2.3.101 Problems 10001 to 10100

Table 2.733: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
10001	5719	\begin{align*} y^{\prime \prime }+y&=8 \cos \left (x \right ) \cos \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	1.199
10002	4054	\begin{align*} x^{2} y^{\prime \prime }+2 x \left (2+x \right ) y^{\prime }+2 \left (x +1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.201
10003	2356	\begin{align*} y^{\prime }&={\mathrm e}^{-t}+\ln \left (1+y^{2}\right ) \\ y \left (0\right ) &= 0 \\ \end{align*}	✗	✗	✗	✗	1.202
10004	3908	\begin{align*} x_{1}^{\prime }&=-x_{1}-4 x_{2}-2 x_{3} \\ x_{2}^{\prime }&=-4 x_{1}-5 x_{2}-6 x_{3} \\ x_{3}^{\prime }&=4 x_{1}+8 x_{2}+7 x_{3} \\ \end{align*}	✓	✓	✓	✓	1.202
10005	10253	\begin{align*} y^{\prime \prime }+y&={\mathrm e}^{\cos \left (x \right ) a} \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	1.202
10006	15656	\begin{align*} x \left (x -3\right ) y^{\prime \prime }+3 y^{\prime }&=x^{2} \\ y \left (5\right ) &= 0 \\ y^{\prime }\left (5\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	1.202
10007	23180	\begin{align*} y^{\prime }&=\frac {y-x +1}{3-x +y} \\ \end{align*}	✓	✓	✓	✓	1.202
10008	2474	\begin{align*} y+y^{\prime }&={\mathrm e}^{t} t \\ \end{align*}	✓	✓	✓	✓	1.203
10009	13255	\begin{align*} x^{2} y^{\prime }&=a \,x^{2} y^{2}+b x y+c \,x^{2 n}+s \,x^{n} \\ \end{align*}	✓	✓	✓	✗	1.203
10010	16161	\begin{align*} x^{2} y^{\prime \prime }+3 y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	1.203
10011	19005	\begin{align*} x_{1}^{\prime }&=-2 x_{1}+2 x_{2}+x_{3} \\ x_{2}^{\prime }&=-2 x_{1}+2 x_{2}+2 x_{3} \\ x_{3}^{\prime }&=2 x_{1}-3 x_{2}-3 x_{3} \\ \end{align*}	✓	✓	✓	✓	1.203
10012	20478	\begin{align*} 8 x {y^{\prime }}^{3}&=y \left (12 {y^{\prime }}^{2}-9\right ) \\ \end{align*}	✓	✓	✓	✗	1.203
10013	23764	\begin{align*} -\frac {u^{\prime \prime }}{2}&=x \\ u \left (0\right ) &= 0 \\ u \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	1.203
10014	1451	\begin{align*} x_{1}^{\prime }&=x_{1}+2 x_{2} \\ x_{2}^{\prime }&=-5 x_{1} \\ \end{align*}	✓	✓	✓	✓	1.204
10015	2529	\begin{align*} y^{\prime }&={\mathrm e}^{\left (-t +y\right )^{2}} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.204
10016	9543	\begin{align*} 4 y^{\prime \prime } x +\frac {y^{\prime }}{2}+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.204
10017	9909	\begin{align*} x^{2} y^{\prime \prime }+x \left (3 x +2\right ) y^{\prime }-2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.204
10018	14217	\begin{align*} x^{\prime }&={\mathrm e}^{x^{2}} \\ \end{align*}	✓	✓	✓	✓	1.204
10019	24847	\begin{align*} 4 y^{3} {y^{\prime }}^{2}-4 y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✗	1.204
10020	19047	\begin{align*} x_{1}^{\prime }&=-\frac {x_{1}}{2}+x_{2}+\frac {x_{3}}{2} \\ x_{2}^{\prime }&=x_{1}-x_{2}+x_{3}-\sin \left (t \right ) \\ x_{3}^{\prime }&=\frac {x_{1}}{2}+x_{2}-\frac {x_{3}}{2} \\ \end{align*}	✓	✓	✓	✓	1.205
10021	16494	\begin{align*} y^{\prime \prime }-8 y^{\prime }+15 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.206
10022	3262	\begin{align*} y^{\prime \prime }+2 {y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	1.207
10023	5472	\begin{align*} x {y^{\prime }}^{2}-2 y y^{\prime }+x +2 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.207
