2.3.133 Problems 13201 to 13300

Table 2.797: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
13201	23047	\begin{align*} T^{\prime \prime }+{T^{\prime }}^{3}&=0 \\ \end{align*}	✓	✓	✓	✓	0.814
13202	10529	\begin{align*} \left (3 x^{2}+x +1\right ) y^{\prime \prime }+\left (2+15 x \right ) y^{\prime }+12 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.815
13203	12869	\begin{align*} y^{\prime \prime }-2 a y y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.815
13204	13903	\begin{align*} x^{n} y^{\prime \prime }+\left (a x +b \right ) y^{\prime }-a y&=0 \\ \end{align*}	✓	✓	✗	✗	0.815
13205	16744	\begin{align*} y^{\prime \prime }+36 y&=6 \sec \left (6 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.815
13206	17009	\begin{align*} x^{\prime }&=4 y \\ y^{\prime }&=-x-2 y \\ \end{align*}	✓	✓	✓	✓	0.815
13207	18354	\begin{align*} y^{\prime \prime }+\lambda y&=0 \\ y \left (0\right ) &= 0 \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.815
13208	21640	\begin{align*} x^{2} y^{\prime \prime }+4 y^{\prime } x +2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.815
13209	3980	\begin{align*} y^{\prime \prime }+4 y^{\prime }+3 y&=\delta \left (t -2\right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.816
13210	7343	\begin{align*} y^{\prime \prime } x +y^{\prime }&=4 x \\ \end{align*}	✓	✓	✓	✓	0.816
13211	14894	\begin{align*} x^{\prime }&=\lambda x \\ \end{align*}	✓	✓	✓	✓	0.816
13212	23261	\begin{align*} y^{\prime \prime }&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.816
13213	23840	\begin{align*} y^{\prime }&=t +y \\ \end{align*}	✓	✓	✓	✓	0.816
13214	3163	\begin{align*} y^{\prime \prime }+9 y&=\sec \left (x \right ) \csc \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.817
13215	3575	\begin{align*} x^{2} y^{\prime \prime }+5 y^{\prime } x +4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.817
13216	3588	\begin{align*} y^{\prime \prime }&=x \,{\mathrm e}^{x} \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	0.817
13217	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*}	✓	✓	✓	✓	0.817
13218	6273	\begin{align*} \left (a -x \right )^{2} \left (b -x \right )^{2} y^{\prime \prime }&=k^{2} y \\ \end{align*}	✓	✓	✓	✗	0.817
13219	22991	\begin{align*} n^{\prime }&=k n-b t \\ n \left (0\right ) &= n_{0} \\ \end{align*}	✓	✓	✓	✓	0.817
13220	3912	\begin{align*} x_{1}^{\prime }&=2 x_{1}+13 x_{2} \\ x_{2}^{\prime }&=-x_{1}-2 x_{2} \\ x_{3}^{\prime }&=2 x_{3}+4 x_{4} \\ x_{4}^{\prime }&=2 x_{4} \\ \end{align*}	✓	✓	✓	✓	0.818
13221	8415	\begin{align*} y^{\prime }&=-\frac {8 x +5}{3 y^{2}+1} \\ y \left (-1\right ) &= 4 \\ \end{align*}	✓	✓	✗	✗	0.818
13222	15469	\begin{align*} x^{\prime }&=2 x+y \\ y^{\prime }&=-x+y \\ \end{align*}	✓	✓	✓	✓	0.818
13223	16967	\begin{align*} y^{\prime \prime }+9 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.818
13224	23624	\begin{align*} x^{\prime }&=3 x-y \\ y^{\prime }&=-x+2 y-z \\ z^{\prime }&=-y+3 z \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 0 \\ z \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.818
13225	24993	\begin{align*} y^{\prime }+a y&={\mathrm e}^{-a t} \\ \end{align*}	✓	✓	✓	✓	0.818
13226	891	\begin{align*} y^{\prime \prime }+y&=\cos \left (x \right )^{3} x \\ \end{align*}	✓	✓	✓	✓	0.819
