2.3.249 Problems 24801 to 24900

Table 2.1029: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
24801	4459	\begin{align*} y^{\prime \prime }+2 y^{\prime }+2 y&=\cosh \left (x \right ) \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✗	65.111
24802	24576	\begin{align*} y^{\prime \prime }+9 y&=\sin \left (3 x \right ) \\ y \left (0\right ) &= 1 \\ y \left (\frac {\pi }{2}\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	65.112
24803	17291	\begin{align*} y^{4}+\left (t^{4}-t y^{3}\right ) y^{\prime }&=0 \\ y \left (1\right ) &= 2 \\ \end{align*}	✓	✓	✗	✓	65.209
24804	20757	\begin{align*} \left (x +1\right )^{2} y^{\prime \prime }+\left (x +1\right ) y^{\prime }+y&=4 \cos \left (\ln \left (x +1\right )\right ) \\ \end{align*}	✓	✓	✓	✗	65.213
24805	1344	\begin{align*} y^{\prime \prime }+4 y&=g \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	65.243
24806	23076	\begin{align*} y^{\prime \prime }-2 y^{\prime }-y&=2 \cos \left (3 x \right )-3 \sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	65.268
24807	6148	\begin{align*} 4 y+2 \left (1-2 x \right ) y^{\prime }+\left (1-2 x \right ) \left (1-x \right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	65.350
24808	12113	\begin{align*} y^{\prime }&=\frac {2 a +\sqrt {-y^{2}+4 a x}+x^{2} \sqrt {-y^{2}+4 a x}+x^{3} \sqrt {-y^{2}+4 a x}}{y} \\ \end{align*}	✗	✓	✓	✗	65.386
24809	12993	\begin{align*} y^{2} y^{\prime \prime }-a&=0 \\ \end{align*}	✓	✓	✓	✓	65.427
24810	13386	\begin{align*} y^{\prime } x&=a \cos \left (\lambda x \right )^{m} y^{2}+k y+a \,b^{2} x^{2 k} \cos \left (\lambda x \right )^{m} \\ \end{align*}	✓	✓	✓	✗	65.467
24811	10144	\begin{align*} y^{\prime \prime }+y^{\prime }+y&=\sin \left (x \right ) \\ y^{\prime }\left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	65.526
24812	10401	\begin{align*} y^{\prime \prime }+y&=x^{3}+x^{2}+x +1 \\ \end{align*}	✓	✓	✓	✓	65.615
24813	5117	\begin{align*} \left (a x +b y\right ) y^{\prime }+x&=0 \\ \end{align*}	✓	✓	✓	✗	65.641
24814	3204	\begin{align*} 4 y+y^{\prime \prime }&=x \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	65.669
24815	6090	\begin{align*} \left (c^{2} x^{2}+b^{2}\right ) y-y^{\prime } x +\left (a^{2}-x^{2}\right ) y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	65.684
24816	1328	\begin{align*} t^{2} y^{\prime \prime }+2 y^{\prime } t +\frac {y}{4}&=0 \\ \end{align*}	✓	✓	✓	✓	65.760
24817	17282	\begin{align*} t \left (\ln \left (t \right )-\ln \left (y\right )\right ) y^{\prime }&=y \\ \end{align*}	✓	✓	✓	✓	65.766
24818	12534	\begin{align*} \left (2 x^{2}+6 x +4\right ) y^{\prime \prime }+\left (10 x^{2}+21 x +8\right ) y^{\prime }+\left (12 x^{2}+17 x +8\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	65.768
24819	391	\begin{align*} x^{\prime \prime }+3 x^{\prime }+3 x&=8 \cos \left (10 t \right )+6 \sin \left (10 t \right ) \\ \end{align*}	✓	✓	✓	✓	65.790
24820	17038	\begin{align*} \frac {y^{\prime }}{t}&=\sqrt {y} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	65.797
24821	4682	\begin{align*} y^{\prime }&=a \,x^{m}+b \,x^{n} y^{2} \\ \end{align*}	✓	✓	✓	✗	65.845
24822	2350	\begin{align*} y^{\prime }&={\mathrm e}^{-t^{2}}+y^{2} \\ y \left (1\right ) &= 0 \\ \end{align*}	✗	✗	✗	✗	65.867
24823	14267	\begin{align*} x^{\prime }&=\frac {2 x}{3 t}+\frac {2 t}{x} \\ \end{align*}	✓	✓	✓	✓	65.881
24824	5735	\begin{align*} 4 y+y^{\prime \prime }&=2 \tan \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	65.905
24825	16109	\begin{align*} y^{\prime \prime }+4 y&=6+t^{2}+{\mathrm e}^{t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	65.906
