2.3.103 Problems 10201 to 10300

Table 2.737: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
10201	73	\begin{align*} y^{\prime }+y&=2 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.530
10202	1018	\begin{align*} x_{1}^{\prime }&=-3 x_{1}-4 x_{3} \\ x_{2}^{\prime }&=-x_{1}-x_{2}-x_{3} \\ x_{3}^{\prime }&=x_{1}+x_{3} \\ \end{align*}	✓	✓	✓	✓	0.530
10203	1453	\begin{align*} x_{1}^{\prime }&=2 x_{1}-\frac {5 x_{2}}{2} \\ x_{2}^{\prime }&=\frac {9 x_{1}}{5}-x_{2} \\ \end{align*}	✓	✓	✓	✓	0.530
10204	2036	\begin{align*} 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 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.530
10205	4036	\begin{align*} x^{2} y^{\prime \prime }+x^{2} y^{\prime }-\left (2+x \right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.530
10206	5741	\begin{align*} y^{\prime \prime }+a^{2} y&=\sin \left (b x \right ) \\ \end{align*}	✓	✓	✓	✓	0.530
10207	6040	\begin{align*} \left (3 a x +5\right ) y-x \left (a x +5\right ) y^{\prime }+x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.530
10208	6319	\begin{align*} y^{\prime \prime }&=f \left (x \right ) y^{2}+y^{3}+y \left (-2 f \left (x \right )^{2}+f^{\prime }\left (x \right )\right )+\left (3 f \left (x \right )-y\right ) y^{\prime } \\ \end{align*}	✗	✓	✗	✗	0.530
10209	9648	\begin{align*} y^{\prime \prime }+4 y^{\prime }+5 y&=\delta \left (t -2 \pi \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.530
10210	9704	\begin{align*} x^{\prime }&=x-8 y \\ y^{\prime }&=x-3 y \\ \end{align*}	✓	✓	✓	✓	0.530
10211	9847	\begin{align*} y^{\prime \prime }+y^{\prime } x +3 y&=x^{2} \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.530
10212	9849	\begin{align*} y^{\prime \prime }+3 y^{\prime } x +7 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.530
10213	12933	\begin{align*} y y^{\prime \prime }-{y^{\prime }}^{2}-f \left (x \right ) y y^{\prime }-g \left (x \right ) y^{2}&=0 \\ \end{align*}	✗	✓	✓	✗	0.530
10214	16644	\begin{align*} y^{\prime \prime }+y&=6 \cos \left (x \right )-3 \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.530
10215	18203	\begin{align*} y^{\prime \prime }-2 m y^{\prime }+m^{2} y&=\sin \left (n x \right ) \\ \end{align*}	✓	✓	✓	✓	0.530
10216	18730	\begin{align*} t y^{\prime \prime }+3 y&=t \\ y \left (1\right ) &= 1 \\ y^{\prime }\left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✗	0.530
10217	20598	\begin{align*} {\mathrm e}^{x} \left (-y^{\prime }+y^{\prime \prime } x \right )&=x^{3} \\ \end{align*}	✓	✓	✓	✓	0.530
10218	21722	\begin{align*} y^{\prime \prime \prime }+4 y^{\prime \prime }+5 y^{\prime }+2 y&=10 \cos \left (t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 3 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.530
10219	21740	\begin{align*} x^{\prime }&=x+2 y \\ y^{\prime }&=4 x+3 y \\ \end{align*}	✓	✓	✓	✓	0.530
10220	22100	\begin{align*} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.530
10221	23400	\begin{align*} \left (x -4\right ) y^{\prime \prime }+4 y^{\prime }-\frac {4 y}{x -4}&=0 \\ \end{align*}	✓	✓	✓	✓	0.530
10222	25339	\begin{align*} 2 t y^{\prime \prime }+y^{\prime }+t y&=0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	0.530
10223	25355	\begin{align*} t^{2} y^{\prime \prime }+t \left (1-2 t \right ) y^{\prime }+\left (t^{2}-t +1\right ) y&=0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	0.530