10024	13670	\begin{align*} y^{\prime \prime }-a \,x^{-2+n} \left (a \,x^{n}+n +1\right ) y&=0 \\ \end{align*}	✗	✓	✗	✗	1.207
10025	3866	\begin{align*} x_{1}^{\prime }&=-2 x_{1}+3 x_{2} \\ x_{2}^{\prime }&=3 x_{1}-2 x_{2} \\ x_{3}^{\prime }&=x_{1}+x_{3}+x_{4} \\ x_{4}^{\prime }&=x_{2}+x_{4} \\ \end{align*}	✓	✓	✓	✓	1.208
10026	6812	\begin{align*} 3 y^{\prime \prime } y^{\prime \prime \prime \prime }&=5 {y^{\prime \prime \prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	1.208
10027	13203	\begin{align*} y^{\prime }&=f \left (x \right ) g \left (y\right ) \\ \end{align*}	✓	✓	✓	✓	1.208
10028	11221	\begin{align*} y x -x^{2} y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.209
10029	993	\begin{align*} x_{1}^{\prime }&=2 x_{1} \\ x_{2}^{\prime }&=-21 x_{1}-5 x_{2}-27 x_{3}-9 x_{4} \\ x_{3}^{\prime }&=5 x_{3} \\ x_{4}^{\prime }&=-21 x_{3}-2 x_{4} \\ \end{align*}	✓	✓	✓	✓	1.210
10030	6993	\begin{align*} {\mathrm e}^{y} \left (1+y^{\prime }\right )&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	1.210
10031	10732	\begin{align*} u^{\prime \prime }-\frac {2 u^{\prime }}{x}-a^{2} u&=0 \\ \end{align*}	✓	✓	✓	✓	1.210
10032	15391	\begin{align*} y&=y {y^{\prime }}^{2}+2 y^{\prime } x \\ \end{align*}	✓	✓	✓	✓	1.210
10033	23261	\begin{align*} y^{\prime \prime }&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	1.210
10034	101	\begin{align*} y^{\prime }&=2 y x +1 \\ \end{align*}	✓	✓	✓	✓	1.211
10035	15722	\begin{align*} y^{\prime \prime }-4 y^{\prime }+5 y&=\left \{\begin {array}{cc} x & 0\le x <1 \\ 1 & 1\le x \end {array}\right . \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	1.211
10036	19693	\begin{align*} x^{\prime \prime }+x&=0 \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.211
10037	21894	\begin{align*} y^{\prime }-3 z&=5 \\ y-z^{\prime }-x&=3-2 t \\ z+x^{\prime }&=-1 \\ \end{align*}	✓	✓	✓	✓	1.211
10038	22331	\begin{align*} y^{\prime \prime }+y&={\mathrm e}^{-x^{2}} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.211
10039	8093	\begin{align*} \left (-x +3\right ) y-x \left (4-x \right ) y^{\prime }+2 \left (-x +2\right ) x^{2} y^{\prime \prime }&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	1.212
10040	20466	\begin{align*} y^{2} \left (-y^{\prime } x +y\right )&=x^{4} {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	1.212
10041	8110	\begin{align*} x \left (2+x \right ) y^{\prime \prime }+\left (x +1\right ) y^{\prime }-4 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.213
10042	13414	\begin{align*} y^{\prime }&=y^{2}-m y \tan \left (x \right )+b^{2} \cos \left (x \right )^{2 m} \\ \end{align*}	✓	✓	✓	✗	1.213
10043	3877	\begin{align*} x_{1}^{\prime }&=x_{1}-{\mathrm e}^{t} \\ x_{2}^{\prime }&=2 x_{1}-3 x_{2}+2 x_{3}+6 \,{\mathrm e}^{-t} \\ x_{3}^{\prime }&=x_{1}-2 x_{2}+2 x_{3}+{\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	1.214
10044	5356	\begin{align*} {y^{\prime }}^{2}&=x -y \\ \end{align*}	✓	✓	✓	✓	1.214
10045	9903	\begin{align*} x^{2} y^{\prime \prime }+x \left (2 x +3\right ) y^{\prime }+\left (1+3 x \right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.214
10046	14280	\begin{align*} x^{\prime \prime }-2 x^{\prime }&=0 \\ x \left (0\right ) &= 1 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.214
