| # | ODE | Mathematica | Maple | Sympy |
| \[
{} y-y^{\prime } \left (1+x \right )+2 \left (1+x \right )^{2} y^{\prime \prime } = x
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (4 k x -4 p^{2}-x^{2}+1\right ) y+4 x^{2} y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} -\left (4 x^{2}+1\right ) y+4 x y^{\prime }+4 x^{2} y^{\prime \prime } = 4 x^{{3}/{2}} {\mathrm e}^{x}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (x +3\right ) y-2 x \left (x +2\right ) y^{\prime }+4 x^{2} y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} -\left (-4 x^{2}+4 x +1\right ) y+4 x \left (1-2 x \right ) y^{\prime }+4 x^{2} y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} -\left (-2 x^{2}+3\right ) y+4 x^{3} y^{\prime }+4 x^{2} y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (x^{4}+2 x^{2}+1\right ) y+4 x^{3} y^{\prime }+4 x^{2} y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (x^{4}+2 x^{2}+a \right ) y+4 x^{3} y^{\prime }+4 x^{2} y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} -y-8 x y^{\prime }+4 \left (-x^{2}+1\right ) y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} -\left (4 p^{2}+1\right ) y-8 x y^{\prime }+4 \left (-x^{2}+1\right ) y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} -a \left (2+a \right ) y+4 a x y^{\prime }+4 \left (-x^{2}+1\right ) y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y+2 \left (1-x \right ) y^{\prime }+4 \left (1-x \right ) x y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (b x +a \right ) y+2 \left (1-2 x \right ) y^{\prime }+4 \left (1-x \right ) x y^{\prime \prime } = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} \left (c \,x^{2}+b x +a \right ) y+2 \left (1-2 x \right ) y^{\prime }+4 \left (1-x \right ) x y^{\prime \prime } = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} -\left (k -p \right ) \left (1+k +p \right ) y+2 \left (1-\left (3-2 k \right ) x \right ) y^{\prime }+4 \left (1-x \right ) x y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (k^{2} x +b \right ) y+2 \left (a x +1\right ) y^{\prime }+4 \left (1-x \right ) x y^{\prime \prime } = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} -12 y-2 \left (2 x +1\right ) y^{\prime }+\left (2 x +1\right )^{2} y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} -12 y-2 \left (2 x +1\right ) y^{\prime }+\left (2 x +1\right )^{2} y^{\prime \prime } = 3 x +1
\]
|
✓ |
✓ |
✗ |
|
| \[
{} -9 y-3 \left (1-3 x \right ) y^{\prime }+\left (1-3 x \right )^{2} y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y b^{2}+a x y^{\prime }+\left (x^{2} a +1\right ) y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} c y+b x y^{\prime }+\left (x^{2} a +1\right ) y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} -2 b y+2 a y^{\prime }+x \left (b x +a \right ) y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 2 \operatorname {a2} y+\left (\operatorname {b1} x +\operatorname {a1} \right ) y^{\prime }+\left (\operatorname {c0} \,x^{2}+\operatorname {b0} x +\operatorname {a0} \right ) y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \operatorname {a2} y+\operatorname {a1} \left (b x +a \right ) y^{\prime }+\left (b x +a \right )^{2} y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} -y+x y^{\prime }+x^{3} y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} -2 y+x y^{\prime }+x^{3} y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} -y+2 x y^{\prime }+x^{3} y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (\operatorname {b2} x +\operatorname {a2} \right ) y+\operatorname {a1} x y^{\prime }+x^{3} y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (c \,x^{2}+b x +a \right ) y+x^{2} y^{\prime }+x^{3} y^{\prime \prime } = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} \left (c x +b \right ) y+a \,x^{2} y^{\prime }+x^{3} y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \operatorname {a2} x y+\left (\operatorname {b1} \,x^{2}+\operatorname {a1} \right ) y^{\prime }+x^{3} y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \operatorname {a2} y+x \left (\operatorname {b1} x +\operatorname {a1} \right ) y^{\prime }+x^{3} y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (\operatorname {b2} x +\operatorname {a2} \right ) y+x \left (\operatorname {b1} x +\operatorname {a1} \right ) y^{\prime }+x^{3} y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{3}-y^{\prime }+x \left (-x^{2}+1\right ) y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} a \,x^{3} y-y^{\prime }+x \left (-x^{2}+1\right ) y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 4 x y-\left (x^{2}+7\right ) y^{\prime }+x \left (-x^{2}+1\right ) y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 2 x y-2 \left (x^{2}+1\right ) y^{\prime }+x \left (x^{2}+1\right ) y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} -2 x y-2 y^{\prime } \left (-x^{2}+1\right )+x \left (x^{2}+1\right ) y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} -2 x y-2 y^{\prime } \left (-x^{2}+1\right )+x \left (-x^{2}+1\right ) y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} c x y+\left (b \,x^{2}+a \right ) y^{\prime }+x \left (x^{2}+1\right ) y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (a -1\right ) \left (a +b \right ) x y+\left (b \,x^{2}+a \right ) y^{\prime }+x \left (-x^{2}+1\right ) y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 2 \left (1-b \right ) x y+\left (b \,x^{2}+a \right ) y^{\prime }+x \left (-x^{2}+1\right ) y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} c x y+\left (a -\left (a +1\right ) x^{2}\right ) y^{\prime }+x \left (-x^{2}+1\right ) y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} c x y+\left (b \,x^{2}+a \right ) y^{\prime }+x \left (-x^{2}+1\right ) y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} -6 x y-y^{\prime }+x \left (x^{2}+2\right ) y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} -\left (x^{2}+4 x +2\right ) y-\left (-x^{3}-3 x^{2}+2 x +2\right ) y^{\prime }+x \left (-x^{2}+2\right ) y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \operatorname {a2} x y+\left (\operatorname {b1} \,x^{2}+\operatorname {a1} \right ) y^{\prime }+x \left (x^{2}+\operatorname {a0} \right ) y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} -\left (1+x \right )^{3} y+x y^{\prime }+x^{2} \left (1+x \right ) y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y-x \left (1+x \right ) y^{\prime }+\left (1-x \right ) x^{2} y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (2 x +1\right ) y-x \left (2 x +1\right ) y^{\prime }+x^{2} \left (1+x \right ) y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 2 \left (1+x \right ) y+2 \left (2-x \right ) x y^{\prime }+\left (1-x \right ) x^{2} y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (6-9 x \right ) y-\left (4-5 x \right ) x y^{\prime }+\left (1-x \right ) x^{2} y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 2 \left (3 x +1\right ) y+2 x \left (2+3 x \right ) y^{\prime }+x^{2} \left (1+x \right ) y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (\operatorname {b2} x +\operatorname {a2} \right ) y+x \left (\operatorname {b1} x +\operatorname {a1} \right ) y^{\prime }+\left (1-x \right ) x^{2} y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (\operatorname {b2} x +\operatorname {a2} \right ) y+x \left (\operatorname {b1} x +\operatorname {a1} \right ) y^{\prime }+x^{2} \left (\operatorname {a0} +x \right ) y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} -2 y+\left (1-x \right )^{2} x y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y+x \left (1+x \right ) y^{\prime }+x \left (x^{2}+1\right ) y^{\prime \prime } = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} 2 y+2 \left (2-x \right ) y^{\prime }+\left (2-x \right )^{2} x y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \operatorname {a0} \operatorname {a1} \left (-k +x \right ) y+\left (1-\operatorname {a0} +\operatorname {a1} +\operatorname {a0} \operatorname {a2} -\operatorname {a3} +\left (\operatorname {a2} +\operatorname {a3} \right ) x +\left (1+\operatorname {a0} +\operatorname {a1} \right ) x^{2}\right ) y^{\prime }+\left (1-x \right ) \left (a -x \right ) x y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (\operatorname {c1} x +\operatorname {c0} \right ) y+\left (\operatorname {b2} \,x^{2}+\operatorname {b1} x +\operatorname {b0} \right ) y^{\prime }+\left (\operatorname {a1} -x \right ) \left (\operatorname {a2} -x \right ) \left (\operatorname {a3} -x \right ) y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} -\left (1+x \right ) y+\left (3-5 x \right ) x y^{\prime }+2 \left (1-x \right ) x^{2} y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (3-x \right ) y-\left (4-x \right ) x y^{\prime }+2 \left (2-x \right ) x^{2} y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} -6 x y+2 y^{\prime }+x \left (3 x^{2}+1\right ) y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 2 \left (b x +3 a \right ) y-2 x \left (b x +2 a \right ) y^{\prime }+x^{2} \left (b x +a \right ) y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (b x +a \right ) y+2 \left (1-3 x \right ) \left (1-x \right ) y^{\prime }+4 \left (1-x \right ) x y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (\operatorname {b1} \,x^{2}+\operatorname {b0} \right ) y+\left (\operatorname {a2} \,x^{2}+\operatorname {a1} x +\operatorname {a0} \right ) y^{\prime }+4 \left (1-x \right ) x \left (-a x +1\right ) y^{\prime \prime } = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} \left (-a^{2}+{\mathrm e}^{\frac {2}{x}}\right ) y+x^{4} y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} -2 y+x y^{\prime }+x^{4} y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (2 x +1\right ) y-2 x^{2} y^{\prime }+x^{4} y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} -\left (1+x \right ) y+x^{3} y^{\prime }+x^{4} y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (c \,x^{4}+b \,x^{2}+a \right ) y+x^{3} y^{\prime }+x^{4} y^{\prime \prime } = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} y+x \left (x^{2}+1\right ) y^{\prime }+x^{4} y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (-x^{2}+1\right ) y-x \left (-x^{2}+1\right ) y^{\prime }+x^{4} y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} -y+x \left (2 x^{2}+1\right ) y^{\prime }+x^{4} y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} b y+2 x^{2} \left (x +a \right ) y^{\prime }+x^{4} y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} -x^{2} y-\left (-x^{3}+1\right ) y^{\prime }+x \left (x^{3}+1\right ) y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (-x^{2}+2\right ) y-x \left (-x^{2}+2\right ) y^{\prime }+x^{2} \left (-x^{2}+1\right ) y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} a \left (a +1\right ) y-2 x^{3} y^{\prime }+x^{2} \left (-x^{2}+1\right ) y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y+2 x \left (x^{2}+1\right ) y^{\prime }+\left (x^{2}+1\right )^{2} y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 4 y+2 x \left (x^{2}+1\right ) y^{\prime }+\left (x^{2}+1\right )^{2} y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} -a^{2} y-2 x \left (-x^{2}+1\right ) y^{\prime }+\left (x^{2}+1\right )^{2} y^{\prime \prime } = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} -\left (m^{2}-n \left (n +1\right ) \left (-x^{2}+1\right )\right ) y-2 x \left (-x^{2}+1\right ) y^{\prime }+\left (-x^{2}+1\right )^{2} y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} -\left (k^{2}-p \left (p +1\right ) \left (-x^{2}+1\right )\right ) y-2 x \left (-x^{2}+1\right ) y^{\prime }+\left (-x^{2}+1\right )^{2} y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} -\left (a^{2}-k \left (-x^{2}+1\right )\right ) y-2 x \left (-x^{2}+1\right ) y^{\prime }+\left (-x^{2}+1\right )^{2} y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (\operatorname {a4} \,x^{4}+\operatorname {a2} \,x^{2}+\operatorname {a0} \right ) y-2 x \left (-x^{2}+1\right ) y^{\prime }+\left (-x^{2}+1\right )^{2} y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} b y+a x \left (-x^{2}+1\right ) y^{\prime }+\left (x^{2}+1\right )^{2} y^{\prime \prime } = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} \left (\operatorname {c2} \,x^{2}+\operatorname {b2} x +\operatorname {a2} \right ) y+\operatorname {a1} x \left (-x^{2}+1\right ) y^{\prime }+\left (-x^{2}+1\right )^{2} y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y b^{2}+x \left (a^{2}+2 x^{2}\right ) y^{\prime }+x^{2} \left (a^{2}+x^{2}\right )^{2} y^{\prime \prime } = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} -\left (\operatorname {a4} \,x^{4}+\operatorname {a2} \,x^{2}+\operatorname {a0} \right ) y+2 x \left (a^{2}+2 x^{2}\right ) y^{\prime }+\left (a^{2}+x^{2}\right )^{2} y^{\prime \prime } = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} \left (\operatorname {a4} \,x^{4}+\operatorname {a2} \,x^{2}+\operatorname {a0} \right ) y-2 x \left (a^{2}-x^{2}\right ) y^{\prime }+\left (a^{2}-x^{2}\right )^{2} y^{\prime \prime } = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} \left (\operatorname {b1} \,x^{2}+\operatorname {a1} \right ) y+x \left (\operatorname {b0} \,x^{2}+\operatorname {a0} \right ) y^{\prime }+\left (a^{2}+x^{2}\right )^{2} \left (b^{2}+x^{2}\right ) y^{\prime \prime } = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} \left (\operatorname {c1} \,x^{4}+\operatorname {b1} \,x^{2}+\operatorname {a1} \right ) y+x \left (\operatorname {b0} \,x^{2}+\operatorname {a0} \right ) y^{\prime }+\left (a^{2}-x^{2}\right )^{2} \left (b^{2}-x^{2}\right ) y^{\prime \prime } = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} -2 \left (1-x \right ) y+2 \left (3-x \right ) x \left (1+x \right ) y^{\prime }+\left (1-x \right ) x \left (1+x \right )^{2} y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (c \,x^{2}+b x +a \right ) y+\left (1-x \right )^{2} x^{2} y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} -y+\left (1-2 x \right ) \left (1-x \right ) x y^{\prime }+\left (1-x \right )^{2} x^{2} y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (\operatorname {c2} \,x^{2}+\operatorname {b2} x +\operatorname {a2} \right ) y+\left (1-x \right ) x \left (\operatorname {b2} x +\operatorname {a1} \right ) y^{\prime }+\left (1-x \right )^{2} x^{2} y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} b y+\left (a -x \right )^{2} x^{2} y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (a -x \right )^{2} \left (-x +b \right )^{2} y^{\prime \prime } = k^{2} y
\]
|
✓ |
✓ |
✗ |
|
| \[
{} B y+\left (a -x \right ) \left (-x +b \right ) \left (A +2 x \right ) y^{\prime }+\left (a -x \right )^{2} \left (-x +b \right )^{2} y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 2 \left (3 x +1\right ) y+2 \left (2-3 x \right ) x y^{\prime }+\left (1-2 x \right ) \left (1-x \right ) x^{2} y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|