Problems 1001 to 1100

2.2.11 Problems 1001 to 1100

Table 2.35: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	Maple	Mma	Sympy	time(sec)

1001	\begin{align} x_{1}^{\prime }&=47 x_{1}-8 x_{2}+5 x_{3}-5 x_{4} \\ x_{2}^{\prime }&=-10 x_{1}+32 x_{2}+18 x_{3}-2 x_{4} \\ x_{3}^{\prime }&=139 x_{1}-40 x_{2}-167 x_{3}-121 x_{4} \\ x_{4}^{\prime }&=-232 x_{1}+64 x_{2}+360 x_{3}+248 x_{4} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	2.577

1002	\begin{align} x_{1}^{\prime }&=139 x_{1}-14 x_{2}-52 x_{3}-14 x_{4}+28 x_{5} \\ x_{2}^{\prime }&=-22 x_{1}+5 x_{2}+7 x_{3}+8 x_{4}-7 x_{5} \\ x_{3}^{\prime }&=370 x_{1}-38 x_{2}-139 x_{3}-38 x_{4}+76 x_{5} \\ x_{4}^{\prime }&=152 x_{1}-16 x_{2}-59 x_{3}-13 x_{4}+35 x_{5} \\ x_{5}^{\prime }&=95 x_{1}-10 x_{2}-38 x_{3}-7 x_{4}+23 x_{5} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	4.085

1003	\begin{align} x_{1}^{\prime }&=9 x_{1}+13 x_{2}-13 x_{6} \\ x_{2}^{\prime }&=-14 x_{1}+19 x_{2}-10 x_{3}-20 x_{4}+10 x_{5}+4 x_{6} \\ x_{3}^{\prime }&=-30 x_{1}+12 x_{2}-7 x_{3}-30 x_{4}+12 x_{5}+18 x_{6} \\ x_{4}^{\prime }&=-12 x_{1}+10 x_{2}-10 x_{3}-9 x_{4}+10 x_{5}+2 x_{6} \\ x_{5}^{\prime }&=6 x_{1}+9 x_{2}+6 x_{4}+5 x_{5}-15 x_{6} \\ x_{6}^{\prime }&=-14 x_{1}+23 x_{2}-10 x_{3}-20 x_{4}+10 x_{5} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	4.377

1004	\begin{align} x_{1}^{\prime }&=9 x_{1}+4 x_{2} \\ x_{2}^{\prime }&=-6 x_{1}-x_{2} \\ x_{3}^{\prime }&=6 x_{1}+4 x_{2}+3 x_{3} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.591

1005	\begin{align} x_{1}^{\prime }&=x_{1}-3 x_{2} \\ x_{2}^{\prime }&=3 x_{1}+7 x_{2} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.325

1006	\begin{align} x_{1}^{\prime }&=x_{2}+2 x_{3} \\ x_{2}^{\prime }&=-5 x_{1}-3 x_{2}-7 x_{3} \\ x_{3}^{\prime }&=x_{1} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.582

1007	\begin{align} x_{1}^{\prime }&=x_{3} \\ x_{2}^{\prime }&=x_{4} \\ x_{3}^{\prime }&=-2 x_{1}+2 x_{2}-3 x_{3}+x_{4} \\ x_{4}^{\prime }&=2 x_{1}-2 x_{2}+x_{3}-3 x_{4} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.926

1008	\begin{align} x_{1}^{\prime }&=-2 x_{1}+x_{2} \\ x_{2}^{\prime }&=-x_{1}-4 x_{2} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.325

1009	\begin{align} x_{1}^{\prime }&=3 x_{1}-x_{2} \\ x_{2}^{\prime }&=x_{1}+x_{2} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.308

1010	\begin{align} x_{1}^{\prime }&=x_{1}-2 x_{2} \\ x_{2}^{\prime }&=2 x_{1}+5 x_{2} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.327

1011	\begin{align} x_{1}^{\prime }&=3 x_{1}-x_{2} \\ x_{2}^{\prime }&=x_{1}+5 x_{2} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.318