10047	15121	\begin{align*} y^{\prime }&=t \ln \left (y^{2 t}\right )+t^{2} \\ \end{align*}	✗	✗	✓	✗	1.214
10048	16329	\begin{align*} 2 y^{3}+\left (4 x^{3} y^{3}-3 x y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.214
10049	13277	\begin{align*} \left (a \,x^{n}+b \,x^{m}+c \right ) y^{\prime }&=c y^{2}-b \,x^{m -1} y+a \,x^{-2+n} \\ \end{align*}	✓	✗	✗	✗	1.215
10050	7040	\begin{align*} y^{\prime \prime }+2 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.216
10051	7958	\begin{align*} y^{2} {y^{\prime }}^{2}+3 y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✗	1.216
10052	10740	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\frac {\left (-9 a^{2}+4 x^{2}\right ) y}{4 a^{2}}&=0 \\ \end{align*}	✓	✓	✓	✓	1.216
10053	22354	\begin{align*} y^{\prime }&=\frac {1}{x^{2}+4 y^{2}} \\ \end{align*}	✓	✓	✗	✗	1.216
10054	2473	\begin{align*} \frac {2 t y}{t^{2}+1}+y^{\prime }&=\frac {1}{t^{2}+1} \\ \end{align*}	✓	✓	✓	✓	1.217
10055	7181	\begin{align*} y^{\prime \prime } x +y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.217
10056	7945	\begin{align*} 3 x^{4} {y^{\prime }}^{2}-y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✓	1.217
10057	8683	\begin{align*} y^{\prime }-y&=2 x -3 \\ \end{align*}	✓	✓	✓	✓	1.217
10058	9541	\begin{align*} 2 y^{\prime \prime } x -y^{\prime }+2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.217
10059	10570	\begin{align*} 6 x^{2} y^{\prime \prime }+x \left (6 x^{2}+1\right ) y^{\prime }+\left (9 x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	1.217
10060	13671	\begin{align*} y^{\prime \prime }+\left (a \,x^{2 n}+b \,x^{n -1}\right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	1.217
10061	15909	\begin{align*} -2 y+y^{\prime }&=7 \,{\mathrm e}^{2 t} \\ y \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	1.217
10062	25261	\begin{align*} \left (\cos \left (2 t \right )+1\right ) y^{\prime \prime }-4 y&=0 \\ \end{align*}	✗	✓	✓	✗	1.217
10063	9586	\begin{align*} 2 y^{\prime \prime } x +y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.218
10064	9590	\begin{align*} y^{\prime \prime } x -\left (2+x \right ) y^{\prime }+2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.218
10065	19500	\begin{align*} y^{\prime \prime }+y&=2 \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	1.219
10066	22251	\begin{align*} y^{\prime \prime }+5 y^{\prime }-3 y&=\operatorname {Heaviside}\left (t -4\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	1.219
10067	24971	\begin{align*} -y+y^{\prime }&=y^{2} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	1.219
10068	4227	\begin{align*} y^{\prime } x&=y x +y \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.220
10069	13669	\begin{align*} y^{\prime \prime }-a \left (a \,x^{2 n}+n \,x^{n -1}\right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	1.220
10070	14322	\begin{align*} x^{\prime \prime }&=\frac {4 x}{t^{2}} \\ \end{align*}	✓	✓	✓	✓	1.220
10071	23134	\begin{align*} y^{\prime } x +\left (x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	1.220
10072	25585	\begin{align*} y^{\prime \prime }&=4 \\ \end{align*}	✓	✓	✓	✓	1.220
10073	4073	\begin{align*} x^{2} y^{\prime \prime }-x \left (-x +2\right ) y^{\prime }+\left (x^{2}+2\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.221
