2.3.1 Problems 1 to 100

Table 2.533: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
1	22907	\begin{align*} y^{\prime \prime }&=x-2 \\ x^{\prime \prime }&=2+y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 1 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= -3 \\ \end{align*}	✗	✓	✓	✓	0.016
2	22908	\begin{align*} x^{\prime }+y^{\prime }&=\cos \left (t \right ) \\ x+y^{\prime \prime }&=2 \\ \end{align*} With initial conditions \begin{align*} x \left (\pi \right ) &= 2 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= {\frac {1}{2}} \\ \end{align*}	✗	✓	✓	✓	0.016
3	22911	\begin{align*} x^{\prime \prime }&=y+4 \,{\mathrm e}^{-2 t} \\ y^{\prime \prime }&=x-{\mathrm e}^{-2 t} \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✗	✓	✓	✓	0.017
4	22906	\begin{align*} x^{\prime \prime }&=-2 y \\ y^{\prime }&=y-x^{\prime } \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 10 \\ y \left (0\right ) &= 5 \\ \end{align*}	✗	✓	✓	✓	0.018
5	22257	\begin{align*} y^{\prime \prime }+z+y&=0 \\ y^{\prime }+z^{\prime }&=0 \\ \end{align*} With initial conditions \begin{align*} y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ z \left (0\right ) &= 1 \\ \end{align*}	✗	✓	✓	✓	0.019
6	22264	\begin{align*} u^{\prime \prime }-2 v&=2 \\ u+v^{\prime }&=5 \,{\mathrm e}^{2 t}+1 \\ \end{align*} With initial conditions \begin{align*} u \left (0\right ) &= 2 \\ u^{\prime }\left (0\right ) &= 2 \\ v \left (0\right ) &= 1 \\ \end{align*}	✗	✓	✓	✓	0.019
7	18420	\begin{align*} x^{\prime \prime }&=x^{2}+y \\ y^{\prime }&=-2 x x^{\prime }+x \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ x^{\prime }\left (0\right ) &= 1 \\ y \left (0\right ) &= 0 \\ \end{align*}	✗	✓	✗	✗	0.020
8	22258	\begin{align*} z^{\prime \prime }+y^{\prime }&=\cos \left (t \right ) \\ y^{\prime \prime }-z&=\sin \left (t \right ) \\ \end{align*} With initial conditions \begin{align*} y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ z \left (0\right ) &= -1 \\ z^{\prime }\left (0\right ) &= -1 \\ \end{align*}	✗	✓	✓	✓	0.020
9	22885	\begin{align*} y^{\prime \prime }&=x \\ y^{\prime \prime }&=y \\ \end{align*}	✗	✓	✓	✓	0.020
10	22886	\begin{align*} y^{\prime \prime }&=x-2 \\ y^{\prime \prime }&=2+y \\ \end{align*}	✗	✓	✓	✓	0.020
11	23446	\begin{align*} y^{\prime \prime \prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✓	✓	✗	0.021
12	24088	\begin{align*} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }-2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✓	✓	✗	0.021
13	24089	\begin{align*} \left (-x^{4}+1\right ) y^{\prime \prime \prime }-24 y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✓	✓	✗	0.021
14	24092	\begin{align*} x^{2} y^{\prime \prime \prime }-y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✓	✓	✗	0.021
15	13058	\begin{align*} y^{\prime \prime \prime }&=f \left (y\right ) \\ \end{align*}	✗	✗	✗	✗	0.022