13227	988	\begin{align*} x_{1}^{\prime }&=2 x_{1}+x_{2}-x_{3} \\ x_{2}^{\prime }&=-4 x_{1}-3 x_{2}-x_{3} \\ x_{3}^{\prime }&=4 x_{1}+4 x_{2}+2 x_{3} \\ \end{align*}	✓	✓	✓	✓	0.819
13228	1253	\begin{align*} y^{\prime \prime }+5 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.819
13229	8108	\begin{align*} \sin \left (x \right ) y^{\prime \prime }-2 \cos \left (x \right ) y^{\prime }-y \sin \left (x \right )&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.819
13230	9034	\begin{align*} y^{\prime \prime }+y^{\prime }&=1 \\ \end{align*}	✓	✓	✓	✓	0.819
13231	9394	\begin{align*} 4 x^{2} y^{\prime \prime }+\left (2 x^{4}-5 x \right ) y^{\prime }+\left (3 x^{2}+2\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.819
13232	9863	\begin{align*} 2 \left (1-x \right ) x^{2} y^{\prime \prime }-x \left (1+7 x \right ) y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.819
13233	10093	\begin{align*} y^{\prime \prime }-y^{\prime }-y x -x^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	0.819
13234	22077	\begin{align*} 2 y^{\prime \prime } x +x^{2} y^{\prime }-y \sin \left (x \right )&=0 \\ \end{align*}	✗	✗	✗	✗	0.819
13235	25605	\begin{align*} -y+y^{\prime }&={\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	0.819
13236	3253	\begin{align*} x^{\prime \prime }+t x^{\prime }&=t^{3} \\ \end{align*}	✓	✓	✓	✓	0.820
13237	6193	\begin{align*} y x +3 x^{2} y^{\prime }+x^{3} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.820
13238	7266	\begin{align*} y^{\prime \prime }+5 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.820
13239	14509	\begin{align*} y^{\prime }+y&=\left \{\begin {array}{cc} {\mathrm e}^{-x} & 0\le x <2 \\ {\mathrm e}^{-2} & 2\le x \end {array}\right . \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	0.820
13240	16095	\begin{align*} y^{\prime \prime }+2 y&=-3 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.820
13241	20098	\begin{align*} x^{2} y^{\prime \prime }+2 y^{\prime } x -20 y&=\left (x +1\right )^{2} \\ \end{align*}	✓	✓	✓	✓	0.820
13242	4604	\begin{align*} y^{\prime \prime } x +2 y^{\prime }-y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.821
13243	14781	\begin{align*} 2 x^{\prime }+y^{\prime }+x+5 y&=4 t \\ x^{\prime }+y^{\prime }+2 x+2 y&=2 \\ \end{align*}	✓	✓	✓	✓	0.821
13244	17845	\begin{align*} y^{\prime }&=1-\cot \left (y\right ) \\ \end{align*}	✓	✓	✓	✓	0.821
13245	19006	\begin{align*} x_{1}^{\prime }&=2 x_{1}-4 x_{2}-x_{3} \\ x_{2}^{\prime }&=x_{1}+x_{2}+3 x_{3} \\ x_{3}^{\prime }&=3 x_{1}-4 x_{2}-2 x_{3} \\ \end{align*}	✓	✓	✓	✓	0.821
13246	23625	\begin{align*} x^{\prime }&=2 x+y \\ y^{\prime }&=z-x \\ z^{\prime }&=x+3 y+z \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 1 \\ z \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	0.821
13247	3396	\begin{align*} 9 x^{2} y^{\prime \prime }+10 y^{\prime } x +y&=x -1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.822
13248	7571	\begin{align*} m y^{\prime \prime }+b y^{\prime }+k y&=0 \\ \end{align*}	✓	✓	✓	✓	0.822
13249	8755	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✗	0.822
13250	9244	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x -16 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.822
13251	11745	\begin{align*} x^{4} {y^{\prime }}^{2}-y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✓	0.822
13252	17079	\begin{align*} y^{\prime }+k y&=0 \\ \end{align*}	✓	✓	✓	✓	0.822