1012	\begin{align} x_{1}^{\prime }&=7 x_{1}+x_{2} \\ x_{2}^{\prime }&=-4 x_{1}+3 x_{2} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.342

1013	\begin{align} x_{1}^{\prime }&=x_{1}-4 x_{2} \\ x_{2}^{\prime }&=4 x_{1}+9 x_{2} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.326

1014	\begin{align} x_{1}^{\prime }&=2 x_{1} \\ x_{2}^{\prime }&=-7 x_{1}+9 x_{2}+7 x_{3} \\ x_{3}^{\prime }&=2 x_{3} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.500

1015	\begin{align} x_{1}^{\prime }&=25 x_{1}+12 x_{2} \\ x_{2}^{\prime }&=-18 x_{1}-5 x_{2} \\ x_{3}^{\prime }&=6 x_{1}+6 x_{2}+13 x_{3} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.605

1016	\begin{align} x_{1}^{\prime }&=-19 x_{1}+12 x_{2}+84 x_{3} \\ x_{2}^{\prime }&=5 x_{2} \\ x_{3}^{\prime }&=-8 x_{1}+4 x_{2}+33 x_{3} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.605

1017	\begin{align} x_{1}^{\prime }&=-13 x_{1}+40 x_{2}-48 x_{3} \\ x_{2}^{\prime }&=-8 x_{1}+23 x_{2}-24 x_{3} \\ x_{3}^{\prime }&=3 x_{3} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.605

1018	\begin{align} x_{1}^{\prime }&=-3 x_{1}-4 x_{3} \\ x_{2}^{\prime }&=-x_{1}-x_{2}-x_{3} \\ x_{3}^{\prime }&=x_{1}+x_{3} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.530

1019	\begin{align} x_{1}^{\prime }&=-x_{1}+x_{3} \\ x_{2}^{\prime }&=-x_{2}+x_{3} \\ x_{3}^{\prime }&=x_{1}-x_{2}-x_{3} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.500

1020	\begin{align} x_{1}^{\prime }&=-x_{1}+x_{3} \\ x_{2}^{\prime }&=x_{2}-4 x_{3} \\ x_{3}^{\prime }&=x_{2}-3 x_{3} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.497

1021	\begin{align} x_{1}^{\prime }&=x_{3} \\ x_{2}^{\prime }&=-5 x_{1}-x_{2}-5 x_{3} \\ x_{3}^{\prime }&=4 x_{1}+x_{2}-2 x_{3} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.566

1022	\begin{align} x_{1}^{\prime }&=-2 x_{1}-9 x_{2} \\ x_{2}^{\prime }&=x_{1}+4 x_{2} \\ x_{3}^{\prime }&=x_{1}+3 x_{2}+x_{3} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.584

1023	\begin{align} x_{1}^{\prime }&=x_{1} \\ x_{2}^{\prime }&=-2 x_{1}-2 x_{2}-3 x_{3} \\ x_{3}^{\prime }&=2 x_{1}+3 x_{2}+4 x_{3} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.585

1024	\begin{align} x_{1}^{\prime }&=x_{1} \\ x_{2}^{\prime }&=18 x_{1}+7 x_{2}+4 x_{3} \\ x_{3}^{\prime }&=-27 x_{1}-9 x_{2}-5 x_{3} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.565

1025	\begin{align} x_{1}^{\prime }&=x_{1} \\ x_{2}^{\prime }&=x_{1}+3 x_{2}+x_{3} \\ x_{3}^{\prime }&=-2 x_{1}-4 x_{2}-x_{3} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.533

1026	\begin{align} x_{1}^{\prime }&=x_{1}-4 x_{2}-2 x_{4} \\ x_{2}^{\prime }&=x_{2} \\ x_{3}^{\prime }&=6 x_{1}-12 x_{2}-x_{3}-6 x_{4} \\ x_{4}^{\prime }&=-4 x_{2}-x_{4} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.763

1027	\begin{align} x_{1}^{\prime }&=2 x_{1}+x_{2}+x_{4} \\ x_{2}^{\prime }&=2 x_{2}+x_{3} \\ x_{3}^{\prime }&=2 x_{3}+x_{4} \\ x_{4}^{\prime }&=2 x_{4} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.733

