2.3.202 Problems 20101 to 20200

Table 2.977: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
20101	23914	\begin{align*} y^{\prime }-y x&=x^{3} \\ \end{align*}	✓	✓	✓	✓	3.669
20102	24224	\begin{align*} y \left (y^{2} x^{2}-m \right )+x \left (y^{2} x^{2}+n \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.669
20103	9160	\begin{align*} 2 x +3 y-1-4 \left (x +1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.670
20104	1579	\begin{align*} \sin \left (x \right ) \sin \left (y\right )+y^{\prime } \cos \left (y\right )&=0 \\ \end{align*}	✓	✓	✓	✓	3.671
20105	1522	\begin{align*} 2 y^{\prime }+x \left (-1+y^{2}\right )&=0 \\ \end{align*}	✓	✓	✓	✓	3.672
20106	12613	\begin{align*} y^{\prime \prime }&=-\frac {2 y^{\prime }}{x}-\frac {a^{2} y}{x^{4}} \\ \end{align*}	✓	✓	✓	✓	3.673
20107	1154	\begin{align*} y^{\prime }&=2 \left (x +1\right ) \left (1+y^{2}\right ) \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.674
20108	17953	\begin{align*} y^{\prime }+2 y x&=2 x y^{2} \\ \end{align*}	✓	✓	✓	✓	3.675
20109	18300	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +y&=x \left (6-\ln \left (x \right )\right ) \\ \end{align*}	✓	✓	✓	✓	3.675
20110	23403	\begin{align*} 5 y^{\prime \prime }+\frac {3 y^{\prime }}{x -3}+\frac {3 y}{\left (x -3\right )^{2}}&=0 \\ \end{align*}	✓	✓	✓	✗	3.676
20111	1669	\begin{align*} 3 y^{2} y^{\prime } x&=y^{3}+x \\ \end{align*}	✓	✓	✓	✓	3.678
20112	5374	\begin{align*} {y^{\prime }}^{2}+f \left (x \right ) \left (y-a \right )^{2} \left (y-b \right ) \left (y-c \right )&=0 \\ \end{align*}	✓	✓	✓	✓	3.678
20113	23126	\begin{align*} y^{\prime } x +\frac {y}{2 x +3}&=\ln \left (x -2\right ) \\ \end{align*}	✓	✓	✓	✓	3.678
20114	26198	\begin{align*} y^{\prime }&=\left (1-y\right ) \left (1-x \right ) \\ \end{align*}	✓	✓	✓	✓	3.678
20115	8365	\begin{align*} \left (x^{4}+1\right ) y^{\prime }+x \left (1+4 y^{2}\right )&=0 \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✗	✓	3.679
20116	21056	\begin{align*} x^{\prime }&={\mathrm e}^{t} \left (x^{2}+1\right ) \\ x \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.679
20117	22000	\begin{align*} x +\frac {y^{\prime }}{y}&=0 \\ \end{align*}	✓	✓	✓	✓	3.679
20118	18503	\begin{align*} y^{\prime }&=2 y^{2}+x y^{2} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.680
20119	18848	\begin{align*} y^{\prime \prime }+y&=\left \{\begin {array}{cc} t & 0\le t \le \pi \\ \pi \,{\mathrm e}^{\pi -t} & \pi <t \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.680
20120	5312	\begin{align*} x \left (1-2 x y^{3}\right ) y^{\prime }+\left (1-2 x^{3} y\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	3.681
20121	16693	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x -9 y&=12 x^{3} \\ \end{align*}	✓	✓	✓	✓	3.681
20122	6387	\begin{align*} y^{\prime \prime } x +2 y^{\prime }&=a \,x^{2 k} {y^{\prime }}^{k} \\ \end{align*}	✓	✓	✓	✗	3.682
20123	4822	\begin{align*} y^{\prime } x +\tan \left (y\right )&=0 \\ \end{align*}	✓	✓	✓	✓	3.684