16	6608	\begin{align*} y^{\prime \prime \prime }&=y x \\ \end{align*}	✗	✓	✓	✗	0.023
17	10458	\begin{align*} y^{\prime \prime \prime }-y x&=0 \\ \end{align*}	✗	✓	✓	✗	0.023
18	23451	\begin{align*} y^{\prime \prime \prime }-2 y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✓	✓	✗	0.023
19	23775	\begin{align*} x^{\prime }&=y^{2}-x^{2} \\ y^{\prime }&=2 x y \\ \end{align*}	✗	✓	✓	✗	0.023
20	23819	\begin{align*} x^{\prime }&=x-x y \\ y^{\prime }&=-y+x y \\ \end{align*}	✗	✓	✓	✗	0.023
21	13080	\begin{align*} t x^{\prime }+y&=0 \\ t y^{\prime }+x&=0 \\ \end{align*}	✗	✓	✓	✓	0.024
22	15114	\begin{align*} x^{\prime }&=y \\ y^{\prime }&=\frac {y^{2}}{x} \\ \end{align*}	✗	✓	✓	✓	0.024
23	18417	\begin{align*} x^{\prime \prime }&=y \\ y^{\prime \prime }&=x \\ \end{align*}	✗	✓	✓	✓	0.024
24	18635	\begin{align*} x^{\prime }&=x+y+4 \\ y^{\prime }&=-2 x+\sin \left (t \right ) y \\ \end{align*}	✗	✓	✗	✗	0.024
25	22799	\begin{align*} y^{\prime \prime \prime }&=\frac {24 x +24 y}{x^{3}} \\ \end{align*}	✗	✓	✓	✓	0.024
26	22895	\begin{align*} x^{\prime \prime }+y^{\prime }+x&=y+\sin \left (t \right ) \\ y^{\prime \prime }+x^{\prime }-y&=2 t^{2}-x \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 2 \\ x^{\prime }\left (0\right ) &= -1 \\ y \left (0\right ) &= -{\frac {9}{2}} \\ y^{\prime }\left (0\right ) &= -{\frac {7}{2}} \\ \end{align*}	✗	✓	✓	✓	0.024
27	23798	\begin{align*} x^{\prime }&=y+x^{2}-x y \\ y^{\prime }&=-2 x+3 y+y^{2} \\ \end{align*}	✗	✗	✗	✗	0.024
28	24094	\begin{align*} x^{4} y^{\prime \prime \prime }-\frac {x^{2} y^{\prime }}{x +1}+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.024
29	18715	\begin{align*} x^{\prime }&=y \\ y^{\prime }&=x-\frac {x^{3}}{5}-\frac {y}{5} \\ \end{align*}	✗	✗	✗	✗	0.025
30	19062	\begin{align*} x^{\prime }&=1+5 y \\ y^{\prime }&=1-6 x^{2} \\ \end{align*}	✗	✓	✓	✗	0.025
31	22890	\begin{align*} x^{\prime \prime }+2 y^{\prime }+8 x&=32 t \\ y^{\prime \prime }+3 x^{\prime }-2 y&=60 \,{\mathrm e}^{-t} \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 6 \\ x^{\prime }\left (0\right ) &= 0 \\ y \left (0\right ) &= -24 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✗	✓	✓	✓	0.025
32	23093	\begin{align*} x^{\prime \prime }+y^{\prime \prime }&=t \\ x^{\prime \prime }-y^{\prime \prime }&=3 t \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✗	✓	✓	✓	0.025
33	23951	\begin{align*} y^{\prime } x&=y \\ z^{\prime }&=3 y-x \\ \end{align*}	✗	✓	✓	✓	0.025
34	24093	\begin{align*} x^{4} y^{\prime \prime \prime }+\frac {x^{2} y^{\prime \prime }}{x +1}-\left (x +1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.025
35	3831	\begin{align*} x_{1}^{\prime }&=\frac {x_{1}}{t} \\ x_{2}^{\prime }&=x_{2} \\ \end{align*}	✗	✓	✓	✓	0.026
36	6750	\begin{align*} y^{2}-2 y^{\prime \prime \prime }+y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✗	✗	✗	✗	0.026