1028	\begin{align} x_{1}^{\prime }&=-x_{1}-4 x_{2} \\ x_{2}^{\prime }&=x_{1}+3 x_{2} \\ x_{3}^{\prime }&=x_{1}+2 x_{2}+x_{3} \\ x_{4}^{\prime }&=x_{2}+x_{4} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.614

1029	\begin{align} x_{1}^{\prime }&=x_{1}+3 x_{2}+7 x_{3} \\ x_{2}^{\prime }&=-x_{2}-4 x_{3} \\ x_{3}^{\prime }&=x_{2}+3 x_{3} \\ x_{4}^{\prime }&=-6 x_{2}-14 x_{3}+x_{4} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.667

1030	\begin{align} x_{1}^{\prime }&=39 x_{1}+8 x_{2}-16 x_{3} \\ x_{2}^{\prime }&=-36 x_{1}-5 x_{2}+16 x_{3} \\ x_{3}^{\prime }&=72 x_{1}+16 x_{2}-29 x_{3} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.651

1031	\begin{align} x_{1}^{\prime }&=28 x_{1}+50 x_{2}+100 x_{3} \\ x_{2}^{\prime }&=15 x_{1}+33 x_{2}+60 x_{3} \\ x_{3}^{\prime }&=-15 x_{1}-30 x_{2}-57 x_{3} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.654

1032	\begin{align} x_{1}^{\prime }&=-2 x_{1}+17 x_{2}+4 x_{3} \\ x_{2}^{\prime }&=-x_{1}+6 x_{2}+x_{3} \\ x_{3}^{\prime }&=x_{2}+2 x_{3} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.554

1033	\begin{align} x_{1}^{\prime }&=5 x_{1}-x_{2}+x_{3} \\ x_{2}^{\prime }&=x_{1}+3 x_{2} \\ x_{3}^{\prime }&=-3 x_{1}+2 x_{2}+x_{3} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.551

1034	\begin{align} x_{1}^{\prime }&=-3 x_{1}+5 x_{2}-5 x_{3} \\ x_{2}^{\prime }&=3 x_{1}-x_{2}+3 x_{3} \\ x_{3}^{\prime }&=8 x_{1}-8 x_{2}+10 x_{3} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.579

1035	\begin{align} x_{1}^{\prime }&=-15 x_{1}-7 x_{2}+4 x_{3} \\ x_{2}^{\prime }&=34 x_{1}+16 x_{2}-11 x_{3} \\ x_{3}^{\prime }&=17 x_{1}+7 x_{2}+5 x_{3} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.636

1036	\begin{align} x_{1}^{\prime }&=-x_{1}+x_{2}+x_{3}-2 x_{4} \\ x_{2}^{\prime }&=7 x_{1}-4 x_{2}-6 x_{3}+11 x_{4} \\ x_{3}^{\prime }&=5 x_{1}-x_{2}+x_{3}+3 x_{4} \\ x_{4}^{\prime }&=6 x_{1}-2 x_{2}-2 x_{3}+6 x_{4} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	1.149

1037	\begin{align} x_{1}^{\prime }&=2 x_{1}+x_{2}-2 x_{3}+x_{4} \\ x_{2}^{\prime }&=3 x_{2}-5 x_{3}+3 x_{4} \\ x_{3}^{\prime }&=-13 x_{2}+22 x_{3}-12 x_{4} \\ x_{4}^{\prime }&=-27 x_{2}+45 x_{3}-25 x_{4} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	1.092

1038	\begin{align} x_{1}^{\prime }&=35 x_{1}-12 x_{2}+4 x_{3}+30 x_{4} \\ x_{2}^{\prime }&=22 x_{1}-8 x_{2}+3 x_{3}+19 x_{4} \\ x_{3}^{\prime }&=-10 x_{1}+3 x_{2}-9 x_{4} \\ x_{4}^{\prime }&=-27 x_{1}+9 x_{2}-3 x_{3}-23 x_{4} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.896

