2.3.109 Problems 10801 to 10900

Table 2.749: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
10801	15160	\begin{align*} y^{\prime \prime }+2 y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✗	1.476
10802	18125	\begin{align*} y^{\prime \prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	1.476
10803	22284	\begin{align*} y^{\prime \prime }+y&=0 \\ y \left (0\right ) &= 0 \\ y \left (\frac {\pi }{2}\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.476
10804	8457	\begin{align*} y^{\prime }+y&=\left \{\begin {array}{cc} 1 & 0\le x \le 1 \\ -1 & 1<x \end {array}\right . \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	1.477
10805	10137	\begin{align*} y^{\prime \prime }+y&=\sin \left (x \right ) \\ y^{\prime }\left (0\right ) &= 1 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.477
10806	15577	\begin{align*} y^{\prime }&=\frac {1}{x^{2}-1} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.477
10807	19065	\begin{align*} y^{\prime \prime }&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	1.477
10808	23286	\begin{align*} y^{\prime \prime }+y x&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.477
10809	7266	\begin{align*} y^{\prime \prime }+5 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.479
10810	8228	\begin{align*} \left (4-y^{2}\right ) y^{\prime }&=x^{2} \\ \end{align*}	✓	✓	✓	✓	1.480
10811	8742	\begin{align*} 2 y^{\prime } x +y&=y^{2} \sqrt {x -y^{2} x^{2}} \\ \end{align*}	✓	✓	✓	✗	1.480
10812	14902	\begin{align*} x^{\prime }+x \tanh \left (t \right )&=3 \\ \end{align*}	✓	✓	✓	✓	1.480
10813	21794	\begin{align*} y^{\prime }+y&=2 \,{\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	1.480
10814	9210	\begin{align*} y y^{\prime \prime }+y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.481
10815	14720	\begin{align*} x^{2} y^{\prime \prime }-2 y&=4 x -8 \\ y \left (1\right ) &= 4 \\ y^{\prime }\left (1\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	1.481
10816	22507	\begin{align*} y&=\tan \left (x \right ) y^{\prime }-{y^{\prime }}^{2} \sec \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✗	1.481
10817	20456	\begin{align*} 4 x \left (x -1\right ) \left (x -2\right ) {y^{\prime }}^{2}-\left (3 x^{2}-6 x +2\right )^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	1.482
10818	20722	\begin{align*} y&=x \left (1+y^{\prime }\right )+{y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	1.482
10819	4345	\begin{align*} x^{2}+y+y^{2}-y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	1.483
10820	16293	\begin{align*} y^{\prime }+3 y&=3 y^{3} \\ \end{align*}	✓	✓	✓	✓	1.483
10821	5086	\begin{align*} 2 \left (x +y\right ) y^{\prime }+x^{2}+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.484
10822	9641	\begin{align*} y+y^{\prime }&=\delta \left (t -1\right ) \\ y \left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	1.484
10823	10233	\begin{align*} x^{\prime }&=x+2 y+2 t +1 \\ y^{\prime }&=5 x+y+3 t -1 \\ \end{align*}	✓	✓	✓	✓	1.484
10824	11682	\begin{align*} {y^{\prime }}^{2}+\left (a y+b x \right ) y^{\prime }+a b x y&=0 \\ \end{align*}	✓	✓	✓	✓	1.484
10825	1596	\begin{align*} y^{\prime }&=-y^{2}+2 y \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.485
10826	6466	\begin{align*} \left (x -y\right ) y^{\prime \prime }&=f \left (y^{\prime }\right ) \\ \end{align*}	✗	✓	✓	✗	1.485
10827	17610	\begin{align*} \left (t^{2}+t \right ) y^{\prime \prime \prime }+\left (-t^{2}+2\right ) y^{\prime \prime }-\left (t +2\right ) y^{\prime }&=-2-t \\ \end{align*}	✓	✓	✓	✗	1.485
10828	24986	\begin{align*} y^{\prime }-3 y&=25 \cos \left (4 t \right ) \\ \end{align*}	✓	✓	✓	✓	1.485
10829	25799	\begin{align*} y^{\prime }&=x +y \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.485
10830	153	\begin{align*} y y^{\prime \prime }+{y^{\prime }}^{2}&=y y^{\prime } \\ \end{align*}	✓	✓	✓	✗	1.487
10831	3847	\begin{align*} x_{1}^{\prime }&=x_{1}+2 x_{2}+3 x_{3}+4 x_{4} \\ x_{2}^{\prime }&=4 x_{1}+3 x_{2}+2 x_{3}+x_{4} \\ x_{3}^{\prime }&=4 x_{1}+5 x_{2}+6 x_{3}+7 x_{4} \\ x_{4}^{\prime }&=7 x_{1}+6 x_{2}+5 x_{3}+4 x_{4} \\ \end{align*}	✓	✓	✓	✓	1.487
10832	8229	\begin{align*} \left (y^{3}+1\right ) y^{\prime }&=x^{2} \\ \end{align*}	✓	✓	✓	✓	1.487