20124	19257	\begin{align*} 1+y^{2}+\left (x^{2}+1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.684
20125	5584	\begin{align*} \left (\left (1-a \right ) x^{2}+y^{2}\right ) {y^{\prime }}^{2}+2 a x y y^{\prime }+x^{2}+\left (1-a \right ) y^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	3.686
20126	17780	\begin{align*} x^{2} y^{\prime \prime }+7 y^{\prime } x +8 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.687
20127	5744	\begin{align*} \left (x^{2}+a \right ) y+y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	3.688
20128	14463	\begin{align*} \left (x +4\right ) \left (1+y^{2}\right )+y \left (x^{2}+3 x +2\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.688
20129	22432	\begin{align*} 2 x^{3}-y+y^{\prime } x&=0 \\ y \left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	3.688
20130	21072	\begin{align*} x +\sin \left (y\right )+x \cos \left (y\right ) y^{\prime }&=0 \\ y \left (2\right ) &= \pi \\ \end{align*}	✓	✓	✗	✓	3.690
20131	16750	\begin{align*} x^{2} y^{\prime \prime }+3 y^{\prime } x +2 y&=6 \\ \end{align*}	✓	✓	✓	✓	3.691
20132	22569	\begin{align*} y^{\prime } x -3 y&=x^{4} {\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	3.691
20133	26468	\begin{align*} 3 y^{\prime \prime }&=\frac {1}{y^{{5}/{3}}} \\ \end{align*}	✓	✓	✓	✓	3.691
20134	15347	\begin{align*} x -x y^{2}+\left (y-x^{2} y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.693
20135	210	\begin{align*} y^{\prime }&=x y^{3}-y x \\ \end{align*}	✓	✓	✓	✓	3.694
20136	26331	\begin{align*} y \left (a^{2}+x^{2}+y^{2}\right ) y^{\prime }+x \left (-a^{2}+x^{2}+y^{2}\right )&=0 \\ \end{align*}	✓	✓	✓	✗	3.694
20137	1286	\begin{align*} y^{\prime \prime }+y&=0 \\ y \left (\frac {\pi }{3}\right ) &= 2 \\ y^{\prime }\left (\frac {\pi }{3}\right ) &= -4 \\ \end{align*}	✓	✓	✓	✓	3.695
20138	25057	\begin{align*} y^{\prime }&=y^{2} \\ y \left (t_{0} \right ) &= y_{0} \\ \end{align*}	✓	✓	✓	✓	3.695
20139	15948	\begin{align*} y^{\prime }&=\frac {t y}{t^{2}+1} \\ \end{align*}	✓	✓	✓	✓	3.698
20140	16234	\begin{align*} y^{\prime }&=y x -4 x \\ \end{align*}	✓	✓	✓	✓	3.698
20141	19180	\begin{align*} \sin \left (x \right )^{2} y^{\prime \prime }+\cos \left (x \right ) \sin \left (x \right ) y^{\prime }&=y \\ \end{align*}	✓	✓	✓	✗	3.699
20142	24262	\begin{align*} y^{\prime }&=x^{3}-2 y x \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.699
20143	4077	\begin{align*} 2 x \tan \left (y\right )+\left (x -x^{2} \tan \left (y\right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.700
20144	4681	\begin{align*} y^{\prime }&=x^{n} \left (a +b y^{2}\right ) \\ \end{align*}	✓	✓	✓	✓	3.700
20145	17838	\begin{align*} y^{\prime }&=\frac {x}{y} \\ \end{align*}	✓	✓	✓	✓	3.700
20146	25781	\begin{align*} y^{\prime }&=\cos \left (y\right ) \sin \left (x \right ) \\ y \left (3\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	3.700
20147	23197	\begin{align*} y-2 x -y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	3.701
20148	17857	\begin{align*} y^{\prime }&=x^{2}-y^{2} \\ \end{align*}	✓	✓	✓	✗	3.702