1039	\begin{align} x_{1}^{\prime }&=11 x_{1}-x_{2}+26 x_{3}+6 x_{4}-3 x_{5} \\ x_{2}^{\prime }&=3 x_{2} \\ x_{3}^{\prime }&=-9 x_{1}-24 x_{3}-6 x_{4}+3 x_{5} \\ x_{4}^{\prime }&=3 x_{1}+9 x_{3}+5 x_{4}-x_{5} \\ x_{5}^{\prime }&=-48 x_{1}-3 x_{2}-138 x_{3}-30 x_{4}+18 x_{5} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	1.386

1040	\begin{align} x_{1}^{\prime }&=3 x_{1}-4 x_{2}+x_{3} \\ x_{2}^{\prime }&=4 x_{1}+3 x_{2}+x_{4} \\ x_{3}^{\prime }&=3 x_{3}-4 x_{4} \\ x_{4}^{\prime }&=4 x_{3}+3 x_{4} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.783

1041	\begin{align} x_{1}^{\prime }&=2 x_{1}-8 x_{3}-3 x_{4} \\ x_{2}^{\prime }&=-18 x_{1}-x_{2} \\ x_{3}^{\prime }&=-9 x_{1}-3 x_{2}-25 x_{3}-9 x_{4} \\ x_{4}^{\prime }&=33 x_{1}+10 x_{2}+90 x_{3}+32 x_{4} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	1.417

1042	\begin{align} y^{\prime }&=y \\ \end{align} Series expansion around \(x=0\).	[_quadrature]	✓	✓	✓	✓	0.207

1043	\begin{align} y^{\prime }&=4 y \\ \end{align} Series expansion around \(x=0\).	[_quadrature]	✓	✓	✓	✓	0.234

1044	\begin{align} 2 y^{\prime }+3 y&=0 \\ \end{align} Series expansion around \(x=0\).	[_quadrature]	✓	✓	✓	✓	0.229

1045	\begin{align} y^{\prime }+2 y x&=0 \\ \end{align} Series expansion around \(x=0\).	[_separable]	✓	✓	✓	✓	0.236

1046	\begin{align} y^{\prime }&=x^{2} y \\ \end{align} Series expansion around \(x=0\).	[_separable]	✓	✓	✓	✓	0.207

1047	\begin{align} \left (x -2\right ) y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	[_separable]	✓	✓	✓	✓	0.243

1048	\begin{align} \left (2 x -1\right ) y^{\prime }+2 y&=0 \\ \end{align} Series expansion around \(x=0\).	[_separable]	✓	✓	✓	✓	0.244

1049	\begin{align} 2 \left (x +1\right ) y^{\prime }&=y \\ \end{align} Series expansion around \(x=0\).	[_separable]	✓	✓	✓	✓	0.247

1050	\begin{align} \left (x -1\right ) y^{\prime }+2 y&=0 \\ \end{align} Series expansion around \(x=0\).	[_separable]	✓	✓	✓	✓	0.253

1051	\begin{align} 2 \left (x -1\right ) y^{\prime }&=3 y \\ \end{align} Series expansion around \(x=0\).	[_separable]	✓	✓	✓	✓	0.239

1052	\begin{align} y^{\prime \prime }&=y \\ \end{align} Series expansion around \(x=0\).	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.236

1053	\begin{align} y^{\prime \prime }&=4 y \\ \end{align} Series expansion around \(x=0\).	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.243

1054	\begin{align} y^{\prime \prime }+9 y&=0 \\ \end{align} Series expansion around \(x=0\).	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.260

1055	\begin{align} y^{\prime \prime }+y&=x \\ \end{align} Series expansion around \(x=0\).	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗	0.271

1056	\begin{align} y^{\prime } x +y&=0 \\ \end{align} Series expansion around \(x=0\).	[_separable]	✓	✓	✓	✗	0.144

1057	\begin{align} 2 y^{\prime } x&=y \\ \end{align} Series expansion around \(x=0\).	[_separable]	✓	✓	✓	✗	0.145

1058	\begin{align} x^{2} y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	[_separable]	✗	✗	✓	✗	0.047

