|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime \prime }-\left (a^{2} x^{2 n}-1\right ) y = 0
\] |
[_Titchmarsh] |
✗ |
0.176 |
|
|
\[
{}y^{\prime \prime }+\left (a \,x^{2 c}+b \,x^{c -1}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.332 |
|
|
\[
{}y^{\prime \prime }+\left ({\mathrm e}^{2 x}-v^{2}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.677 |
|
|
\[
{}y^{\prime \prime }+a \,{\mathrm e}^{b x} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.756 |
|
|
\[
{}y^{\prime \prime }-\left (4 a^{2} b^{2} x^{2} {\mathrm e}^{2 b \,x^{2}}-1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.201 |
|
|
\[
{}y^{\prime \prime }+\left (a \,{\mathrm e}^{2 x}+b \,{\mathrm e}^{x}+c \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.313 |
|
|
\[
{}y^{\prime \prime }+\left (a \cosh \left (x \right )^{2}+b \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.803 |
|
|
\[
{}y^{\prime \prime }+\left (a \cos \left (2 x \right )+b \right ) y = 0
\] |
[_ellipsoidal] |
✗ |
0.641 |
|
|
\[
{}y^{\prime \prime }+\left (a \cos \left (x \right )^{2}+b \right ) y = 0
\] |
[_ellipsoidal] |
✗ |
0.864 |
|
|
\[
{}y^{\prime \prime }-\left (1+2 \tan \left (x \right )^{2}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.793 |
|
|
\[
{}y^{\prime \prime }-\left (\frac {m \left (m -1\right )}{\cos \left (x \right )^{2}}+\frac {n \left (n -1\right )}{\sin \left (x \right )^{2}}+a \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
5.335 |
|
|
\[
{}y^{\prime \prime }-\left (n \left (n +1\right ) \operatorname {WeierstrassP}\left (x , \operatorname {g2} , \operatorname {g3}\right )+B \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.164 |
|
|
\[
{}y^{\prime \prime }-\left (n \left (n +1\right ) k^{2} \operatorname {JacobiSN}\left (x , k\right )^{2}+b \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.305 |
|
|
\[
{}y^{\prime \prime }-\left (\frac {p^{\prime \prime \prime \prime }\left (x \right )}{30}+\frac {7 p^{\prime \prime }\left (x \right )}{3}+a p \left (x \right )+b \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.214 |
|
|
\[
{}y^{\prime \prime }-\left (f \left (x \right )^{2}+f^{\prime }\left (x \right )\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.322 |
|
|
\[
{}y^{\prime \prime }+\left (P \left (x \right )+l \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.141 |
|
|
\[
{}y^{\prime \prime }-f \left (x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.127 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+a \,{\mathrm e}^{-2 x} y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.178 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }+{\mathrm e}^{2 x} y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.088 |
|
|
\[
{}y^{\prime \prime }+a y^{\prime }+b y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.135 |
|
|
\[
{}y^{\prime \prime }+a y^{\prime }+b y-f \left (x \right ) = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.184 |
|
|
\[
{}y^{\prime \prime }+a y^{\prime }-\left (b^{2} x^{2}+c \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.608 |
|
|
\[
{}y^{\prime \prime }+2 a y^{\prime }+f \left (x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.205 |
|
|
\[
{}y^{\prime \prime }+x y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.230 |
|
|
\[
{}y^{\prime \prime }+x y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.528 |
|
|
\[
{}y^{\prime \prime }+x y^{\prime }+\left (n +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.536 |
|
|
\[
{}y^{\prime \prime }+x y^{\prime }-n y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.538 |
|
|
\[
{}y^{\prime \prime }-x y^{\prime }+2 y = 0
\] |
[_Hermite] |
✓ |
1.339 |
|
|
\[
{}y^{\prime \prime }-x y^{\prime }-a y = 0
\] |
[_Hermite] |
✗ |
0.557 |
|
|
\[
{}y^{\prime \prime }-x y^{\prime }+\left (x -1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.318 |
|
|
\[
{}y^{\prime \prime }-2 x y^{\prime }+a y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.523 |