10074	7962	\begin{align*} y&=-y^{\prime } x +x^{4} {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	1.221
10075	9399	\begin{align*} 2 y^{\prime \prime } x +\left (x +1\right ) y^{\prime }+3 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.221
10076	10864	\begin{align*} y^{\prime \prime }-x^{2} y^{\prime }-3 y x&=0 \\ \end{align*}	✓	✓	✓	✗	1.221
10077	11827	\begin{align*} y^{2} {y^{\prime }}^{3}+2 y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✗	1.221
10078	18618	\begin{align*} y^{\prime }-4 y^{2} {\mathrm e}^{x}&=y \\ \end{align*}	✓	✓	✓	✓	1.221
10079	3270	\begin{align*} \left (1+y\right ) y^{\prime \prime }&=3 {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	1.222
10080	4305	\begin{align*} y^{2} y^{\prime }&=2+3 y^{6} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.222
10081	10158	\begin{align*} y^{\prime \prime }+\sin \left (y\right ) {y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	1.222
10082	11106	\begin{align*} y^{\prime \prime }-x^{2} y^{\prime }-3 y x&=0 \\ \end{align*}	✓	✓	✓	✗	1.222
10083	13638	\begin{align*} y^{\prime }&=-y^{3}+3 y a^{2} x^{2}-2 a^{3} x^{3}+a \\ \end{align*}	✗	✓	✓	✗	1.222
10084	19008	\begin{align*} x_{1}^{\prime }&=-4 x_{1}+2 x_{2}-x_{3} \\ x_{2}^{\prime }&=-6 x_{1}-3 x_{3} \\ x_{3}^{\prime }&=\frac {8 x_{2}}{3}-2 x_{3} \\ \end{align*}	✓	✓	✓	✓	1.222
10085	9947	\begin{align*} x^{2} y^{\prime \prime }+2 x^{2} y^{\prime }-2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.223
10086	19029	\begin{align*} x_{1}^{\prime }&=-3 x_{1}+4 x_{2} \\ x_{2}^{\prime }&=-x_{1}-2 x_{2} \\ \end{align*}	✓	✓	✓	✓	1.223
10087	2099	\begin{align*} x^{2} y^{\prime \prime }+x \left (-3 x^{2}+1\right ) y^{\prime }-4 \left (-3 x^{2}+1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.224
10088	9907	\begin{align*} x^{2} y^{\prime \prime }+2 x \left (x -2\right ) y^{\prime }+2 \left (2-3 x \right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.224
10089	13665	\begin{align*} y^{\prime \prime }-\left (a \,x^{2}+b \right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	1.224
10090	13771	\begin{align*} a y+x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.224
10091	20431	\begin{align*} 4 x {y^{\prime }}^{2}+4 y y^{\prime }&=y^{4} \\ \end{align*}	✓	✓	✓	✗	1.224
10092	5471	\begin{align*} x {y^{\prime }}^{2}-2 y y^{\prime }+a x&=0 \\ \end{align*}	✓	✓	✗	✓	1.225
10093	14365	\begin{align*} x^{\prime \prime }-4 x&=1-\operatorname {Heaviside}\left (t -1\right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	1.225
10094	22060	\begin{align*} y^{\prime }+y&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	1.225
10095	10646	\begin{align*} x^{2} y^{\prime \prime }+x \left (-3 x^{2}+1\right ) y^{\prime }-4 \left (-3 x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	1.226
10096	25456	\begin{align*} y^{\prime }&=y+{\mathrm e}^{t} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.226
10097	85	\begin{align*} y^{\prime }+y&={\mathrm e}^{x} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.227
10098	5520	\begin{align*} \left (a^{2}-x^{2}\right ) {y^{\prime }}^{2}+b^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	1.227
10099	5870	\begin{align*} 3 y+2 \tan \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.227
10100	5646	\begin{align*} x {y^{\prime }}^{3}-y {y^{\prime }}^{2}+a&=0 \\ \end{align*}	✓	✓	✓	✗	1.228