } = \left (x^{2}+y^{2}\right ) \left (x y^{\prime }-y\right )
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (a^{2}-x^{2}\right ) y {y^{\prime }}^{2}+\left (a^{2}-x^{2}\right ) \left (a^{2}-y^{2}\right ) y^{\prime \prime } = x \left (a^{2}-y^{2}\right ) y^{\prime }
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \operatorname {a2} x \left (1-y\right ) y^{2}+\operatorname {a3} \,x^{3} y^{2} \left (1+y\right )+\left (1-y\right )^{3} \left (\operatorname {a0} +\operatorname {a1} y^{2}\right )+2 x \left (1-y\right ) y y^{\prime }-x^{2} \left (1-3 y\right ) {y^{\prime }}^{2}+2 x^{2} \left (1-y\right ) y y^{\prime \prime } = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} \left (x +y\right ) \left (x y^{\prime }-y\right )^{3}+x^{3} y^{2} y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (1-3 y^{2}\right ) {y^{\prime }}^{2}+y \left (1+y^{2}\right ) y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (-\left (1-y\right ) \left (a -y\right )+y \left (1-y\right )+\left (a -y\right ) y\right ) {y^{\prime }}^{2}+2 \left (1-y\right ) \left (a -y\right ) y y^{\prime \prime } = \operatorname {a3} \left (1-y\right )^{2} \left (a -y\right )^{2}+\operatorname {a1} \left (1-y\right )^{2} y^{2}+\operatorname {a2} \left (a -y\right )^{2} y^{2}+\operatorname {a0} \left (a -y\right )^{2} y^{2} \left (1-y^{2}\right )
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (\left (a -y\right ) \left (b -y\right )+\left (a -y\right ) \left (c -y\right )+\left (b -y\right ) \left (c -y\right )\right ) {y^{\prime }}^{2}+2 \left (a -y\right ) \left (b -y\right ) \left (c -y\right ) y^{\prime \prime } = \operatorname {a3} \left (a -y\right )^{2} \left (b -y\right )^{2}+2 \operatorname {a2} \left (a -y\right )^{2} \left (c -y\right )^{2}+\operatorname {a1} \left (b -y\right )^{2} \left (c -y\right )^{2}+\operatorname {a0} \left (a -y\right )^{2} \left (b -y\right )^{2} \left (c -y\right )^{2}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 2 \left (1-x \right ) x \left (1-y\right ) \left (x -y\right ) y y^{\prime \prime } = -y^{2} \left (1-y^{2}\right )+2 \left (1-y\right ) y \left (x^{2}+y-2 x y\right ) y^{\prime }+\left (1-x \right ) x \left (x -2 y-2 x y+3 y^{2}\right ) {y^{\prime }}^{2}
\]
|
✗ |
✗ |
✗ |
|
| \[
{} 2 \left (1-x \right ) x \left (1-y\right ) \left (x -y\right ) y y^{\prime \prime } = f \left (x \right ) \left (\left (1-y\right ) \left (x -y\right ) y\right )^{{3}/{2}}-y^{2} \left (1-y^{2}\right )+2 \left (1-y\right ) y \left (x^{2}+y-2 x y\right ) y^{\prime }+\left (1-x \right ) x \left (x -2 y-2 x y+3 y^{2}\right ) {y^{\prime }}^{2}
\]
|
✗ |
✗ |
✗ |
|
| \[
{} 2 \left (1-x \right )^{2} x^{2} \left (1-y\right ) \left (x -y\right ) y y^{\prime \prime } = \operatorname {a0} x \left (1-y\right )^{2} \left (x -y\right )^{2}+\left (\operatorname {a2} -1\right ) \left (1-x \right ) x \left (1-y\right )^{2} y^{2}+\operatorname {a1} \left (1-x \right ) \left (x -y\right )^{2} y^{2}+\operatorname {a3} \left (1-y\right )^{2} \left (x -y\right )^{2} y^{2}+2 \left (1-x \right ) x \left (1-y\right )^{2} y \left (x^{2}+y-2 x y\right ) y^{\prime }+\left (1-x \right )^{2} x^{2} \left (x -2 y-2 x y+3 y^{2}\right ) {y^{\prime }}^{2}
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y \left (1+a^{2}-2 a^{2} y^{2}\right )+b \sqrt {\left (1-y^{2}\right ) \left (1-a^{2} y^{2}\right )}\, {y^{\prime }}^{2}+\left (1-y^{2}\right ) \left (1-a^{2} y^{2}\right ) y^{\prime \prime } = 0
\]
|
✓ |
✗ |
✗ |
|
| \[