20149	4424	\begin{align*} x^{2}+3 \ln \left (y\right )-\frac {x y^{\prime }}{y}&=0 \\ \end{align*}	✓	✓	✓	✓	3.703
20150	4967	\begin{align*} x^{3} y^{\prime }&=b \,x^{2} y+a \\ \end{align*}	✓	✓	✓	✓	3.703
20151	22371	\begin{align*} y^{\prime }&=-\frac {3 x +x y^{2}}{x^{2} y+2 y} \\ \end{align*}	✓	✓	✓	✓	3.703
20152	19723	\begin{align*} y^{\prime }+y x&=x \\ \end{align*}	✓	✓	✓	✓	3.704
20153	5280	\begin{align*} x^{2} \left (a +y\right )^{2} y^{\prime }&=\left (x^{2}+1\right ) \left (y^{2}+a^{2}\right ) \\ \end{align*}	✓	✓	✓	✓	3.705
20154	19869	\begin{align*} y^{\prime \prime }&=-a^{2} y \\ \end{align*}	✓	✓	✓	✓	3.705
20155	21991	\begin{align*} x -y^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.705
20156	24330	\begin{align*} 2 y+x \left (x^{2} \ln \left (y\right )-1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.705
20157	13872	\begin{align*} x^{4} y^{\prime \prime }+\left (a \,x^{2}+b x +c \right ) y&=0 \\ \end{align*}	✗	✓	✗	✗	3.706
20158	23970	\begin{align*} y^{\prime }-5 y&=3 x^{3}+4 x \\ \end{align*}	✓	✓	✓	✓	3.707
20159	7181	\begin{align*} y^{\prime \prime } x +y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	3.708
20160	14277	\begin{align*} x^{2}-t^{2} x^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.708
20161	21079	\begin{align*} x +y^{2}+y y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	3.708
20162	5864	\begin{align*} a \cos \left (x \right )^{2} y+\tan \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.711
20163	17216	\begin{align*} {\mathrm e}^{t} \sin \left (y\right )+\left (1+{\mathrm e}^{t} \cos \left (y\right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.711
20164	14240	\begin{align*} y^{\prime }&=\frac {y^{2}+2 t y}{t^{2}} \\ \end{align*}	✓	✓	✓	✓	3.712
20165	22451	\begin{align*} y^{\prime }-\frac {2 y}{x}&=x^{2} \sin \left (3 x \right ) \\ \end{align*}	✓	✓	✓	✓	3.714
20166	5058	\begin{align*} \left (x +y\right ) y^{\prime }+\tan \left (y\right )&=0 \\ \end{align*}	✓	✓	✓	✓	3.715
20167	7446	\begin{align*} x^{2} y+x^{4} \cos \left (x \right )-x^{3} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.715
20168	14251	\begin{align*} t x^{\prime }&=-x+t^{2} \\ \end{align*}	✓	✓	✓	✓	3.715
20169	7432	\begin{align*} \left (x^{2}+1\right ) y^{\prime }+y x -x&=0 \\ \end{align*}	✓	✓	✓	✓	3.716
20170	15340	\begin{align*} z-\left (-a^{2}+t^{2}\right ) z^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.716
20171	2852	\begin{align*} y^{\prime } x +y&=y^{2} \\ \end{align*}	✓	✓	✓	✓	3.717
20172	5683	\begin{align*} \left (x -y\right ) \sqrt {y^{\prime }}&=a \left (1+y^{\prime }\right ) \\ \end{align*}	✓	✓	✓	✓	3.717
20173	11440	\begin{align*} x^{2} \left (y^{\prime }+y^{2}\right )+a x y+b&=0 \\ \end{align*}	✓	✓	✓	✓	3.717
20174	24323	\begin{align*} x +2 y-1+\left (2 x +4 y-3\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.717
20175	20026	\begin{align*} x {y^{\prime }}^{2}-2 y y^{\prime }+a x&=0 \\ \end{align*}	✓	✓	✗	✓	3.719
20176	17147	\begin{align*} y^{\prime }-\frac {2 t y}{t^{2}+1}&=2 \\ \end{align*}	✓	✓	✓	✓	3.720