37	9437	\begin{align*} x^{3} y^{\prime \prime \prime }-2 x^{2} y^{\prime \prime }+\left (x^{2}+2 x \right ) y^{\prime }-y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✓	✓	✗	0.026
38	9486	\begin{align*} x^{\prime }&=t y+1 \\ y^{\prime }&=-t x+y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 0 \\ y \left (0\right ) &= -1 \\ \end{align*}	✗	✗	✗	✗	0.026
39	18422	\begin{align*} x^{\prime }&=-\frac {1}{y} \\ y^{\prime }&=\frac {1}{x} \\ \end{align*}	✗	✓	✓	✓	0.026
40	18423	\begin{align*} x^{\prime }&=\frac {x}{y} \\ y^{\prime }&=\frac {y}{x} \\ \end{align*}	✗	✓	✓	✓	0.026
41	18708	\begin{align*} x^{\prime }&=x-x y \\ y^{\prime }&=y+2 x y \\ \end{align*}	✗	✓	✓	✗	0.026
42	20209	\begin{align*} x^{\prime \prime }-3 x-4 y&=0 \\ x+y^{\prime \prime }+y&=0 \\ \end{align*}	✗	✓	✓	✓	0.026
43	22265	\begin{align*} w^{\prime \prime }-2 z&=0 \\ w^{\prime }+y^{\prime }-z&=2 t \\ w^{\prime }-2 y+z^{\prime \prime }&=0 \\ \end{align*} With initial conditions \begin{align*} w \left (0\right ) &= 0 \\ w^{\prime }\left (0\right ) &= 0 \\ z \left (0\right ) &= 1 \\ z^{\prime }\left (0\right ) &= 0 \\ y \left (0\right ) &= 0 \\ \end{align*}	✗	✓	✓	✓	0.026
44	22266	\begin{align*} w^{\prime \prime }+y+z&=-1 \\ w+y^{\prime \prime }-z&=0 \\ -w-y^{\prime }+z^{\prime \prime }&=0 \\ \end{align*} With initial conditions \begin{align*} w \left (0\right ) &= 0 \\ w^{\prime }\left (0\right ) &= 1 \\ z \left (0\right ) &= -1 \\ z^{\prime }\left (0\right ) &= 1 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✗	✓	✗	✗	0.026
45	22898	\begin{align*} x^{\prime }&=x y \\ y^{\prime }&=1+y^{2} \\ z^{\prime }&=z \\ \end{align*}	✗	✓	✓	✗	0.026
46	23575	\begin{align*} t x^{\prime }&=3 x-2 y \\ t y^{\prime }&=x+y-t^{2} \\ \end{align*}	✗	✓	✓	✓	0.026
47	4555	\begin{align*} x^{\prime \prime }+x^{\prime }+y^{\prime }-2 y&=40 \,{\mathrm e}^{3 t} \\ x^{\prime }+x-y^{\prime }&=36 \,{\mathrm e}^{t} \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 3 \\ x^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✗	✓	✓	✓	0.027
48	6620	\begin{align*} y+2 y^{\prime } x +y^{\prime \prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	0.027
49	6792	\begin{align*} a y y^{\prime \prime }+y^{\prime \prime \prime }&=0 \\ \end{align*}	✗	✗	✗	✗	0.027
50	9436	\begin{align*} x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-3 y^{\prime } x +\left (x -1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✓	✓	✗	0.027
51	12710	\begin{align*} y^{\prime \prime \prime }-a \,x^{b} y&=0 \\ \end{align*}	✗	✓	✓	✗	0.027
52	12728	\begin{align*} x y^{\prime \prime \prime }+3 y^{\prime \prime }+y x&=0 \\ \end{align*}	✗	✓	✓	✗	0.027
53	12780	\begin{align*} y^{\prime \prime \prime }+y^{\prime } x +n y&=0 \\ \end{align*}	✗	✓	✓	✗	0.027
54	12781	\begin{align*} y^{\prime \prime \prime }-y^{\prime } x -n y&=0 \\ \end{align*}	✗	✓	✓	✗	0.027