13253	19877	\begin{align*} y&=y^{\prime } x -{y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	0.822
13254	22277	\begin{align*} x_{1}^{\prime }&=x_{2} \\ x_{2}^{\prime }&=6 x_{1}+9 \,{\mathrm e}^{-t} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 0 \\ x_{2} \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.822
13255	22967	\begin{align*} {\mathrm e}^{x} \left (y^{\prime }+y\right )&=3 \\ \end{align*}	✓	✓	✓	✓	0.822
13256	23680	\begin{align*} y^{\prime \prime } x +\left (1-x \right ) y^{\prime }+y p&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.822
13257	4602	\begin{align*} x^{2} y^{\prime \prime }+2 y^{\prime } x -\left (x^{2}+2\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.823
13258	6399	\begin{align*} x^{2} y^{\prime \prime }&=\sqrt {b y^{2}+a \,x^{2} {y^{\prime }}^{2}} \\ \end{align*}	✗	✓	✗	✗	0.823
13259	22806	\begin{align*} Q^{\prime \prime }+k Q&=e \left (t \right ) \\ Q \left (0\right ) &= q_{0} \\ Q^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.823
13260	22808	\begin{align*} y^{\prime \prime }+y&=f \left (x \right ) \\ y \left (0\right ) &= 0 \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.823
13261	25224	\begin{align*} 9 t^{2} y^{\prime \prime }+3 t y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.823
13262	3238	\begin{align*} x^{\prime }+2 x&=3 t \\ x^{\prime }+2 y^{\prime }+y&=\cos \left (2 t \right ) \\ \end{align*}	✓	✓	✓	✓	0.824
13263	8996	\begin{align*} 2 x^{2} y^{\prime \prime }+\left (x^{2}+5 x \right ) y^{\prime }+\left (x^{2}-2\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.824
13264	1454	\begin{align*} x_{1}^{\prime }&=x_{1}+x_{2}-2 \\ x_{2}^{\prime }&=x_{1}-x_{2} \\ \end{align*}	✓	✓	✓	✓	0.825
13265	4585	\begin{align*} x_{1}^{\prime }&=2 x_{1}-x_{2}-x_{3}+2 \,{\mathrm e}^{2 t} \\ x_{2}^{\prime }&=3 x_{1}-2 x_{2}-3 x_{3} \\ x_{3}^{\prime }&=-x_{1}+x_{2}+2 x_{3} \\ \end{align*}	✓	✓	✓	✓	0.825
13266	5929	\begin{align*} -8 x^{3} y-\left (2 x^{2}+1\right ) y^{\prime }+y^{\prime \prime } x&=0 \\ \end{align*}	✓	✓	✓	✗	0.825
13267	5960	\begin{align*} -\left (-x^{2}+2\right ) y+x^{2} y^{\prime \prime }&=x^{4} \\ \end{align*}	✓	✓	✓	✗	0.825
13268	9897	\begin{align*} x \left (x -2\right ) y^{\prime \prime }+2 \left (x -1\right ) y^{\prime }-2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.825
13269	19380	\begin{align*} y^{\prime \prime }+2 x {y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.825
13270	25421	\begin{align*} y+y^{\prime }&=\delta \left (t -2\right ) \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.825
13271	2201	\begin{align*} y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+11 y^{\prime \prime }-14 y^{\prime }+10 y&=-{\mathrm e}^{x} \left (\sin \left (x \right )+2 \cos \left (2 x \right )\right ) \\ \end{align*}	✓	✓	✓	✓	0.826
13272	3438	\begin{align*} y^{\prime }&=-y \\ \end{align*}	✓	✓	✓	✓	0.826
13273	6016	\begin{align*} 16 y-7 y^{\prime } x +x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.826
13274	6593	\begin{align*} \left (1+{y^{\prime }}^{2}+y y^{\prime \prime }\right )^{2}&=\left (1+{y^{\prime }}^{2}\right )^{3} \\ \end{align*}	✓	✓	✓	✗	0.826
13275	7317	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x -4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.826
13276	9866	\begin{align*} 2 y^{\prime \prime } x +\left (-x +2\right ) y^{\prime }-2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.826
