2.3.112 Problems 11101 to 11200

Table 2.755: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
11101	23603	\begin{align*} x^{\prime }&=3 x-2 y \\ y^{\prime }&=17 x-7 y \\ \end{align*}	✓	✓	✓	✓	0.594
11102	912	\begin{align*} m x^{\prime \prime }+k x&=F_{0} \cos \left (\omega t \right ) \\ \end{align*}	✓	✓	✓	✓	0.595
11103	1957	\begin{align*} 3 x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.595
11104	1987	\begin{align*} 9 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+3 x \left (13 x^{2}+3\right ) y^{\prime }-\left (-25 x^{2}+1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.595
11105	2650	\begin{align*} t^{2} y^{\prime \prime }+\left (-t^{2}+t \right ) y^{\prime }-y&=0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	0.595
11106	3867	\begin{align*} x_{1}^{\prime }&=-x_{2} \\ x_{2}^{\prime }&=x_{1} \\ x_{3}^{\prime }&=x_{1}-x_{4} \\ x_{4}^{\prime }&=x_{2}+x_{3} \\ \end{align*}	✓	✓	✓	✓	0.595
11107	5559	\begin{align*} \left (1-a y\right ) {y^{\prime }}^{2}&=a y \\ \end{align*}	✓	✓	✓	✓	0.595
11108	6033	\begin{align*} -\left (1-x \right ) y+x \left (1-x \right ) y^{\prime }+x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.595
11109	6204	\begin{align*} 2 y x -2 \left (x^{2}+1\right ) y^{\prime }+x \left (x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.595
11110	6407	\begin{align*} x^{4} y^{\prime \prime }&=-4 y^{2}+x \left (x^{2}+2 y\right ) y^{\prime } \\ \end{align*}	✗	✓	✓	✗	0.595
11111	11768	\begin{align*} x y {y^{\prime }}^{2}+\left (y^{2}+x^{2}\right ) y^{\prime }+y x&=0 \\ \end{align*}	✓	✓	✓	✓	0.595
11112	12363	\begin{align*} y^{\prime \prime } x -y^{\prime }+a y&=0 \\ \end{align*}	✓	✓	✓	✓	0.595
11113	14757	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.595
11114	15684	\begin{align*} y^{\prime \prime \prime \prime }+4 y^{\prime \prime }&=24 x^{2}-6 x +14+32 \cos \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.595
11115	20367	\begin{align*} y+2 y^{\prime \prime }+y^{\prime \prime \prime \prime }&=x^{2} \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.595
11116	22852	\begin{align*} \left (1-x \right ) x y^{\prime \prime }+2 y^{\prime }+2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.595
11117	23547	\begin{align*} y^{\prime \prime }+y&=\sec \left (x \right )^{3} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.595
11118	25282	\begin{align*} y^{\prime \prime }-a^{2} y&=f \left (t \right ) \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.595
11119	25525	\begin{align*} y^{\prime \prime }+100 y&=\cos \left (\omega t \right )-\sin \left (\omega t \right ) \\ \end{align*}	✓	✓	✓	✓	0.595
11120	2022	\begin{align*} x^{2} \left (2 x +1\right ) y^{\prime \prime }+x \left (3+5 x \right ) y^{\prime }+\left (1-2 x \right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.596
11121	6059	\begin{align*} 3 y+y^{\prime } x +\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.596
11122	7474	\begin{align*} 2 y^{3}+2 y^{2}+\left (3 x y^{2}+2 y x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.596
11123	8215	\begin{align*} x^{\prime \prime }+x&=0 \\ x \left (\frac {\pi }{2}\right ) &= 0 \\ x^{\prime }\left (\frac {\pi }{2}\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.596
11124	8512	\begin{align*} y^{\prime \prime } x +y^{\prime }+10 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.596
11125	9734	\begin{align*} 4 y^{3} {y^{\prime }}^{2}-4 y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✗	0.596
11126	10754	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.596
11127	12427	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x -\left (x +a \right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.596
11128	14318	\begin{align*} x^{\prime \prime }+\frac {x^{\prime }}{100}+4 x&=\cos \left (2 t \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.596
11129	15779	\begin{align*} y^{\prime }&={\mathrm e}^{-y} \\ \end{align*}	✓	✓	✓	✓	0.596
11130	16233	\begin{align*} y^{\prime }&=200 y-2 y^{2} \\ \end{align*}	✓	✓	✓	✓	0.596
11131	20068	\begin{align*} y^{\prime \prime }-a^{2} y&={\mathrm e}^{a x}+{\mathrm e}^{n x} \\ \end{align*}	✓	✓	✓	✓	0.596
11132	1813	\begin{align*} y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}+2\right ) y&=4 \,{\mathrm e}^{-x \left (2+x \right )} \\ \end{align*}	✓	✓	✓	✗	0.597
11133	9795	\begin{align*} y^{\prime \prime } x&=y^{\prime } \left (2-3 y^{\prime } x \right ) \\ \end{align*}	✓	✓	✓	✓	0.597