1059	\begin{align} x^{3} y^{\prime }&=2 y \\ \end{align} Series expansion around \(x=0\).	[_separable]	✗	✗	✓	✗	0.056

1060	\begin{align} y^{\prime \prime }+4 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align} Series expansion around \(x=0\).	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.266

1061	\begin{align} y^{\prime \prime }-4 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align} Series expansion around \(x=0\).	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.248

1062	\begin{align} y^{\prime \prime }-2 y^{\prime }+y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align} Series expansion around \(x=0\).	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.294

1063	\begin{align} y^{\prime \prime }+y^{\prime }-2 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -2 \\ \end{align} Series expansion around \(x=0\).	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.292

1064	\begin{align} x^{2} y^{\prime \prime }+x^{2} y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗	0.617

1065	\begin{align} y^{\prime }&=1+y^{2} \\ y \left (0\right ) &= 0 \\ \end{align}	[_quadrature]	✓	✓	✓	✓	3.403

1066	\begin{align} \left (x^{2}-1\right ) y^{\prime \prime }+4 y^{\prime } x +2 y&=0 \\ \end{align} Series expansion around \(x=0\).	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	✓	✓	✓	0.324

1067	\begin{align} \left (x^{2}+2\right ) y^{\prime \prime }+4 y^{\prime } x +2 y&=0 \\ \end{align} Series expansion around \(x=0\).	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	✓	✓	✓	0.330

1068	\begin{align} y^{\prime \prime }+y^{\prime } x +y&=0 \\ \end{align} Series expansion around \(x=0\).	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	✓	✓	✓	0.290

1069	\begin{align} \left (x^{2}+1\right ) y^{\prime \prime }+6 y^{\prime } x +4 y&=0 \\ \end{align} Series expansion around \(x=0\).	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	✓	✓	✓	0.352

1070	\begin{align} \left (x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x&=0 \\ \end{align} Series expansion around \(x=0\).	[[_2nd_order, _missing_y]]	✓	✓	✓	✓	0.282

1071	\begin{align} \left (x^{2}-1\right ) y^{\prime \prime }-6 y^{\prime } x +12 y&=0 \\ \end{align} Series expansion around \(x=0\).	[_Gegenbauer]	✓	✓	✓	✓	0.270

1072	\begin{align} \left (x^{2}+3\right ) y^{\prime \prime }-7 y^{\prime } x +16 y&=0 \\ \end{align} Series expansion around \(x=0\).	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓	0.337

1073	\begin{align} \left (-x^{2}+2\right ) y^{\prime \prime }-y^{\prime } x +16 y&=0 \\ \end{align} Series expansion around \(x=0\).	[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	✓	✓	✓	0.335

1074	\begin{align} \left (x^{2}-1\right ) y^{\prime \prime }+8 y^{\prime } x +12 y&=0 \\ \end{align} Series expansion around \(x=0\).	[_Gegenbauer]	✓	✓	✓	✓	0.356

1075	\begin{align} 3 y^{\prime \prime }+y^{\prime } x -4 y&=0 \\ \end{align} Series expansion around \(x=0\).	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓	0.293

1076	\begin{align} 5 y^{\prime \prime }-2 y^{\prime } x +10 y&=0 \\ \end{align} Series expansion around \(x=0\).	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓	0.301

1077	\begin{align} y^{\prime \prime }-x^{2} y^{\prime }-3 y x&=0 \\ \end{align} Series expansion around \(x=0\).	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓	0.291

1078	\begin{align} y^{\prime \prime }+x^{2} y^{\prime }+2 y x&=0 \\ \end{align} Series expansion around \(x=0\).	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	✓	✓	✓	0.301

1079	\begin{align} y^{\prime \prime }+y x&=0 \\ \end{align} Series expansion around \(x=0\).	[[_Emden, _Fowler]]	✓	✓	✓	✓	0.219

1080	\begin{align} y^{\prime \prime }+x^{2} y&=0 \\ \end{align} Series expansion around \(x=0\).	[[_Emden, _Fowler]]	✓	✓	✓	✓	0.218