|
|
\[
{}y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}+2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.798 |
|
|
\[
{}y^{\prime \prime }-4 x y^{\prime }+\left (3 x^{2}+2 n -1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.560 |
|
|
\[
{}y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-1\right ) y-{\mathrm e}^{x} = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.901 |
|
|
\[
{}y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.733 |
|
|
\[
{}y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-3\right ) y-{\mathrm e}^{x^{2}} = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.211 |
|
|
\[
{}y^{\prime \prime }+a x y^{\prime }+b y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.619 |
|
|
\[
{}y^{\prime \prime }+2 a x y^{\prime }+a^{2} x^{2} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.518 |
|
|
\[
{}y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+\left (c x +d \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.786 |
|
|
\[
{}y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+\left (\operatorname {a1} \,x^{2}+\operatorname {b1} x +\operatorname {c1} \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
2.464 |
|
|
\[
{}y^{\prime \prime }-x^{2} y^{\prime }+x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.590 |
|
|
\[
{}y^{\prime \prime }-x^{2} y^{\prime }-\left (x +1\right )^{2} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.378 |
|
|
\[
{}y^{\prime \prime }-x^{2} \left (x +1\right ) y^{\prime }+x \left (x^{4}-2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.309 |
|
|
\[
{}y^{\prime \prime }+x^{4} y^{\prime }-x^{3} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.849 |
|
|
\[
{}y^{\prime \prime }+a \,x^{q -1} y^{\prime }+b \,x^{q -2} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.615 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } \sqrt {x}+\left (\frac {1}{4 \sqrt {x}}+\frac {x}{4}-9\right ) y-x \,{\mathrm e}^{-\frac {x^{{3}/{2}}}{3}} = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.601 |
|
|
\[
{}y^{\prime \prime }-\frac {y^{\prime }}{\sqrt {x}}+\frac {\left (x +\sqrt {x}-8\right ) y}{4 x^{2}} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.326 |
|
|
\[
{}y^{\prime \prime }-\left (2 \,{\mathrm e}^{x}+1\right ) y^{\prime }+{\mathrm e}^{2 x} y-{\mathrm e}^{3 x} = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.799 |
|
|
\[
{}y^{\prime \prime }+a y^{\prime }+\tan \left (x \right )+b y = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.889 |
|
|
\[
{}y^{\prime \prime }+2 n y^{\prime } \cot \left (x \right )+\left (-a^{2}+n^{2}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
1.753 |
|
|
\[
{}y^{\prime \prime }+\tan \left (x \right ) y^{\prime }+\cos \left (x \right )^{2} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
3.019 |
|
|
\[
{}y^{\prime \prime }+\tan \left (x \right ) y^{\prime }-\cos \left (x \right )^{2} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.924 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } \cot \left (x \right )+v \left (v +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
1.326 |
|
|
\[
{}y^{\prime \prime }-y^{\prime } \cot \left (x \right )+y \sin \left (x \right )^{2} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.952 |
|
|
\[
{}y^{\prime \prime }+a y^{\prime } \tan \left (x \right )+b y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
1.473 |
|
|
\[
{}y^{\prime \prime }+2 a y^{\prime } \cot \left (a x \right )+\left (-a^{2}+b^{2}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.101 |
|
|
\[
{}y^{\prime \prime }+a p^{\prime \prime }\left (x \right ) y^{\prime }+\left (a +b p \left (x \right )-4 n a p \left (x \right )^{2}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.348 |
|
|
\[