24826	11650	\begin{align*} x y^{\prime } \ln \left (x \right ) \sin \left (y\right )+\cos \left (y\right ) \left (1-x \cos \left (y\right )\right )&=0 \\ \end{align*}	✗	✓	✓	✓	65.995
24827	6158	\begin{align*} -\left (\left (2 n +1\right )^{2}-4 x^{2}\right ) y+4 y^{\prime } x +4 x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	66.010
24828	3146	\begin{align*} 4 y+y^{\prime \prime }&=x^{2} \\ \end{align*}	✓	✓	✓	✓	66.044
24829	3159	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=\frac {{\mathrm e}^{x}}{\left (1-x \right )^{2}} \\ \end{align*}	✓	✓	✓	✗	66.120
24830	12510	\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }-2 \left (v -1\right ) x y^{\prime }-2 v y&=0 \\ \end{align*}	✓	✓	✓	✗	66.188
24831	2406	\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&=t^{{5}/{2}} {\mathrm e}^{-2 t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	66.211
24832	3742	\begin{align*} y^{\prime \prime }-2 y^{\prime }+10 y&=24 \,{\mathrm e}^{x} \cos \left (3 x \right ) \\ \end{align*}	✓	✓	✓	✓	66.270
24833	514	\begin{align*} x^{2} y^{\prime \prime }-y^{\prime } x +\left (x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	66.382
24834	23083	\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&=8 \sin \left (2 x \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	66.405
24835	3425	\begin{align*} y^{\prime }&=-y^{3} \\ y \left (1\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	66.491
24836	23379	\begin{align*} \left (x -2\right )^{2} y^{\prime \prime }-\left (x -2\right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	66.573
24837	12512	\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }+a x y^{\prime }+\left (b \,x^{2}+c x +d \right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	66.579
24838	5734	\begin{align*} 4 y+y^{\prime \prime }&=2 \tan \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	66.624
24839	4503	\begin{align*} y^{\prime \prime }-y&={\mathrm e}^{-2 x} \sin \left ({\mathrm e}^{-x}\right ) \\ \end{align*}	✓	✓	✓	✓	66.635
24840	17525	\begin{align*} y^{\prime \prime }+9 y&=\csc \left (3 t \right ) \\ y \left (\frac {\pi }{12}\right ) &= 0 \\ y^{\prime }\left (\frac {\pi }{12}\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	66.643
24841	4258	\begin{align*} 2 x y^{3}+\cos \left (x \right ) y+\left (3 y^{2} x^{2}+\sin \left (x \right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	66.661
24842	520	\begin{align*} x^{2} y^{\prime \prime }+3 y^{\prime } x +\left (x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	66.799
24843	21600	\begin{align*} \left (x -1\right )^{2} y^{\prime \prime }-4 \left (x -1\right ) y^{\prime }-14 y&=x^{3}-3 x^{2}+3 x -8 \\ \end{align*}	✓	✓	✓	✗	66.829
24844	18832	\begin{align*} y^{\prime \prime }-2 y^{\prime }+y&={\mathrm e}^{t} t +4 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	66.871
24845	22529	\begin{align*} \tan \left (y\right )-\tan \left (y\right )^{2} \cos \left (x \right )-x \sec \left (y\right )^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	66.994
24846	5731	\begin{align*} -2 y+y^{\prime \prime }&=4 x^{2} {\mathrm e}^{x^{2}} \\ \end{align*}	✓	✓	✓	✓	67.003
24847	331	\begin{align*} 2 y^{\prime \prime }+9 y&=2 \cos \left (3 x \right )+3 \sin \left (3 x \right ) \\ \end{align*}	✓	✓	✓	✓	67.020
24848	11548	\begin{align*} \left (x^{2} y-1\right ) y^{\prime }-x y^{2}+1&=0 \\ \end{align*}	✗	✓	✓	✗	67.051
24849	2404	\begin{align*} y^{\prime \prime }-3 y^{\prime }+2 y&=t \,{\mathrm e}^{3 t}+1 \\ \end{align*}	✓	✓	✓	✓	67.085
