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