1081	\begin{align} \left (x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x -2 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align} Series expansion around \(x=0\).	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓	0.293

1082	\begin{align} y^{\prime \prime }+y^{\prime } x -2 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align} Series expansion around \(x=0\).	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓	0.263

1083	\begin{align} y^{\prime \prime }+\left (x -1\right ) y^{\prime }+y&=0 \\ y \left (1\right ) &= 2 \\ y^{\prime }\left (1\right ) &= 0 \\ \end{align} Series expansion around \(x=1\).	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	✓	✓	✓	0.320

1084	\begin{align} \left (-x^{2}+2 x \right ) y^{\prime \prime }-6 \left (x -1\right ) y^{\prime }-4 y&=0 \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= 1 \\ \end{align} Series expansion around \(x=1\).	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	✓	✓	✓	0.404

1085	\begin{align} \left (x^{2}-6 x +10\right ) y^{\prime \prime }-4 \left (x -3\right ) y^{\prime }+6 y&=0 \\ y \left (3\right ) &= 2 \\ y^{\prime }\left (3\right ) &= 0 \\ \end{align} Series expansion around \(x=3\).	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓	0.312

1086	\begin{align} \left (4 x^{2}+16 x +17\right ) y^{\prime \prime }&=8 y \\ y \left (-2\right ) &= 1 \\ y^{\prime }\left (-2\right ) &= 0 \\ \end{align} Series expansion around \(x=-2\).	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	✓	✓	✓	0.352

1087	\begin{align} \left (x^{2}+6 x \right ) y^{\prime \prime }+\left (3 x +9\right ) y^{\prime }-3 y&=0 \\ y \left (-3\right ) &= 1 \\ y^{\prime }\left (-3\right ) &= 0 \\ \end{align} Series expansion around \(x=-3\).	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓	0.355

1088	\begin{align} y^{\prime \prime }+\left (x +1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓	0.300

1089	\begin{align} \left (x^{2}-1\right ) y^{\prime \prime }+2 y^{\prime } x +2 y x&=0 \\ \end{align} Series expansion around \(x=0\).	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓	0.434

1090	\begin{align} y^{\prime \prime }+x^{2} y^{\prime }+x^{2} y&=0 \\ \end{align} Series expansion around \(x=0\).	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓	0.303

1091	\begin{align} \left (x^{3}+1\right ) y^{\prime \prime }+x^{4} y&=0 \\ \end{align} Series expansion around \(x=0\).	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓	0.309

1092	\begin{align} y^{\prime \prime }+y^{\prime } x +\left (2 x^{2}+1\right ) y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align} Series expansion around \(x=0\).	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓	0.350

1093	\begin{align} y^{\prime \prime }+{\mathrm e}^{-x} y&=0 \\ \end{align} Series expansion around \(x=0\).	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓	0.458

1094	\begin{align} \cos \left (x \right ) y^{\prime \prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓	0.529

1095	\begin{align} y^{\prime \prime } x +\sin \left (x \right ) y^{\prime }+y x&=0 \\ \end{align} Series expansion around \(x=0\).	[_Lienard]	✓	✓	✓	✓	1.294

1096	\begin{align} y^{\prime \prime }-2 y^{\prime } x +2 \alpha y&=0 \\ \end{align} Series expansion around \(x=0\).	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓	0.342

1097	\begin{align} y^{\prime \prime }&=y x \\ \end{align} Series expansion around \(x=0\).	[[_Emden, _Fowler]]	✓	✓	✓	✓	0.220

1098	\begin{align} 3 y+y^{\prime }&={\mathrm e}^{-2 t}+t \\ \end{align}	[[_linear, ‘class A‘]]	✓	✓	✓	✓	1.845

1099	\begin{align} -2 y+y^{\prime }&={\mathrm e}^{2 t} t^{2} \\ \end{align}	[[_linear, ‘class A‘]]	✓	✓	✓	✓	2.111

1100	\begin{align} y+y^{\prime }&=1+t \,{\mathrm e}^{-t} \\ \end{align}	[[_linear, ‘class A‘]]	✓	✓	✓	✓	2.316

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