10833	23151	\begin{align*} y^{\prime } x +y&=3 \\ \end{align*}	✓	✓	✓	✓	1.487
10834	5811	\begin{align*} \left (c x +b \right ) y+a y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.488
10835	9911	\begin{align*} x \left (x +1\right ) y^{\prime \prime }+\left (x +5\right ) y^{\prime }-4 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.488
10836	10585	\begin{align*} 4 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+12 x^{2} \left (x +1\right ) y^{\prime }+\left (3 x^{2}+3 x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	1.488
10837	5759	\begin{align*} -\left (a^{2}-b \,{\mathrm e}^{x}\right ) y+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.490
10838	9920	\begin{align*} x \left (1-2 x \right ) y^{\prime \prime }-2 \left (2+x \right ) y^{\prime }+8 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.490
10839	15045	\begin{align*} x^{\prime }+5 x&=10 t +2 \\ x \left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	1.490
10840	15596	\begin{align*} y^{\prime }&=y x +2 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.490
10841	18526	\begin{align*} -2 y+y^{\prime }&={\mathrm e}^{2 t} \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	1.490
10842	19868	\begin{align*} x^{2} y^{\prime \prime }&=\ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	1.491
10843	8875	\begin{align*} y^{\prime }+a y&=b \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	1.492
10844	10095	\begin{align*} y^{\prime \prime }-y^{\prime }-y x -x^{2}-1&=0 \\ \end{align*}	✓	✓	✓	✗	1.492
10845	5157	\begin{align*} 2 y y^{\prime } x +1-2 x^{3}-y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	1.493
10846	7279	\begin{align*} y^{\prime \prime }+y&=2 \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	1.493
10847	22008	\begin{align*} y^{\prime }&=\frac {x +y}{x} \\ \end{align*}	✓	✓	✓	✓	1.493
10848	24984	\begin{align*} y^{\prime }&=-\frac {y}{t}+\cos \left (t^{2}\right ) \\ \end{align*}	✓	✓	✓	✓	1.494
10849	1794	\begin{align*} y^{\prime }+y^{2}+8 y+7&=0 \\ \end{align*}	✓	✓	✓	✓	1.495
10850	9915	\begin{align*} \left (1-x \right ) x y^{\prime \prime }-3 y^{\prime }+2 y&=0 \\ \end{align*} Series expansion around \(x=1\).	✓	✓	✓	✓	1.495
10851	18950	\begin{align*} y^{\prime \prime }+\frac {y^{\prime }}{4}+y&=\delta \left (t -1\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	1.495
10852	21563	\begin{align*} y^{\prime \prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	1.495
10853	5666	\begin{align*} y^{4} {y^{\prime }}^{3}-6 y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✗	1.496
10854	5958	\begin{align*} \left (b x +a \right ) y+x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.496
10855	23045	\begin{align*} y^{\prime \prime }&={y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	1.496
10856	1130	\begin{align*} y^{\prime }&=\frac {x^{2}}{\left (x^{3}+1\right ) y} \\ \end{align*}	✓	✓	✓	✓	1.497
10857	2340	\begin{align*} \frac {y^{2}}{2}-2 \,{\mathrm e}^{t} y+\left (-{\mathrm e}^{t}+y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.497
10858	2362	\begin{align*} y^{\prime \prime }+y^{\prime } t +y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	1.497
10859	9582	\begin{align*} y^{\prime \prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	1.497
10860	23137	\begin{align*} y^{\prime } x +y&=3 \\ \end{align*}	✓	✓	✓	✓	1.497
10861	10418	\begin{align*} y^{\prime }&=\left (x +y\right )^{4} \\ \end{align*}	✓	✓	✓	✓	1.498
10862	21687	\begin{align*} 2 \left (1-x \right ) y^{\prime \prime }+\left (x +1\right ) y^{\prime }+\left (x -3-\left (x -1\right )^{2} {\mathrm e}^{x}\right ) y&=0 \\ \end{align*} Series expansion around \(x=1\).	✓	✓	✓	✓	1.498
10863	23907	\begin{align*} y^{\prime }-y&=2 \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	1.498
10864	1118	\begin{align*} -\frac {y}{2}+y^{\prime }&=2 \cos \left (t \right ) \\ y \left (0\right ) &= a \\ \end{align*}	✓	✓	✓	✓	1.499
10865	1493	\begin{align*} y^{\prime \prime }+4 y&=\left \{\begin {array}{cc} 1 & 0\le t <1 \\ 0 & 1\le t <\infty \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	1.499
10866	13	\begin{align*} x^{\prime \prime }&=3 t \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 5 \\ \end{align*}	✓	✓	✓	✓	1.500
