| # | ODE | Mathematica | Maple | Sympy |
| \[
{} -\left (a^{2}-{\mathrm e}^{2 x}\right ) y+y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (a +b \,{\mathrm e}^{x}+c \,{\mathrm e}^{2 x}\right ) y+y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} a \,{\mathrm e}^{b x} y+y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (a +b \cosh \left (x \right )^{2}\right ) y+y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (a +b \sinh \left (x \right )^{2}\right ) y+y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (a +b \sin \left (x \right )^{2}\right ) y+y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \frac {\left (a +b \right ) y}{x^{2}}+y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x y-y^{\prime }+y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (c x +b \right ) y+a y^{\prime }+y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (c \,x^{2}+b \right ) y+a y^{\prime }+y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (b +{\mathrm e}^{x} c \right ) y+a y^{\prime }+y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} b \,{\mathrm e}^{2 a x} y+a y^{\prime }+y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} b \,{\mathrm e}^{k x} y+a y^{\prime }+y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y+x y^{\prime }+y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} -y+x y^{\prime }+y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 2 y-x y^{\prime }+y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} n y-x y^{\prime }+y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} -a y-x y^{\prime }+y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} -\left (1-x \right ) y-x y^{\prime }+y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 6 y-2 x y^{\prime }+y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} -8 y+2 x y^{\prime }+y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 2 n y-2 x y^{\prime }+y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} -\left (-x^{2}-x +1\right ) y-\left (2 x +1\right ) y^{\prime }+y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 2 \left (2 x^{2}+1\right ) y+4 x y^{\prime }+y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} -\left (-4 x^{2}+3\right ) y-4 x y^{\prime }+y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} a^{2} x^{2} y-2 a x y^{\prime }+y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} b y+a x y^{\prime }+y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} c y+\left (b x +a \right ) y^{\prime }+y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (\operatorname {b1} x +\operatorname {a1} \right ) y+\left (\operatorname {b0} x +\operatorname {a0} \right ) y^{\prime }+y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (\operatorname {c1} \,x^{2}+\operatorname {b1} x +\operatorname {a1} \right ) y+\left (\operatorname {b0} x +\operatorname {a0} \right ) y^{\prime }+y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} -2 a \left (-2 x^{2} a +1\right ) y-4 a x y^{\prime }+y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x y-x^{2} y^{\prime }+y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} -4 x y+x^{2} y^{\prime }+y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} -x^{3} y+x^{4} y^{\prime }+y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} a \left (1+k \right ) x^{k -1} y+a \,x^{k} y^{\prime }+y^{\prime \prime } = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} a k \,x^{k -1} y+a \,x^{k} y^{\prime }+y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} -a \,x^{k -1} y+a \,x^{k} y^{\prime }+y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} b \,x^{k -1} y+a \,x^{k} y^{\prime }+y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 2 y-\cot \left (x \right ) y^{\prime }+y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} k \left (1+k \right ) y+\cot \left (x \right ) y^{\prime }+y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} -\csc \left (x \right )^{2} y+\cot \left (x \right ) y^{\prime }+y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (p \left (p +1\right )-k^{2} \csc \left (x \right )^{2}\right ) y+\cot \left (x \right ) y^{\prime }+y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (\operatorname {a0} -\operatorname {a2} \csc \left (x \right )^{2}+4 \operatorname {a1} \sin \left (x \right )^{2}\right ) y+\cot \left (x \right ) y^{\prime }+y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 3 y+2 \cot \left (x \right ) y^{\prime }+y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (b +k^{2} \cos \left (x \right )^{2}\right ) y+a \cot \left (x \right ) y^{\prime }+y^{\prime \prime } = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} \left (a \cot \left (x \right )^{2}+b \cot \left (x \right ) \csc \left (x \right )+c \csc \left (x \right )^{2}\right ) y+k \cot \left (x \right ) y^{\prime }+y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 2 y-\cot \left (2 x \right ) y^{\prime }+y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} a \tan \left (x \right )^{2} y-2 \cot \left (2 x \right ) y^{\prime }+y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} c y+a \cot \left (b x \right ) y^{\prime }+y^{\prime \prime } = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} \left (-a^{2}+b^{2}\right ) y+2 a \cot \left (a x \right ) y^{\prime }+y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} a \tan \left (\frac {x}{2}\right )^{2} y-\csc \left (x \right ) y^{\prime }+y^{\prime \prime } = 0
\]
|
✓ |
✗ |
✗ |
|
| \[