24850	2346	\begin{align*} y^{\prime }&=y^{2}+\cos \left (t^{2}\right ) \\ y \left (0\right ) &= 0 \\ \end{align*}	✗	✗	✗	✗	67.116
24851	7790	\begin{align*} y^{\prime \prime }-5 y&=2 \,{\mathrm e}^{5 x} \\ \end{align*}	✓	✓	✓	✓	67.189
24852	4480	\begin{align*} 4 y+y^{\prime \prime }&=4 \sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	67.211
24853	19781	\begin{align*} \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}}&=r y^{\prime \prime } \\ \end{align*}	✓	✓	✓	✗	67.214
24854	3178	\begin{align*} y^{\prime \prime }+3 y^{\prime }-2 y&=\sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	67.278
24855	7786	\begin{align*} y^{\prime \prime }-6 y^{\prime }+25 y&=64 \,{\mathrm e}^{-t} \\ \end{align*}	✓	✓	✓	✓	67.300
24856	17276	\begin{align*} y+2 \sqrt {t^{2}+y^{2}}-y^{\prime } t&=0 \\ \end{align*}	✓	✓	✓	✓	67.316
24857	3162	\begin{align*} -2 y+y^{\prime \prime }&={\mathrm e}^{-x} \sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	67.338
24858	7772	\begin{align*} y^{\prime \prime }-9 y&={\mathrm e}^{3 x}+\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	67.370
24859	14169	\begin{align*} \left (x -1\right )^{2} y^{\prime \prime }+4 \left (x -1\right ) y^{\prime }+2 y&=\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✗	67.402
24860	5077	\begin{align*} \left (y-\cot \left (x \right ) \csc \left (x \right )\right ) y^{\prime }+\csc \left (x \right ) \left (1+\cos \left (x \right ) y\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	67.403
24861	5741	\begin{align*} y^{\prime \prime }+a^{2} y&=\sin \left (b x \right ) \\ \end{align*}	✓	✓	✓	✓	67.420
24862	13421	\begin{align*} y^{\prime }&=-\left (1+k \right ) x^{k} y^{2}+\lambda \arcsin \left (x \right )^{n} \left (x^{1+k} y-1\right ) \\ \end{align*}	✓	✓	✗	✗	67.426
24863	20483	\begin{align*} \left (-y+y^{\prime } x \right ) \left (x -y y^{\prime }\right )&=2 y^{\prime } \\ \end{align*}	✗	✗	✓	✗	67.546
24864	4132	\begin{align*} y^{\prime \prime }+2 y&=x +{\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	67.560
24865	4156	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=\sin \left (2 x \right ) x \\ \end{align*}	✓	✓	✓	✓	67.569
24866	11989	\begin{align*} y^{\prime }&=-\frac {\left (-\ln \left (-1+y\right )+\ln \left (1+y\right )+2 \ln \left (x \right )\right ) x \left (1+y\right )^{2}}{8} \\ \end{align*}	✗	✓	✓	✗	67.592
24867	15406	\begin{align*} {y^{\prime \prime }}^{2}+{y^{\prime }}^{2}&=a^{2} \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	67.599
24868	5738	\begin{align*} y^{\prime \prime }+a^{2} y&=x^{2}+x +1 \\ \end{align*}	✓	✓	✓	✓	67.679
24869	7285	\begin{align*} y^{\prime \prime }+2 y^{\prime }+10 y&=100 \cos \left (4 x \right ) \\ \end{align*}	✓	✓	✓	✓	67.685
24870	5415	\begin{align*} {y^{\prime }}^{2}-2 y y^{\prime }-2 x&=0 \\ \end{align*}	✓	✓	✓	✗	67.690
24871	11450	\begin{align*} \left (x^{2}+1\right ) y^{\prime }+\left (1+y^{2}\right ) \left (2 y x -1\right )&=0 \\ \end{align*}	✗	✓	✓	✗	67.729
24872	9276	\begin{align*} \left (x^{2}+x \right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }-\left (2+x \right ) y&=x \left (x +1\right )^{2} \\ \end{align*}	✓	✓	✓	✗	67.730
24873	5092	\begin{align*} \left (\sec \left (x \right ) \tan \left (x \right )-2 y\right ) y^{\prime }+\sec \left (x \right ) \left (1+2 \sin \left (x \right ) y\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	67.737
24874	23400	\begin{align*} \left (x -4\right ) y^{\prime \prime }+4 y^{\prime }-\frac {4 y}{x -4}&=0 \\ \end{align*}	✓	✓	✓	✓	67.744
24875	15357	\begin{align*} 3 y-7 x +7-\left (3 x -7 y-3\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	67.798