10224	2013	\begin{align*} 4 x^{2} y^{\prime \prime }+\left (4 x +1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.531
10225	9931	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.531
10226	11184	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.531
10227	14382	\begin{align*} x^{\prime }&=-2 x-3 y \\ y^{\prime }&=-x+4 y \\ \end{align*}	✓	✓	✓	✓	0.531
10228	21161	\begin{align*} x^{\prime \prime }+x^{\prime }+x&=0 \\ \end{align*}	✓	✓	✓	✓	0.531
10229	22270	\begin{align*} x^{\prime }&=y \\ y^{\prime }&=-9 x+6 y+t \\ \end{align*}	✓	✓	✓	✓	0.531
10230	23401	\begin{align*} \left (2+x \right ) y^{\prime \prime }-y^{\prime }+\frac {y}{2+x}&=0 \\ \end{align*}	✓	✓	✓	✓	0.531
10231	24742	\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&=f \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.531
10232	1921	\begin{align*} \left (3 x^{2}+8 x +4\right ) y^{\prime \prime }+\left (16+12 x \right ) y^{\prime }+6 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.532
10233	2041	\begin{align*} x^{2} y^{\prime \prime }-x \left (-x^{2}+1\right ) y^{\prime }+\left (x^{2}+1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.532
10234	6252	\begin{align*} \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 \\ \end{align*}	✓	✓	✓	✗	0.532
10235	6883	\begin{align*} x^{2} \left (1+{y^{\prime }}^{2}\right )^{3}-a^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.532
10236	7996	\begin{align*} y^{\prime \prime }-y&=\frac {1}{\left (1+{\mathrm e}^{-x}\right )^{2}} \\ \end{align*}	✓	✓	✓	✓	0.532
10237	8001	\begin{align*} y^{\prime \prime }-4 y^{\prime }+3 y&=\frac {1}{1+{\mathrm e}^{-x}} \\ \end{align*}	✓	✓	✓	✗	0.532
10238	9766	\begin{align*} y y^{\prime \prime }+{y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	0.532
10239	11690	\begin{align*} 3 {y^{\prime }}^{2}-2 y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✗	0.532
10240	11717	\begin{align*} a x {y^{\prime }}^{2}+\left (b x -a y+c \right ) y^{\prime }-b y&=0 \\ \end{align*}	✓	✓	✓	✗	0.532
10241	19520	\begin{align*} y^{\prime \prime }+y&=\tan \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.532
10242	21381	\begin{align*} y^{\prime }&=2 x \\ \end{align*}	✓	✓	✓	✓	0.532
10243	22167	\begin{align*} 4 y+y^{\prime \prime }&=\sin \left (2 x \right )^{2} \\ y \left (\pi \right ) &= 0 \\ y^{\prime }\left (\pi \right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.532
10244	25550	\begin{align*} y^{\prime \prime }+2 y^{\prime }+y&={\mathrm e}^{i \omega t} \\ \end{align*}	✓	✓	✓	✓	0.532
10245	384	\begin{align*} x^{\prime \prime }+4 x&=5 \sin \left (3 t \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.533
10246	481	\begin{align*} 2 y^{\prime \prime } x +\left (x +1\right ) y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.533
10247	525	\begin{align*} y^{\prime \prime } x +4 x^{3} y&=0 \\ \end{align*}	✓	✓	✓	✗	0.533
10248	566	\begin{align*} x^{\prime \prime }+4 x^{\prime }+4 x&=1+\delta \left (t -2\right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.533
10249	1025	\begin{align*} x_{1}^{\prime }&=x_{1} \\ x_{2}^{\prime }&=x_{1}+3 x_{2}+x_{3} \\ x_{3}^{\prime }&=-2 x_{1}-4 x_{2}-x_{3} \\ \end{align*}	✓	✓	✓	✓	0.533
10250	1191	\begin{align*} y^{\prime }&=y^{2} \left (4-y^{2}\right ) \\ \end{align*}	✓	✓	✓	✓	0.533