11134	13937	\begin{align*} y^{\prime \prime }+2 a \,{\mathrm e}^{\lambda x} y^{\prime }+a \,{\mathrm e}^{\lambda x} \left (a \,{\mathrm e}^{\lambda x}+\lambda \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.597
11135	20	\begin{align*} y^{\prime }&=x +y \\ \end{align*}	✓	✓	✓	✓	0.598
11136	22	\begin{align*} y^{\prime }&=x -y \\ \end{align*}	✓	✓	✓	✓	0.598
11137	876	\begin{align*} y^{\prime \prime }-4 y&=\cosh \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.598
11138	2017	\begin{align*} 25 x^{2} y^{\prime \prime }+x \left (15+x \right ) y^{\prime }+\left (x +1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.598
11139	2023	\begin{align*} 2 x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (6-x \right ) y^{\prime }+\left (8-x \right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.598
11140	2653	\begin{align*} t^{2} y^{\prime \prime }+t \left (t +1\right ) y^{\prime }-y&=0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	0.598
11141	6096	\begin{align*} 2 y+3 y^{\prime }+\left (1-x \right ) x y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.598
11142	6097	\begin{align*} \left (1-x \right ) x y^{\prime \prime }-3 y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.598
11143	6339	\begin{align*} y^{\prime \prime }&={\mathrm e}^{x} {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	0.598
11144	7207	\begin{align*} y^{\prime \prime }+n^{2} y&=\frac {6 y}{x^{2}} \\ \end{align*}	✓	✓	✓	✓	0.598
11145	8550	\begin{align*} y^{\prime \prime } x +3 y^{\prime }+x^{3} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.598
11146	8608	\begin{align*} y^{\prime \prime } x +y^{\prime }+36 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.598
11147	10165	\begin{align*} 2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y&=1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.598
11148	14115	\begin{align*} y+2 y^{\prime \prime }+y^{\prime \prime \prime \prime }&=\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.598
11149	16877	\begin{align*} y^{\prime }+\sqrt {2 x^{2}+1}\, y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.598
11150	17767	\begin{align*} y^{\prime \prime }+3 y^{\prime }-4 y&={\mathrm e}^{t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	0.598
11151	17769	\begin{align*} y^{\prime \prime }+y&=\cos \left (t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.598
11152	18113	\begin{align*} y^{\prime \prime }&=2 y^{\prime } y \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✗	✗	0.598
11153	19266	\begin{align*} y^{\prime } x&=2 x^{2}+1 \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.598
11154	21548	\begin{align*} y^{\prime \prime }+y&=\tan \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.598
11155	25758	\begin{align*} 1+{y^{\prime }}^{2}&=\frac {1}{y^{2}} \\ \end{align*}	✓	✓	✓	✓	0.598
11156	25804	\begin{align*} y^{\prime }&=y^{2}-3 y \\ \end{align*}	✓	✓	✓	✓	0.598
11157	2021	\begin{align*} x^{2} \left (1-4 x \right ) y^{\prime \prime }+3 x \left (1-6 x \right ) y^{\prime }+\left (1-12 x \right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.599
11158	2804	\begin{align*} x^{\prime }&=2 y+z \\ y^{\prime }&=-x-3 y-z \\ z^{\prime }&=x+y-z \\ \end{align*}	✓	✓	✓	✓	0.599
11159	3057	\begin{align*} y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.599
11160	5649	\begin{align*} 2 x {y^{\prime }}^{3}-3 y {y^{\prime }}^{2}-x&=0 \\ \end{align*}	✓	✓	✓	✗	0.599
11161	5753	\begin{align*} y^{\prime \prime }&=2 \csc \left (x \right )^{2} y \\ \end{align*}	✓	✓	✓	✗	0.599
11162	8528	\begin{align*} y^{\prime \prime } x +y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.599
11163	8580	\begin{align*} y^{\prime \prime } x +2 y^{\prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.599
11164	8619	\begin{align*} y^{\prime \prime } x +3 y^{\prime }+4 x^{3} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.599
11165	9564	\begin{align*} 4 x^{2} y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}-25\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.599
11166	9624	\begin{align*} y+y^{\prime }&=\left \{\begin {array}{cc} 1 & 0\le t <1 \\ -1 & 1\le t \end {array}\right . \\ y \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	0.599
11167	9730	\begin{align*} 3 x^{4} {y^{\prime }}^{2}-y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✓	0.599