24876	2403	\begin{align*} 2 y^{\prime \prime }-3 y^{\prime }+y&=\left (t^{2}+1\right ) {\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	67.837
24877	13606	\begin{align*} y y^{\prime }&=\left (a \,{\mathrm e}^{x}+b \right ) y+c \,{\mathrm e}^{2 x}-a b \,{\mathrm e}^{x}-b^{2} \\ \end{align*}	✗	✓	✗	✗	67.855
24878	13291	\begin{align*} y^{\prime }&=a \,{\mathrm e}^{\lambda x} y^{2}+b y+c \,{\mathrm e}^{-\lambda x} \\ \end{align*}	✓	✓	✓	✓	67.860
24879	1825	\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x -\left (x^{2}-2\right ) y&=3 x^{4} \\ \end{align*}	✓	✓	✓	✗	67.865
24880	2526	\begin{align*} y^{\prime }&={\mathrm e}^{-t^{2}}+y^{2} \\ y \left (0\right ) &= 1 \\ \end{align*}	✗	✗	✗	✗	67.868
24881	5739	\begin{align*} y^{\prime \prime }+a^{2} y&=\cos \left (b x \right ) \\ \end{align*}	✓	✓	✓	✓	67.898
24882	20468	\begin{align*} {y^{\prime }}^{4}&=4 y \left (y^{\prime } x -2 y\right )^{2} \\ \end{align*}	✓	✓	✓	✗	68.022
24883	1820	\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x +\left (x^{2}+2\right ) y&=\cos \left (x \right ) x^{3} \\ \end{align*}	✓	✓	✓	✗	68.033
24884	1340	\begin{align*} y^{\prime \prime }+4 y&=3 \csc \left (2 t \right ) \\ \end{align*}	✓	✓	✓	✓	68.071
24885	5733	\begin{align*} 4 y+y^{\prime \prime }&=x \sin \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✓	68.079
24886	920	\begin{align*} x^{\prime \prime }+2 x^{\prime }+26 x&=600 \cos \left (10 t \right ) \\ x \left (0\right ) &= 10 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	68.105
24887	2349	\begin{align*} y^{\prime }&={\mathrm e}^{-t^{2}}+y^{2} \\ y \left (0\right ) &= 0 \\ \end{align*}	✗	✗	✗	✗	68.148
24888	7086	\begin{align*} 4 y+y^{\prime \prime }&=\sin \left (2 x \right ) x \\ \end{align*}	✓	✓	✓	✓	68.169
24889	2905	\begin{align*} 2 x +3 y+2+\left (-x +y\right ) y^{\prime }&=0 \\ y \left (0\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	68.180
24890	23965	\begin{align*} 3 y^{2}-2 x^{2}&=2 y y^{\prime } x \\ \end{align*}	✓	✓	✓	✓	68.194
24891	13343	\begin{align*} \left (a \coth \left (\lambda x \right )+b \right ) y^{\prime }&=y^{2}+c \coth \left (\mu x \right ) y-d^{2}+c d \coth \left (\mu x \right ) \\ \end{align*}	✓	✓	✓	✗	68.246
24892	5779	\begin{align*} 5 y+2 y^{\prime }+y^{\prime \prime }&=8 \sinh \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	68.253
24893	6145	\begin{align*} a y-\left (1-2 x \right ) y^{\prime }+2 \left (1-x \right ) x y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	68.302
24894	17530	\begin{align*} 4 y^{\prime \prime }+4 y^{\prime }+y&={\mathrm e}^{-\frac {t}{2}} \\ y \left (0\right ) &= a \\ y^{\prime }\left (0\right ) &= b \\ \end{align*}	✓	✓	✓	✓	68.317
24895	4250	\begin{align*} \sin \left (x \right ) \tan \left (y\right )+1+\cos \left (x \right ) \sec \left (y\right )^{2} y^{\prime }&=0 \\ \end{align*}	✓	✗	✓	✗	68.421
24896	398	\begin{align*} x^{\prime \prime }+6 x^{\prime }+45 x&=50 \cos \left (\omega t \right ) \\ \end{align*}	✓	✓	✓	✓	68.467
24897	6047	\begin{align*} -\left (a -x \cot \left (x \right )\right ) y+x \left (1+2 x \cot \left (x \right )\right ) y^{\prime }+x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	68.470
24898	21822	\begin{align*} \left (x^{2}+y^{2}\right ) \left (y^{\prime } x +y\right )&=x y \left (-y+y^{\prime } x \right ) \\ \end{align*}	✓	✓	✓	✓	68.625
24899	22020	\begin{align*} y^{\prime }&=\frac {y^{2}}{y x +\left (x y^{2}\right )^{{1}/{3}}} \\ \end{align*}	✓	✓	✓	✗	68.626
24900	15555	\begin{align*} y^{\prime }&=\left (y x \right )^{{1}/{3}} \\ \end{align*}	✓	✓	✓	✗	68.642