55	12831	\begin{align*} x^{2} y^{\prime \prime \prime \prime }-a y&=0 \\ \end{align*}	✗	✓	✓	✗	0.027
56	13044	\begin{align*} a y y^{\prime \prime }+y^{\prime \prime \prime }&=0 \\ \end{align*}	✗	✗	✗	✗	0.027
57	15129	\begin{align*} y^{\prime \prime }+y y^{\prime \prime \prime \prime }&=1 \\ \end{align*}	✗	✗	✗	✗	0.027
58	15130	\begin{align*} y^{\prime \prime \prime }+y x&=\cosh \left (x \right ) \\ \end{align*}	✗	✓	✓	✗	0.027
59	18421	\begin{align*} x^{\prime }&=x^{2}+y^{2} \\ y^{\prime }&=2 x y \\ \end{align*}	✗	✓	✓	✗	0.027
60	18713	\begin{align*} x^{\prime }&=\left (2+x\right ) \left (-x+y\right ) \\ y^{\prime }&=y-x^{2}-y^{2} \\ \end{align*}	✗	✗	✗	✗	0.027
61	22893	\begin{align*} r^{\prime \prime }\left (t \right )&=r \left (t \right )+y \\ y^{\prime \prime }&=5 r \left (t \right )-3 y+t^{2} \\ \end{align*}	✗	✗	✓	✓	0.027
62	23114	\begin{align*} y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.027
63	23799	\begin{align*} x^{\prime }&=x-x y \\ y^{\prime }&=-y+x y \\ \end{align*}	✗	✓	✓	✗	0.027
64	23815	\begin{align*} x^{\prime }&=-2 x+y-x^{2}+2 y^{2} \\ y^{\prime }&=3 x+2 y+x^{2} y^{2} \\ \end{align*}	✗	✗	✗	✗	0.027
65	23935	\begin{align*} y^{\prime } y&=-x \\ y z^{\prime }&=2 \\ \end{align*}	✗	✓	✓	✗	0.027
66	25169	\begin{align*} y_{1}^{\prime }-2 y_{1}&=2 y_{2} \\ y_{2}^{\prime \prime }+2 y_{2}^{\prime }+y_{2}&=-2 y_{1} \\ \end{align*} With initial conditions \begin{align*} y_{1} \left (0\right ) &= 3 \\ y_{2} \left (0\right ) &= 0 \\ y_{2}^{\prime }\left (0\right ) &= 3 \\ \end{align*}	✗	✓	✓	✓	0.027
67	9485	\begin{align*} x^{\prime }&=x y+1 \\ y^{\prime }&=-x+y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 2 \\ y \left (0\right ) &= -1 \\ \end{align*}	✗	✗	✗	✗	0.028
68	12825	\begin{align*} y^{\left (5\right )}-a x y-b&=0 \\ \end{align*}	✗	✗	✗	✗	0.028
69	15132	\begin{align*} y^{\prime \prime \prime }+y x&=\cosh \left (x \right ) \\ \end{align*}	✗	✓	✓	✗	0.028
70	18419	\begin{align*} x^{\prime \prime }&=3 x+y \\ y^{\prime }&=-2 x \\ \end{align*}	✗	✓	✓	✓	0.028
71	18634	\begin{align*} x^{\prime }&=-x+t y \\ y^{\prime }&=t x-y \\ \end{align*}	✗	✓	✓	✓	0.028
72	22800	\begin{align*} x y^{\prime \prime \prime }+2 y^{\prime \prime } x -y^{\prime } x -2 y x&=1 \\ \end{align*}	✗	✓	✓	✓	0.028
73	22929	\begin{align*} x^{\prime \prime }&=y+4 \,{\mathrm e}^{-2 t} \\ y^{\prime \prime }&=x-{\mathrm e}^{-2 t} \\ \end{align*}	✗	✓	✓	✓	0.028
74	23240	\begin{align*} y^{\prime \prime \prime }+x^{2} y&={\mathrm e}^{x} \\ \end{align*}	✗	✓	✓	✗	0.028
75	23241	\begin{align*} y^{\prime \prime }+y y^{\prime \prime \prime \prime }&=5 \\ \end{align*}	✗	✗	✗	✗	0.028
76	23259	\begin{align*} y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.028
77	23552	\begin{align*} y^{\left (5\right )}-y^{\prime }-\frac {4 y}{x}&=0 \\ \end{align*}	✗	✗	✓	✓	0.028