{}y^{\prime \prime }+\frac {\left (11 \operatorname {WeierstrassP}\left (x , a , b\right ) \operatorname {WeierstrassPPrime}\left (x , a , b\right )-6 \operatorname {WeierstrassP}\left (x , a , b\right )^{2}+\frac {a}{2}\right ) y^{\prime }}{\operatorname {WeierstrassPPrime}\left (x , a , b\right )+\operatorname {WeierstrassP}\left (x , a , b\right )^{2}}+\frac {\left (\operatorname {WeierstrassPPrime}\left (x , a , b\right )^{2}-\operatorname {WeierstrassP}\left (x , a , b\right )^{2} \operatorname {WeierstrassPPrime}\left (x , a , b\right )-\operatorname {WeierstrassP}\left (x , a , b\right ) \left (6 \operatorname {WeierstrassP}\left (x , a , b\right )^{2}-\frac {a}{2}\right )\right ) y}{\operatorname {WeierstrassPPrime}\left (x , a , b\right )+\operatorname {WeierstrassP}\left (x , a , b\right )^{2}} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
42.775 |
|
|
\[
{}y^{\prime \prime }+f \left (x \right ) y^{\prime }+g \left (x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.257 |
|
|
\[
{}y^{\prime \prime }+f \left (x \right ) y^{\prime }+\left (f^{\prime }\left (x \right )+a \right ) y-g \left (x \right ) = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
0.299 |
|
|
\[
{}y^{\prime \prime }+\left (a f \left (x \right )+b \right ) y^{\prime }+\left (c f \left (x \right )+d \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.284 |
|
|
\[
{}y^{\prime \prime }+f \left (x \right ) y^{\prime }+\left (\frac {f \left (x \right )^{2}}{4}+\frac {f^{\prime }\left (x \right )}{2}+a \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.056 |
|
|
\[
{}y^{\prime \prime }-\frac {a f^{\prime }\left (x \right ) y^{\prime }}{f \left (x \right )}+b f \left (x \right )^{2 a} y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.104 |
|
|
\[
{}y^{\prime \prime }-\left (\frac {f^{\prime }\left (x \right )}{f \left (x \right )}+2 a \right ) y^{\prime }+\left (\frac {a f^{\prime }\left (x \right )}{f \left (x \right )}+a^{2}-b^{2} f \left (x \right )^{2}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
1.056 |
|
|
\[
{}y^{\prime \prime }+\frac {f \left (x \right ) f^{\prime \prime \prime }\left (x \right ) y^{\prime }}{f \left (x \right )^{2}+b^{2}}-\frac {a^{2} {f^{\prime }\left (x \right )}^{2} y}{f \left (x \right )^{2}+b^{2}} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.636 |
|
|
\[
{}y^{\prime \prime }-\left (\frac {2 f^{\prime }\left (x \right )}{f \left (x \right )}+\frac {g^{\prime \prime }\left (x \right )}{g^{\prime }\left (x \right )}-\frac {g^{\prime }\left (x \right )}{g \left (x \right )}\right ) y^{\prime }+\left (\frac {f^{\prime }\left (x \right ) \left (\frac {2 f^{\prime }\left (x \right )}{f \left (x \right )}+\frac {g^{\prime \prime }\left (x \right )}{g^{\prime }\left (x \right )}-\frac {g^{\prime }\left (x \right )}{g \left (x \right )}\right )}{f \left (x \right )}-\frac {f^{\prime \prime }\left (x \right )}{f \left (x \right )}-\frac {v^{2} {g^{\prime }\left (x \right )}^{2}}{g \left (x \right )^{2}}+{g^{\prime }\left (x \right )}^{2}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
1.712 |
|
|
\[
{}y^{\prime \prime }-\left (\frac {g^{\prime \prime }\left (x \right )}{g^{\prime }\left (x \right )}+\frac {\left (2 v -1\right ) g^{\prime }\left (x \right )}{g \left (x \right )}+\frac {2 h^{\prime }\left (x \right )}{h \left (x \right )}\right ) y^{\prime }+\left (\frac {h^{\prime }\left (x \right ) \left (\frac {g^{\prime \prime }\left (x \right )}{g^{\prime }\left (x \right )}+\frac {\left (2 v -1\right ) g^{\prime }\left (x \right )}{g \left (x \right )}+\frac {2 h^{\prime }\left (x \right )}{h \left (x \right )}\right )}{h \left (x \right )}-\frac {h^{\prime \prime }\left (x \right )}{h \left (x \right )}+{g^{\prime }\left (x \right )}^{2}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
1.790 |
|
|
\[
{}4 y^{\prime \prime }+9 x y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.029 |
|
|
\[
{}4 y^{\prime \prime }-\left (x^{2}+a \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.402 |
|
|
\[