{} a^{2} y+\left (x^{2}+y^{2}\right )^{2} y^{\prime \prime } = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} A y+\left (a +2 b x +c \,x^{2}+y^{2}\right )^{2} y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \operatorname {f3} \left (y\right )+\operatorname {f2} \left (y\right ) y^{\prime }+\operatorname {f1} \left (y\right ) {y^{\prime }}^{2}+\operatorname {f0} \left (y\right ) y^{\prime \prime } = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} \operatorname {a2} \left (\operatorname {a3} +\operatorname {a1} \sin \left (y\right )^{2}\right ) y+\operatorname {a1} {y^{\prime }}^{2}+\operatorname {a1} \cos \left (y\right ) \sin \left (y\right ) {y^{\prime }}^{2}+\left (\operatorname {a0} +\operatorname {a1} \sin \left (y\right )^{2}\right ) y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (1+\ln \left (y\right )\right ) {y^{\prime }}^{2}+\left (1-\ln \left (y\right )\right ) y y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime } y^{\prime \prime } = x y^{2}+x^{2} y y^{\prime }
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y+x y^{\prime }+2 \left (x +y\right ) {y^{\prime }}^{2}+\left (y^{2}+2 x^{2} y^{\prime }\right ) y^{\prime \prime } = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} a y^{2}+x^{3} y^{\prime } y^{\prime \prime } = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} \operatorname {f5} y^{2}+\operatorname {f4} y y^{\prime }+\operatorname {f3} {y^{\prime }}^{2}+\operatorname {f2} y y^{\prime \prime }+\operatorname {f1} y^{\prime } y^{\prime \prime } = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} y+3 x y^{\prime }+2 {y^{\prime }}^{3} y+\left (x^{2}+2 y^{2} y^{\prime }\right ) y^{\prime \prime } = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y^{3}+\left ({y^{\prime }}^{2}+y^{2}\right ) y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime }-x y^{\prime \prime }+{y^{\prime \prime }}^{2} = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} a^{2} {y^{\prime \prime }}^{2} = \left (1+{y^{\prime }}^{2}\right )^{3}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 2 \left (x -y^{\prime }\right ) y^{\prime }-x \left (x +4 y^{\prime }\right ) y^{\prime \prime }+2 \left (x^{2}+1\right ) {y^{\prime \prime }}^{2} = 2 y
\]
|
✗ |
✗ |
✗ |
|
| \[
{} 4 {y^{\prime }}^{2}-2 \left (3 x y^{\prime }+y\right ) y^{\prime \prime }+3 x^{2} {y^{\prime \prime }}^{2} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 6 y y^{\prime \prime }-6 \left (1-6 x \right ) x y^{\prime } y^{\prime \prime }+\left (2-9 x \right ) x^{2} {y^{\prime \prime }}^{2} = 36 x {y^{\prime }}^{2}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} h y^{2}+\operatorname {g1} y y^{\prime }+\operatorname {g0} {y^{\prime }}^{2}+\operatorname {f2} y y^{\prime \prime }+\operatorname {f1} y^{\prime } y^{\prime \prime }+\operatorname {f0} {y^{\prime \prime }}^{2} = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} -{y^{\prime }}^{2}+4 {y^{\prime }}^{3} y+y y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (1+{y^{\prime }}^{2}+y y^{\prime \prime }\right )^{2} = \left (1+{y^{\prime }}^{2}\right )^{3}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} {y^{\prime }}^{2} \left (1-b^{2} {y^{\prime }}^{2}\right )+2 b^{2} y {y^{\prime }}^{2} y^{\prime \prime }+\left (a^{2}-b^{2} y^{2}\right ) {y^{\prime \prime }}^{2} = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} \left (y^{2}-x^{2} {y^{\prime }}^{2}+x^{2} y y^{\prime \prime }\right )^{2} = 4 x y \left (x y^{\prime }-y\right )^{3}
\]
|
✓ |
✗ |
✗ |
|
| \[
{} {y^{\prime \prime }}^{3} = 12 y^{\prime } \left (x y^{\prime \prime }-2 y^{\prime }\right )
\]
|
✗ |
✓ |
✗ |
|