| # | ODE | Mathematica | Maple | Sympy |
| \[
{} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (-2 x^{2}+1\right ) y^{\prime }+y = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} 2 x^{2} \left (x^{2}+2\right ) y^{\prime \prime }+7 x^{3} y^{\prime }+\left (3 x^{2}+1\right ) y = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (-4 x^{2}+1\right ) y^{\prime }+\left (2 x^{2}+1\right ) y = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} 4 x^{2} \left (x^{2}+4\right ) y^{\prime \prime }+3 x \left (3 x^{2}+8\right ) y^{\prime }+\left (-9 x^{2}+1\right ) y = 0
\]
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✓ |
✓ |
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| \[
{} 3 x^{2} \left (x^{2}+3\right ) y^{\prime \prime }+x \left (11 x^{2}+3\right ) y^{\prime }+\left (5 x^{2}+1\right ) y = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} 4 x^{2} \left (4 x^{2}+1\right ) y^{\prime \prime }+32 x^{3} y^{\prime }+y = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} 9 x^{2} y^{\prime \prime }-3 x \left (-2 x^{2}+7\right ) y^{\prime }+\left (2 x^{2}+25\right ) y = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+x \left (7 x^{2}+3\right ) y^{\prime }+\left (-3 x^{2}+1\right ) y = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (8 x^{2}+3\right ) y^{\prime }+\left (12 x^{2}+1\right ) y = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} x^{2} y^{\prime \prime }-x \left (-x^{2}+1\right ) y^{\prime }+\left (x^{2}+1\right ) y = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} x^{2} \left (-2 x^{2}+1\right ) y^{\prime \prime }+x \left (-9 x^{2}+5\right ) y^{\prime }+\left (-3 x^{2}+4\right ) y = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} x^{2} \left (x^{2}+2\right ) y^{\prime \prime }+x \left (-x^{2}+14\right ) y^{\prime }+2 \left (x^{2}+9\right ) y = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (7 x^{2}+3\right ) y^{\prime }+\left (8 x^{2}+1\right ) y = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} x^{2} \left (1-2 x \right ) y^{\prime \prime }+3 x y^{\prime }+\left (1+4 x \right ) y = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} y+\left (1-x \right ) y^{\prime }+x \left (1+x \right ) y^{\prime \prime } = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} \left (1-x \right ) x^{2} y^{\prime \prime }+x \left (3-2 x \right ) y^{\prime }+\left (2 x +1\right ) y = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} 4 x^{2} \left (1+x \right ) y^{\prime \prime }+4 x^{2} y^{\prime }+\left (1-5 x \right ) y = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} \left (1-x \right ) x^{2} y^{\prime \prime }-\left (3-5 x \right ) x y^{\prime }+\left (4-5 x \right ) y = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (9 x^{2}+1\right ) y^{\prime }+\left (25 x^{2}+1\right ) y = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} 9 x^{2} y^{\prime \prime }+3 x \left (-x^{2}+1\right ) y^{\prime }+\left (7 x^{2}+1\right ) y = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} x \left (x^{2}+1\right ) y^{\prime \prime }+y^{\prime } \left (-x^{2}+1\right )-8 x y = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} 4 x^{2} y^{\prime \prime }+2 x \left (-x^{2}+4\right ) y^{\prime }+\left (7 x^{2}+1\right ) y = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} 4 x^{2} \left (1+x \right ) y^{\prime \prime }+8 x^{2} y^{\prime }+\left (1+x \right ) y = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} 9 x^{2} \left (x +3\right ) y^{\prime \prime }+3 x \left (3+7 x \right ) y^{\prime }+\left (4 x +3\right ) y = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }-x \left (3 x^{2}+2\right ) y^{\prime }+\left (-x^{2}+2\right ) y = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} 16 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+8 x \left (9 x^{2}+1\right ) y^{\prime }+\left (49 x^{2}+1\right ) y = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} x^{2} \left (3 x +4\right ) y^{\prime \prime }-x \left (4-3 x \right ) y^{\prime }+4 y = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} 4 x^{2} \left (x^{2}+3 x +1\right ) y^{\prime \prime }+8 x^{2} \left (2 x +3\right ) y^{\prime }+\left (9 x^{2}+3 x +1\right ) y = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} \left (1-x \right )^{2} x^{2} y^{\prime \prime }-x \left (-3 x^{2}+2 x +1\right ) y^{\prime }+\left (x^{2}+1\right ) y = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} 9 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+3 x \left (13 x^{2}+7 x +1\right ) y^{\prime }+\left (25 x^{2}+4 x +1\right ) y = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} 2 x^{2} \left (x +2\right ) y^{\prime \prime }-x \left (4-7 x \right ) y^{\prime }-\left (5-3 x \right ) y = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} x^{2} \left (1-2 x \right ) y^{\prime \prime }+x \left (8-9 x \right ) y^{\prime }+\left (6-3 x \right ) y = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (10 x^{2}+3\right ) y^{\prime }-\left (-14 x^{2}+15\right ) y = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} x^{2} \left (-2 x^{2}+1\right ) y^{\prime \prime }+x \left (-13 x^{2}+7\right ) y^{\prime }-14 x^{2} y = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} x^{2} y^{\prime \prime }-3 x y^{\prime }+\left (4 x +3\right ) y = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} y+x y^{\prime \prime } = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} 4 x^{2} \left (1+x \right ) y^{\prime \prime }+4 x \left (2 x +1\right ) y^{\prime }-\left (3 x +1\right ) y = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} x \left (1+x \right ) y^{\prime \prime }+x y^{\prime }+y = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} 2 x^{2} \left (2+3 x \right ) y^{\prime \prime }+x \left (4+21 x \right ) y^{\prime }-\left (1-9 x \right ) y = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} x^{2} y^{\prime \prime }+x \left (x +2\right ) y^{\prime }-\left (2-3 x \right ) y = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} 4 x^{2} y^{\prime \prime }+4 x y^{\prime }-\left (9-x \right ) y = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} x^{2} y^{\prime \prime }+10 x y^{\prime }+\left (14+x \right ) y = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} 4 x^{2} \left (1+x \right ) y^{\prime \prime }+4 x \left (3+8 x \right ) y^{\prime }-\left (5-49 x \right ) y = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} x^{2} \left (1+x \right ) y^{\prime \prime }-x \left (3+10 x \right ) y^{\prime }+30 x y = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} x^{2} y^{\prime \prime }+x \left (1+x \right ) y^{\prime }-3 \left (x +3\right ) y = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} x^{2} y^{\prime \prime }+x \left (1-2 x \right ) y^{\prime }-\left (x +4\right ) y = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} x \left (1+x \right ) y^{\prime \prime }-4 y^{\prime }-2 y = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} x^{2} \left (2 x +1\right ) y^{\prime \prime }+x \left (9+13 x \right ) y^{\prime }+\left (7+5 x \right ) y = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} 4 x^{2} \left (2 x +1\right ) y^{\prime \prime }-2 \left (4-x \right ) x y^{\prime }-\left (7+5 x \right ) y = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} 3 x^{2} \left (x +3\right ) y^{\prime \prime }-x \left (15+x \right ) y^{\prime }-20 y = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} x^{2} \left (1+x \right ) y^{\prime \prime }+x \left (1-10 x \right ) y^{\prime }-\left (9-10 x \right ) y = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} x^{2} \left (1+x \right ) y^{\prime \prime }+3 x^{2} y^{\prime }-\left (6-x \right ) y = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} x^{2} \left (2 x +1\right ) y^{\prime \prime }-2 x \left (3+14 x \right ) y^{\prime }+\left (6+100 x \right ) y = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} x^{2} \left (1+x \right ) y^{\prime \prime }-x \left (6+11 x \right ) y^{\prime }+\left (6+32 x \right ) y = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} 4 x^{2} \left (1+x \right ) y^{\prime \prime }+4 x \left (1+4 x \right ) y^{\prime }-\left (49+27 x \right ) y = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} x^{2} \left (2 x +1\right ) y^{\prime \prime }-x \left (9+8 x \right ) y^{\prime }-12 x y = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (-2 x^{2}+7\right ) y^{\prime }+12 y = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} x^{2} y^{\prime \prime }-x \left (-x^{2}+7\right ) y^{\prime }+12 y = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} x y^{\prime \prime }-5 y^{\prime }+x y = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} x^{2} y^{\prime \prime }+x \left (2 x^{2}+1\right ) y^{\prime }-\left (-10 x^{2}+1\right ) y = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} x^{2} y^{\prime \prime }-x y^{\prime }-\left (-x^{2}+3\right ) y = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} 4 x^{2} y^{\prime \prime }+2 x \left (x^{2}+8\right ) y^{\prime }+\left (3 x^{2}+5\right ) y = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} x^{2} y^{\prime \prime }+x \left (x^{2}+1\right ) y^{\prime }-\left (-3 x^{2}+1\right ) y = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} x^{2} y^{\prime \prime }+x \left (-2 x^{2}+1\right ) y^{\prime }-4 \left (2 x^{2}+1\right ) y = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} 4 x^{2} y^{\prime \prime }+8 x y^{\prime }-\left (-x^{2}+35\right ) y = 0