10867	7095	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=5 \sin \left (x \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	1.500
10868	9440	\begin{align*} 9 \left (x -2\right )^{2} \left (x -3\right ) y^{\prime \prime }+6 x \left (x -2\right ) y^{\prime }+16 y&=0 \\ \end{align*} Series expansion around \(x=\infty \).	✓	✓	✓	✗	1.500
10869	23296	\begin{align*} \left (x -1\right ) y^{\prime \prime }+3 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.500
10870	9385	\begin{align*} x^{2} \left (x^{2}-1\right ) y^{\prime \prime }-x \left (1-x \right ) y^{\prime }+2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.501
10871	25762	\begin{align*} y^{\prime \prime }+2 y^{\prime }-3 y&=-12 x +8 \\ y \left (0\right ) &= 5 \\ y^{\prime }\left (0\right ) &= -11 \\ \end{align*}	✓	✓	✓	✓	1.502
10872	5531	\begin{align*} x^{3} {y^{\prime }}^{2}+x^{2} y y^{\prime }+a&=0 \\ \end{align*}	✓	✓	✓	✗	1.503
10873	9494	\begin{align*} y^{\prime \prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	1.503
10874	1793	\begin{align*} y^{\prime }+y^{2}+5 y-6&=0 \\ \end{align*}	✓	✓	✓	✓	1.504
10875	5226	\begin{align*} \left (x^{3}+2 y-y^{2}\right ) y^{\prime }+3 x^{2} y&=0 \\ \end{align*}	✓	✓	✓	✗	1.504
10876	9731	\begin{align*} {y^{\prime }}^{2}-y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✗	1.504
10877	14770	\begin{align*} x^{2} y^{\prime \prime }-y^{\prime } x +\left (x^{2}-3\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.504
10878	19154	\begin{align*} y^{\prime } y^{\prime \prime }-x^{2} y y^{\prime }-x y^{2}&=0 \\ \end{align*}	✗	✗	✗	✗	1.504
10879	3429	\begin{align*} y^{\prime }&=8 \,{\mathrm e}^{4 t}+t \\ y \left (0\right ) &= 12 \\ \end{align*}	✓	✓	✓	✓	1.505
10880	5218	\begin{align*} \left (a^{2}+x^{2}+y^{2}\right ) y^{\prime }+2 y x&=0 \\ \end{align*}	✓	✓	✓	✓	1.505
10881	5750	\begin{align*} a \,x^{k} y+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.505
10882	13258	\begin{align*} \left (x^{2}-1\right ) y^{\prime }+\lambda \left (1-2 y x +y^{2}\right )&=0 \\ \end{align*}	✗	✓	✓	✗	1.505
10883	22001	\begin{align*} x^{2}+1+\left (y^{2}+y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.505
10884	57	\begin{align*} y^{\prime }&=1+x +y+y x \\ \end{align*}	✓	✓	✓	✓	1.506
10885	1208	\begin{align*} y+\left (2 x -{\mathrm e}^{y} y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.506
10886	3139	\begin{align*} y^{\prime \prime }+y&={\mathrm e}^{x} \sin \left (x \right ) \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	1.506
10887	18952	\begin{align*} y^{\prime \prime }+\frac {y^{\prime }}{5}+y&=k \delta \left (t -1\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	1.506
10888	22028	\begin{align*} y+2 x y^{3}+\left (1+3 y^{2} x^{2}+x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.506
10889	25665	\begin{align*} x^{\prime }&=\left (x-1\right ) \left (1-2 x\right ) \\ \end{align*}	✓	✓	✓	✓	1.506
10890	15281	\begin{align*} x^{\prime }&=-7 x+10 y+18 \,{\mathrm e}^{t} \\ y^{\prime }&=-10 x+9 y+37 \\ \end{align*}	✓	✓	✓	✓	1.507
10891	16332	\begin{align*} y^{\prime } x&=2 y-6 x^{3} \\ \end{align*}	✓	✓	✓	✓	1.507
10892	22290	\begin{align*} y^{\prime }&=x^{2}+5 y \\ \end{align*}	✓	✓	✓	✓	1.507
10893	23756	\begin{align*} y^{\prime \prime }+9 y&=0 \\ y \left (0\right ) &= 1 \\ y \left (\pi \right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	1.507
10894	1516	\begin{align*} y^{\prime \prime }+y&=\frac {\operatorname {Heaviside}\left (t -4+k \right )-\operatorname {Heaviside}\left (t -4-k \right )}{2 k} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	1.508
10895	22995	\begin{align*} y^{\prime }+\frac {y \ln \left (x \right )}{x}&=2 \\ \end{align*}	✓	✓	✓	✓	1.508
10896	14268	\begin{align*} x^{\prime }&=x \left (1+{\mathrm e}^{t} x\right ) \\ \end{align*}	✓	✓	✓	✓	1.509
10897	4191	\begin{align*} y^{\prime }+\cot \left (x \right ) y&=x \\ \end{align*}	✓	✓	✓	✓	1.510
10898	5813	\begin{align*} \left (b +c \,{\mathrm e}^{x}\right ) y+a y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.510
10899	8085	\begin{align*} 2 y^{\prime \prime } x +y^{\prime }-y&=x +1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	1.510
10900	11168	\begin{align*} y^{\prime \prime } x +3 y^{\prime }+4 x^{3} y&=0 \\ \end{align*}	✓	✓	✓	✓	1.510