11168	10215	\begin{align*} x^{2} y^{\prime \prime }+\left (x^{2}+6 x \right ) y^{\prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.599
11169	10220	\begin{align*} y^{\prime \prime } x +\left (-x +2\right ) y^{\prime }-y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.599
11170	13020	\begin{align*} \left (c +2 b x +a \,x^{2}+y^{2}\right )^{2} y^{\prime \prime }+d y&=0 \\ \end{align*}	✗	✓	✓	✗	0.599
11171	14181	\begin{align*} y^{\prime } y+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.599
11172	14673	\begin{align*} y^{\prime \prime }+y&=\tan \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✓	0.599
11173	16875	\begin{align*} y^{\prime }+y \sqrt {x^{2}+1}&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.599
11174	16899	\begin{align*} \left (-9 x^{4}+x^{2}\right ) y^{\prime \prime }-6 y^{\prime } x +10 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.599
11175	17490	\begin{align*} y^{\prime \prime }+6 y^{\prime }+25 y&={\mathrm e}^{-3 t} \left (\sec \left (4 t \right )+\csc \left (4 t \right )\right ) \\ \end{align*}	✓	✓	✓	✓	0.599
11176	18218	\begin{align*} y+2 y^{\prime }+y^{\prime \prime }&=x^{2} {\mathrm e}^{-x} \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.599
11177	20362	\begin{align*} y^{\prime \prime }-y&=\cos \left (x \right ) \cosh \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.599
11178	21577	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=x \,{\mathrm e}^{x}+7 x -2 \\ \end{align*}	✓	✓	✓	✓	0.599
11179	24946	\begin{align*} y^{\prime }&=y-t \\ \end{align*}	✓	✓	✓	✓	0.599
11180	25530	\begin{align*} y^{\prime \prime }&={\mathrm e}^{i \omega t} \\ \end{align*}	✓	✓	✓	✓	0.599
11181	2020	\begin{align*} x^{2} y^{\prime \prime }-x \left (3-2 x \right ) y^{\prime }+\left (3 x +4\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.600
11182	2646	\begin{align*} 2 t^{2} y^{\prime \prime }-t y^{\prime }+\left (t +1\right ) y&=0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	0.600
11183	6231	\begin{align*} -6 y x +2 y^{\prime }+x \left (3 x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.600
11184	8263	\begin{align*} y^{\prime \prime }&=y^{\prime } \\ \end{align*}	✓	✓	✓	✓	0.600
11185	15157	\begin{align*} \left (x -1\right ) y^{\prime \prime }-y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✗	0.600
11186	18275	\begin{align*} y^{\prime \prime }-2 y^{\prime }+2 y&=4 \,{\mathrm e}^{x} \cos \left (x \right ) \\ y \left (\pi \right ) &= \pi \,{\mathrm e}^{\pi } \\ y^{\prime }\left (\pi \right ) &= {\mathrm e}^{\pi } \\ \end{align*}	✓	✓	✓	✓	0.600
11187	19840	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=x \\ \end{align*}	✓	✓	✓	✓	0.600
11188	22879	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +6 y&=0 \\ y \left (\frac {1}{2}\right ) &= 10 \\ \end{align*} Series expansion around \(x={\frac {1}{2}}\).	✓	✓	✓	✓	0.600
11189	921	\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*}	✓	✓	✓	✓	0.601
11190	1431	\begin{align*} x_{1}^{\prime }&=x_{1}+x_{2}+{\mathrm e}^{-2 t} \\ x_{2}^{\prime }&=4 x_{1}-2 x_{2}-2 \,{\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	0.601
11191	6206	\begin{align*} -2 y x -2 \left (-x^{2}+1\right ) y^{\prime }+x \left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.601
11192	9409	\begin{align*} \left (x -1\right )^{2} y^{\prime \prime }-3 \left (x -1\right ) y^{\prime }+2 y&=0 \\ \end{align*} Series expansion around \(x=1\).	✓	✓	✓	✗	0.601
11193	14783	\begin{align*} 2 x^{\prime }+y^{\prime }+x+y&=t^{2}+4 t \\ x^{\prime }+y^{\prime }+2 x+2 y&=2 t^{2}-2 t \\ \end{align*}	✓	✓	✓	✓	0.601
11194	14786	\begin{align*} 2 x^{\prime }+y^{\prime }-x-y&=-2 t \\ x^{\prime }+y^{\prime }+x-y&=t^{2} \\ \end{align*}	✓	✓	✓	✓	0.601
11195	17869	\begin{align*} y^{\prime }&=y \\ \end{align*}	✓	✓	✓	✓	0.601
11196	18236	\begin{align*} 2 y^{\prime \prime }-3 y^{\prime }-2 y&=5 \,{\mathrm e}^{x} \cosh \left (x \right ) \\ \end{align*}	✓	✓	✓	✗	0.601
11197	20896	\begin{align*} x^{2} y^{\prime \prime }-x \left (1-x \right ) y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.601
11198	23228	\begin{align*} y^{\prime \prime }&=\frac {1+{y^{\prime }}^{2}}{2 y} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✗	0.601
11199	23729	\begin{align*} y^{\prime \prime } x -y^{\prime }+4 x^{3} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.601
11200	662	\begin{align*} y^{\prime }&=x +y \\ \end{align*}	✓	✓	✓	✓	0.602