10251	2042	\begin{align*} 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 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.533
10252	2059	\begin{align*} 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 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.533
10253	2061	\begin{align*} 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 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.533
10254	2703	\begin{align*} x^{\prime }&=x-y \\ y^{\prime }&=5 x-3 y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.533
10255	3815	\begin{align*} x_{1}^{\prime }&=2 x_{1} \\ x_{2}^{\prime }&=x_{2}-x_{3} \\ x_{3}^{\prime }&=x_{2}+x_{3} \\ \end{align*}	✓	✓	✓	✓	0.533
10256	4020	\begin{align*} 3 x^{2} y^{\prime \prime }+x \left (3 x +7\right ) y^{\prime }+\left (1+6 x \right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.533
10257	8171	\begin{align*} p^{\prime }&=p \left (1-p\right ) \\ \end{align*}	✓	✓	✓	✓	0.533
10258	10945	\begin{align*} y^{\prime \prime }+x^{6} y^{\prime }+7 x^{5} y&=0 \\ \end{align*}	✓	✓	✓	✗	0.533
10259	15445	\begin{align*} x^{\prime }&=1+y \\ y^{\prime }&=1+x \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= -2 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.533
10260	15578	\begin{align*} y^{\prime }&=\tan \left (x \right ) \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.533
10261	19158	\begin{align*} x^{2} y y^{\prime \prime }+x^{2} {y^{\prime }}^{2}-5 x y^{\prime } y&=4 y^{2} \\ \end{align*}	✗	✓	✓	✗	0.533
10262	19516	\begin{align*} y^{\prime \prime }+y&=\sec \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.533
10263	22101	\begin{align*} y^{\prime \prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.533
10264	22683	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.533
10265	22919	\begin{align*} x^{\prime }-x-y&=0 \\ 5 x+y^{\prime }-3 y&=0 \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 2 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.533
10266	23577	\begin{align*} x_{1}^{\prime }&=x_{1}+2 x_{2} \\ x_{2}^{\prime }&=4 x_{1}+x_{2} \\ \end{align*}	✓	✓	✓	✓	0.533
10267	4050	\begin{align*} x^{2} y^{\prime \prime }-x^{2} y^{\prime }-2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.534
10268	4137	\begin{align*} y^{\prime \prime }-2 y^{\prime }+3 y&=x^{3}+\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.534
10269	8407	\begin{align*} {y^{\prime }}^{2}+y^{2}&=1 \\ \end{align*}	✓	✓	✓	✓	0.534
10270	14742	\begin{align*} x^{2} y^{\prime \prime }+3 y^{\prime } x -y&=0 \\ \end{align*} Series expansion around \(x=1\).	✓	✓	✓	✓	0.534
10271	22309	\begin{align*} y^{\prime }&=-\frac {4}{x^{2}} \\ y \left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.534
10272	2288	\begin{align*} y_{1}^{\prime }&=5 y_{1}-6 y_{2} \\ y_{2}^{\prime }&=3 y_{1}-y_{2} \\ \end{align*}	✓	✓	✓	✓	0.535
10273	2752	\begin{align*} x_{1}^{\prime }&=2 x_{1}-x_{3} \\ x_{2}^{\prime }&=2 x_{2}+x_{3} \\ x_{3}^{\prime }&=2 x_{3} \\ x_{4}^{\prime }&=-x_{3}+2 x_{4} \\ \end{align*}	✓	✓	✓	✓	0.535
10274	3237	\begin{align*} x^{\prime }+5 x&=3 t^{2} \\ y+y^{\prime }&={\mathrm e}^{3 t} \\ \end{align*}	✓	✓	✓	✓	0.535
10275	3840	\begin{align*} x_{1}^{\prime }&=x_{2} \\ x_{2}^{\prime }&=-x_{1} \\ x_{3}^{\prime }&=5 x_{3} \\ \end{align*}	✓	✓	✓	✓	0.535
10276	5277	\begin{align*} \left (1-y^{2} x^{2}\right ) y^{\prime }&=\left (y x +1\right ) y^{2} \\ \end{align*}	✓	✓	✓	✓	0.535