\]
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✓ |
✓ |
✓ |
|
| \[
{} 9 x^{2} y^{\prime \prime }-3 x \left (2 x^{2}+11\right ) y^{\prime }+\left (10 x^{2}+13\right ) y = 0
\]
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✓ |
✓ |
✗ |
|
| \[
{} x^{2} y^{\prime \prime }+x \left (-2 x^{2}+1\right ) y^{\prime }-4 \left (-x^{2}+1\right ) y = 0
\]
|
✓ |
✓ |
✓ |
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| \[
{} x^{2} y^{\prime \prime }+x \left (-3 x^{2}+1\right ) y^{\prime }-4 \left (-3 x^{2}+1\right ) y = 0
\]
|
✓ |
✓ |
✓ |
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| \[
{} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (11 x^{2}+5\right ) y^{\prime }+24 x^{2} y = 0
\]
|
✓ |
✓ |
✓ |
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| \[
{} 4 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+8 x y^{\prime }-\left (-x^{2}+35\right ) y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (-x^{2}+5\right ) y^{\prime }-\left (25 x^{2}+7\right ) y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (2 x^{2}+5\right ) y^{\prime }-21 y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }-x \left (x^{2}+3\right ) y^{\prime }-2 x y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} 4 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+4 x \left (x^{2}+2\right ) y^{\prime }-\left (x^{2}+15\right ) y = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} y^{\prime \prime }+t y^{\prime }+y = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} y^{\prime \prime }-t y = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} \left (t^{2}+2\right ) y^{\prime \prime }-t y^{\prime }-3 y = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} y^{\prime \prime }-t^{3} y = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} t \left (2-t \right ) y^{\prime \prime }-6 \left (t -1\right ) y^{\prime }-4 y = 0
\]
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✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+t^{2} y = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} y^{\prime \prime }-t^{3} y = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} y^{\prime \prime }+\left (t^{2}+2 t +1\right ) y^{\prime }-\left (4+4 t \right ) y = 0
\]
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✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }-2 t y^{\prime }+\lambda y = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} \left (-t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+\alpha \left (\alpha +1\right ) y = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} \left (-t^{2}+1\right ) y^{\prime \prime }-t y^{\prime }+\alpha ^{2} y = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} y^{\prime \prime }+t^{3} y^{\prime }+3 t^{2} y = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} y^{\prime \prime }+t^{3} y^{\prime }+3 t^{2} y = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} \left (1-t \right ) y^{\prime \prime }+t y^{\prime }+y = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} y^{\prime \prime }+y^{\prime }+t y = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} y^{\prime \prime }+t y^{\prime }+{\mathrm e}^{t} y = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} y^{\prime \prime }+y^{\prime }+{\mathrm e}^{t} y = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} y^{\prime \prime }+y^{\prime }+{\mathrm e}^{-t} y = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} t \left (t -2\right )^{2} y^{\prime \prime }+t y^{\prime }+y = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} t \left (t -2\right )^{2} y^{\prime \prime }+t y^{\prime }+y = 0
\]
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✓ |
✗ |
✗ |
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| \[
{} \sin \left (t \right ) y^{\prime \prime }+\cos \left (t \right ) y^{\prime }+\frac {y}{t} = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} \left ({\mathrm e}^{t}-1\right ) y^{\prime \prime }+{\mathrm e}^{t} y^{\prime }+y = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} \left (-t^{2}+1\right ) y^{\prime \prime }+\frac {y^{\prime }}{\sin \left (t +1\right )}+y = 0
\]
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✓ |
✗ |
✗ |
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| \[
{} t^{3} y^{\prime \prime }+\sin \left (t^{3}\right ) y^{\prime }+t y = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} 2 t^{2} y^{\prime \prime }+3 t y^{\prime }-\left (t +1\right ) y = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} 2 t y^{\prime \prime }+\left (1-2 t \right ) y^{\prime }-y = 0
\]
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✓ |
✓ |
✓ |
|