13277	10486	\begin{align*} \left (-x^{2}+4\right ) y^{\prime \prime }+y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.826
13278	14507	\begin{align*} y^{\prime }+y&=\left \{\begin {array}{cc} 2 & 0\le x <1 \\ 0 & 1\le x \end {array}\right . \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	0.826
13279	18238	\begin{align*} y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+2 y^{\prime \prime }+2 y^{\prime }+y&=x \,{\mathrm e}^{x}+\frac {\cos \left (x \right )}{2} \\ \end{align*}	✓	✓	✓	✓	0.826
13280	15	\begin{align*} x^{\prime \prime }&=4 \left (t +3\right )^{2} \\ x \left (0\right ) &= 1 \\ x^{\prime }\left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.827
13281	3558	\begin{align*} 4 y+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.827
13282	14778	\begin{align*} x^{\prime }+y^{\prime }-x-3 y&=3 t \\ x^{\prime }+2 y^{\prime }-2 x-3 y&=1 \\ \end{align*}	✓	✓	✓	✓	0.827
13283	16724	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +9 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.827
13284	23623	\begin{align*} x^{\prime }&=3 x+2 y+2 z \\ y^{\prime }&=x+4 y+z \\ z^{\prime }&=-2 x-4 y-z \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 0 \\ z \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.827
13285	23112	\begin{align*} y^{\prime }&=\sqrt {y} \\ \end{align*}	✓	✓	✓	✓	0.828
13286	24468	\begin{align*} y^{\prime \prime }+a^{2} y-2 a y^{\prime }+b^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	0.828
13287	24895	\begin{align*} y y^{\prime \prime }&={y^{\prime }}^{2} \left (1-y^{\prime } \sin \left (y\right )-\cos \left (y\right ) y y^{\prime }\right ) \\ \end{align*}	✓	✓	✓	✗	0.828
13288	25231	\begin{align*} t^{2} y^{\prime \prime }+t y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.828
13289	25812	\begin{align*} y^{\prime }&=\frac {2 y}{\pi }-\sin \left (y\right ) \\ \end{align*}	✓	✓	✓	✓	0.828
13290	11	\begin{align*} x^{\prime \prime }&=50 \\ x \left (0\right ) &= 20 \\ x^{\prime }\left (0\right ) &= 10 \\ \end{align*}	✓	✓	✓	✓	0.829
13291	1185	\begin{align*} y^{\prime }&=-1+{\mathrm e}^{-y} \\ \end{align*}	✓	✓	✓	✓	0.829
13292	3362	\begin{align*} 4 \left (1-x \right ) x^{2} y^{\prime \prime }+3 x \left (2 x +1\right ) y^{\prime }-3 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.829
13293	3565	\begin{align*} x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.829
13294	6184	\begin{align*} -2 b y+2 a y^{\prime }+x \left (b x +a \right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.829
13295	6255	\begin{align*} 4 y+2 x \left (x^{2}+1\right ) y^{\prime }+\left (x^{2}+1\right )^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.829
13296	8202	\begin{align*} y^{\prime \prime }&=f \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.829
13297	15975	\begin{align*} x^{\prime }&=3 y \\ y^{\prime }&=3 \pi y-\frac {x}{3} \\ \end{align*}	✓	✓	✓	✓	0.829
13298	21545	\begin{align*} 4 y+y^{\prime \prime }&=\sec \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.829
13299	10442	\begin{align*} y^{\prime \prime }-2 b x y^{\prime }+b^{2} x^{2} y&=x \\ \end{align*}	✓	✓	✓	✗	0.830
13300	22220	\begin{align*} x^{2} y^{\prime \prime }+\left (x^{2}-3 x \right ) y^{\prime }+\left (3 x -1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.830