10277	9588	\begin{align*} \left (x -1\right ) y^{\prime \prime }+3 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.535
10278	12707	\begin{align*} y^{\prime \prime }&=-\frac {b^{2} y}{\left (-a^{2}+x^{2}\right )^{2}} \\ \end{align*}	✓	✓	✓	✓	0.535
10279	14858	\begin{align*} x^{\prime }&=x-2 y \\ y^{\prime }&=4 x+5 y \\ \end{align*}	✓	✓	✓	✓	0.535
10280	16671	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y&=3 \cos \left (x \right ) x \\ \end{align*}	✓	✓	✓	✓	0.535
10281	21883	\begin{align*} y^{\prime \prime }-2 y^{\prime }-3 y+8 \,{\mathrm e}^{-x}+3 x&=0 \\ \end{align*}	✓	✓	✓	✓	0.535
10282	22690	\begin{align*} 4 i^{\prime \prime }+i&=t^{2}+2 \cos \left (4 t \right ) \\ \end{align*}	✓	✓	✓	✓	0.535
10283	24066	\begin{align*} x^{\prime }-x-y^{\prime }&=0 \\ y^{\prime }+3 x-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.535
10284	25128	\begin{align*} y^{\prime \prime }+2 y^{\prime }+5 y&=8 \,{\mathrm e}^{-t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 8 \\ \end{align*}	✓	✓	✓	✓	0.535
10285	25192	\begin{align*} \left (t^{2}+1\right ) y^{\prime \prime }-4 t y^{\prime }+6 y&=2 t \\ \end{align*}	✓	✓	✓	✗	0.535
10286	25692	\begin{align*} y^{\prime }&=y-y^{2} \\ y \left (-1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.535
10287	395	\begin{align*} x^{\prime \prime }+8 x^{\prime }+25 x&=200 \cos \left (t \right )+520 \sin \left (t \right ) \\ x \left (0\right ) &= -30 \\ x^{\prime }\left (0\right ) &= -10 \\ \end{align*}	✓	✓	✓	✓	0.536
10288	834	\begin{align*} x^{2} y^{\prime \prime }+2 y^{\prime } x -12 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.536
10289	1421	\begin{align*} x_{1}^{\prime }&=x_{2}+x_{3} \\ x_{2}^{\prime }&=x_{1}+x_{3} \\ x_{3}^{\prime }&=x_{1}+x_{2} \\ \end{align*}	✓	✓	✓	✓	0.536
10290	3874	\begin{align*} x_{1}^{\prime }&=-x_{1}+2 x_{2}+54 t \,{\mathrm e}^{3 t} \\ x_{2}^{\prime }&=-2 x_{1}+4 x_{2}+9 \,{\mathrm e}^{3 t} \\ \end{align*}	✓	✓	✓	✓	0.536
10291	4072	\begin{align*} x^{2} y^{\prime \prime }+\frac {3 y^{\prime } x}{2}-\frac {\left (x +1\right ) y}{2}&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.536
10292	5865	\begin{align*} a \cot \left (x \right )^{2} y+\tan \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.536
10293	6093	\begin{align*} 2 y-2 y^{\prime }+\left (1-x \right ) x y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.536
10294	6117	\begin{align*} -a y-\left (a -\left (2-a \right ) x \right ) y^{\prime }+x \left (x +1\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.536
10295	7648	\begin{align*} x^{2} y^{\prime \prime }-y^{\prime } x +2 y&=0 \\ \end{align*} Series expansion around \(x=2\).	✓	✓	✓	✓	0.536
10296	9326	\begin{align*} y^{\prime \prime }+y&={\mathrm e}^{-x} \\ y \left (2\right ) &= 0 \\ y^{\prime }\left (2\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	0.536
10297	9373	\begin{align*} y^{\prime \prime }+y^{\prime }-x^{2} y&=1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.536
10298	9478	\begin{align*} x^{\prime }&=3 x-5 y \\ y^{\prime }&=-x+2 y \\ \end{align*}	✓	✓	✓	✓	0.536
10299	9646	\begin{align*} y^{\prime \prime }+2 y^{\prime }&=\delta \left (-1+t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.536
10300	10249	\begin{align*} y^{\prime \prime }+y^{\prime }+y&=\frac {1}{x} \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.536