78	23584	\begin{align*} t x^{\prime }&=3 x-2 y \\ t y^{\prime }&=x+y-t^{2} \\ \end{align*} With initial conditions \begin{align*} x \left (1\right ) &= 1 \\ y \left (1\right ) &= {\frac {1}{2}} \\ \end{align*}	✗	✓	✓	✓	0.028
79	23778	\begin{align*} x^{\prime }&=x-x y \\ y^{\prime }&=-y+x y \\ \end{align*}	✗	✓	✓	✗	0.028
80	25688	\begin{align*} x^{\prime \prime }&=4 y+{\mathrm e}^{t} \\ y^{\prime \prime }&=4 x-{\mathrm e}^{t} \\ \end{align*}	✗	✓	✓	✓	0.028
81	6621	\begin{align*} a y+2 a x y^{\prime }+y^{\prime \prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	0.029
82	6671	\begin{align*} y x +3 y^{\prime }+x y^{\prime \prime \prime }&=0 \\ \end{align*}	✗	✓	✗	✗	0.029
83	6725	\begin{align*} y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.029
84	6751	\begin{align*} y^{2}-2 y^{\prime \prime \prime }+y^{\prime \prime \prime \prime }&=x^{3} \\ \end{align*}	✗	✗	✗	✗	0.029
85	6791	\begin{align*} -y^{\prime } y+{y^{\prime }}^{2}+y^{\prime \prime \prime }&=0 \\ \end{align*}	✗	✗	✗	✗	0.029
86	6796	\begin{align*} 3 y^{\prime } y^{\prime \prime }+\left (a +y\right ) y^{\prime \prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	0.029
87	8152	\begin{align*} x y^{\prime \prime \prime }-{y^{\prime }}^{4}+y&=0 \\ \end{align*}	✗	✗	✗	✗	0.029
88	9435	\begin{align*} x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }+\left (x^{2}+x \right ) y^{\prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✓	✓	✗	0.029
89	9438	\begin{align*} x^{3} y^{\prime \prime \prime }+\left (2 x^{3}-x^{2}\right ) y^{\prime \prime }-y^{\prime } x +y&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✓	✓	✗	0.029
90	12713	\begin{align*} a y+2 a x y^{\prime }+y^{\prime \prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	0.029
91	12774	\begin{align*} x^{6} y^{\prime \prime \prime }+6 x^{5} y^{\prime \prime }+a y&=0 \\ \end{align*}	✗	✓	✓	✗	0.029
92	12832	\begin{align*} x^{10} y^{\left (5\right )}-a y&=0 \\ \end{align*}	✗	✓	✓	✗	0.029
93	13089	\begin{align*} x^{\prime \prime }+a y&=0 \\ y^{\prime \prime }-a^{2} y&=0 \\ \end{align*}	✗	✓	✓	✓	0.029
94	16952	\begin{align*} x^{\prime }&=x y-6 y \\ y^{\prime }&=x-y-5 \\ \end{align*}	✗	✗	✗	✗	0.029
95	18424	\begin{align*} x^{\prime }&=\frac {y}{x-y} \\ y^{\prime }&=\frac {x}{x-y} \\ \end{align*}	✗	✓	✓	✓	0.029
96	18439	\begin{align*} x^{\prime }&=-4 x-2 y+\frac {2}{{\mathrm e}^{t}-1} \\ y^{\prime }&=6 x+3 y-\frac {3}{{\mathrm e}^{t}-1} \\ \end{align*}	✗	✓	✓	✓	0.029
97	18631	\begin{align*} x^{\prime }&=-2 t x+y \\ y^{\prime }&=3 x-y \\ \end{align*}	✗	✓	✓	✓	0.029
98	18711	\begin{align*} x^{\prime }&=-\left (x-y\right ) \left (1-x-y\right ) \\ y^{\prime }&=x \left (2+y\right ) \\ \end{align*}	✗	✗	✗	✗	0.029
99	19061	\begin{align*} x^{\prime }&=-2 y+x y \\ y^{\prime }&=x+4 x y \\ \end{align*}	✗	✓	✓	✗	0.029
100	22078	\begin{align*} y y^{\prime \prime \prime }+y^{\prime } x +y&=x^{2} \\ \end{align*}	✗	✗	✗	✗	0.029