{} \csc \left (x \right )^{2} \left (2+\sin \left (x \right )^{2}\right ) y-\csc \left (2 x \right ) y^{\prime }+y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} a \csc \left (x \right )^{2} y+\left (2+\cos \left (x \right )\right ) \csc \left (x \right ) y^{\prime }+y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} -2 \left (\cos \left (x \right )+1\right ) \sec \left (x \right ) y-\left (2+3 \cos \left (x \right )\right ) \csc \left (x \right ) y^{\prime }+y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \sin \left (x \right )^{2} y-\left (\cot \left (x \right )-\sin \left (x \right )\right ) y^{\prime }+y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} b \tan \left (x \right )^{2} y-2 \csc \left (2 x \right ) \left (1-a \sin \left (x \right )^{2}\right ) y^{\prime }+y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} a \cos \left (x \right )^{2} y+\tan \left (x \right ) y^{\prime }+y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} a \cot \left (x \right )^{2} y+\tan \left (x \right ) y^{\prime }+y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} -a \left (a +1\right ) \csc \left (x \right )^{2} y-\tan \left (x \right ) y^{\prime }+y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (a \cos \left (x \right )^{2}-\sec \left (x \right )^{2}\right ) y-\tan \left (x \right ) y^{\prime }+y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} -y+2 \tan \left (x \right ) y^{\prime }+y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 3 y+2 \tan \left (x \right ) y^{\prime }+y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} b y-2 \tan \left (x \right ) y^{\prime }+y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} -\left (a^{2}+1\right ) y-2 \tan \left (x \right ) y^{\prime }+y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} b y+a \tan \left (x \right ) y^{\prime }+y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y \,{\mathrm e}^{2 x}-\left (1+2 \,{\mathrm e}^{x}\right ) y^{\prime }+y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (\operatorname {a0} -\operatorname {a2} \operatorname {csch}\left (x \right )^{2}+4 \operatorname {a1} \sinh \left (x \right )^{2}\right ) y+\coth \left (x \right ) y^{\prime }+y^{\prime \prime } = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} \left (\operatorname {a0} +4 \operatorname {a1} \cosh \left (x \right )^{2}-\operatorname {a2} \operatorname {sech}\left (x \right )^{2}\right ) y+\tanh \left (x \right ) y^{\prime }+y^{\prime \prime } = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} b y+2 \tanh \left (x \right ) y^{\prime }+y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} b y+a \tanh \left (x \right ) y^{\prime }+y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} f \left (x \right ) y^{\prime }+y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} a k \,x^{k -1} y+2 a \,x^{k} y^{\prime }+2 y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 4 y^{\prime \prime } = \left (x^{2}+a \right ) y
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (-x^{2}+4 a +2\right ) y+4 y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y+x y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \left (x +a \right ) y+x y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x y^{\prime \prime }+y^{\prime } = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} -y+y^{\prime }+x y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} -\left (1+x \right ) y+y^{\prime }+x y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x y^{\prime \prime }-y^{\prime }+4 x^{3} y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} -a^{2} x^{3} y-y^{\prime }+x y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \left ({\mathrm e}^{x^{2}}-k^{2}\right ) x^{3} y-y^{\prime }+x y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 2 y^{\prime }+x y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} 2 y^{\prime }+x y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} a x y+2 y^{\prime }+x y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} a \,x^{2} y+2 y^{\prime }+x y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} a y^{\prime }+x y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y+\left (a +1\right ) y^{\prime }+x y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y+\left (1-a \right ) y^{\prime }+x y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} -y+\left (a +1\right ) y^{\prime }+x y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} -y+2 n y^{\prime }+x y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} b y+a y^{\prime }+x y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} b x y+a y^{\prime }+x y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (\operatorname {b2} x +\operatorname {b1} \right ) y+a y^{\prime }+x y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (\operatorname {c1} \,x^{2}+\operatorname {b1} x +\operatorname {a1} \right ) y+a y^{\prime }+x y^{\prime \prime } = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} b \,x^{k} y+a y^{\prime }+x y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y-y^{\prime } \left (1+x \right )+x y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} n y+\left (1-x \right ) y^{\prime }+x y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} n y+\left (1+k -x \right ) y^{\prime }+x y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 2 \left (1-x \right ) y-y^{\prime } \left (1+x \right )+x y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|