{}4 y^{\prime \prime }+4 \tan \left (x \right ) y^{\prime }-\left (5 \tan \left (x \right )^{2}+2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
1.978 |
|
|
\[
{}a y^{\prime \prime }-\left (a b +c +x \right ) y^{\prime }+\left (b \left (x +c \right )+d \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.928 |
|
|
\[
{}a^{2} y^{\prime \prime }+a \left (a^{2}-2 b \,{\mathrm e}^{-a x}\right ) y^{\prime }+b^{2} {\mathrm e}^{-2 a x} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.697 |
|
|
\[
{}x \left (y^{\prime \prime }+y\right )-\cos \left (x \right ) = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.947 |
|
|
\[
{}x y^{\prime \prime }+\left (x +a \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.431 |
|
|
\[
{}x y^{\prime \prime }+y^{\prime } = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.898 |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }+a y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.803 |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }+l x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.007 |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }+\left (x +a \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.631 |
|
|
\[
{}x y^{\prime \prime }-y^{\prime }+a y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.868 |
|
|
\[
{}x y^{\prime \prime }-y^{\prime }-y a \,x^{3} = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.452 |
|
|
\[
{}x y^{\prime \prime }-y^{\prime }+x^{3} \left ({\mathrm e}^{x^{2}}-v^{2}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.474 |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime }-x y-{\mathrm e}^{x} = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.009 |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime }+a x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.476 |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime }+a \,x^{2} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.881 |
|
|
\[
{}x y^{\prime \prime }-2 y^{\prime }+a y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.891 |
|
|
\[
{}x y^{\prime \prime }+v y^{\prime }+a y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.075 |
|
|
\[
{}x y^{\prime \prime }+a y^{\prime }+b x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.201 |
|
|
\[
{}x y^{\prime \prime }+a y^{\prime }+b \,x^{\operatorname {a1}} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.208 |
|
|
\[
{}x y^{\prime \prime }+\left (x +b \right ) y^{\prime }+a y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.875 |
|
|
\[
{}x y^{\prime \prime }+\left (x +a +b \right ) y^{\prime }+a y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.993 |
|
|
\[
{}x y^{\prime \prime }-x y^{\prime }-y-x \left (x +1\right ) {\mathrm e}^{x} = 0
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
1.279 |
|
|
\[
{}x y^{\prime \prime }-x y^{\prime }-a y = 0
\] |
[_Laguerre] |
✗ |
0.507 |
|
|
\[
{}x y^{\prime \prime }-\left (x +1\right ) y^{\prime }+y = 0
\] |
[_Laguerre] |
✓ |
1.103 |
|
|
\[
{}x y^{\prime \prime }-\left (x +1\right ) y^{\prime }-2 \left (x -1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.107 |
|
|
\[
{}x y^{\prime \prime }+\left (b -x \right ) y^{\prime }-a y = 0
\] |
[_Laguerre] |
✗ |
0.901 |
|
|
\[
{}x y^{\prime \prime }-2 \left (x -1\right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.554 |
|
|
\[
{}x y^{\prime \prime }-\left (3 x -2\right ) y^{\prime }-\left (2 x -3\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.597 |
|
|
\[
{}x y^{\prime \prime }+\left (a x +b +n \right ) y^{\prime }+n a y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
1.106 |
|
|
\[
{}x y^{\prime \prime }-\left (a +b \right ) \left (x +1\right ) y^{\prime }+a b x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
1.196 |
|
|
\[
{}x y^{\prime \prime }+\left (\left (a +b \right ) x +m +n \right ) y^{\prime }+\left (a b x +a n +b m \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
1.478 |
|