20177	20015	\begin{align*} y&=y^{\prime } x +\frac {m}{y^{\prime }} \\ \end{align*}	✓	✓	✓	✗	3.720
20178	4825	\begin{align*} y^{\prime } x&=\left (1+y^{2}\right ) \left (x^{2}+\arctan \left (y\right )\right ) \\ \end{align*}	✓	✓	✓	✗	3.721
20179	19991	\begin{align*} y^{\prime }+2 y x&=x^{2}+y^{2} \\ \end{align*}	✓	✓	✓	✓	3.721
20180	22544	\begin{align*} \tan \left (x \right ) \sin \left (y\right )+3 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.721
20181	22869	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-9\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	3.721
20182	19807	\begin{align*} x^{3}+4 y x +y^{2}+\left (2 x^{2}+2 y x +4 y^{3}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.722
20183	12432	\begin{align*} x^{2} y^{\prime \prime }-y^{\prime } x +y-3 x^{3}&=0 \\ \end{align*}	✓	✓	✓	✓	3.723
20184	22610	\begin{align*} y^{\prime }&=x y^{2}-2 y+4-4 x \\ \end{align*}	✓	✓	✓	✓	3.723
20185	25727	\begin{align*} y^{\prime \prime }+9 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (\pi \right ) &= 5 \\ \end{align*}	✓	✓	✓	✓	3.723
20186	14008	\begin{align*} y^{4}+2 y+\left (x y^{3}+2 y^{4}-4 x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.724
20187	14502	\begin{align*} 2 x \left (1+y\right )-\left (x^{2}+1\right ) y^{\prime }&=0 \\ y \left (1\right ) &= -5 \\ \end{align*}	✓	✓	✓	✓	3.724
20188	20858	\begin{align*} x^{2} y^{\prime \prime }+3 y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.724
20189	13947	\begin{align*} y^{\prime \prime }+\left (2 a \,{\mathrm e}^{\lambda x}-\lambda \right ) y^{\prime }+\left (a^{2} {\mathrm e}^{2 \lambda x}+c \,{\mathrm e}^{\mu x}\right ) y&=0 \\ \end{align*}	✗	✗	✓	✗	3.725
20190	5967	\begin{align*} x^{k} \left (a +b \,x^{k}\right ) y+x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	3.727
20191	11444	\begin{align*} x^{2} y^{\prime }+a y^{3}-a \,x^{2} y^{2}&=0 \\ \end{align*}	✗	✓	✓	✗	3.727
20192	11555	\begin{align*} 2 x^{2} y y^{\prime }-y^{2}-x^{2} {\mathrm e}^{x -\frac {1}{x}}&=0 \\ \end{align*}	✓	✓	✓	✓	3.727
20193	13392	\begin{align*} y^{\prime }&=a y^{2}+2 a b \tan \left (x \right ) y+b \left (a b -1\right ) \tan \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✓	3.727
20194	26160	\begin{align*} y^{\prime }-\tan \left (x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	3.727
20195	24211	\begin{align*} y \left (x^{4}-y^{2}\right )+x \left (x^{4}+y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.729
20196	1540	\begin{align*} y^{\prime } x +3 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.730
20197	19379	\begin{align*} \left ({\mathrm e}^{x}-3 y^{2} x^{2}\right ) y^{\prime }+{\mathrm e}^{x} y&=2 x y^{3} \\ \end{align*}	✓	✓	✓	✗	3.730
20198	9932	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	3.731
20199	14895	\begin{align*} m v^{\prime }&=-m g +k v^{2} \\ \end{align*}	✓	✓	✓	✓	3.733
20200	18492	\begin{align*} y^{\prime }&=x^{2} {\mathrm e}^{-3 y} \\ y \left (2\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.733