Problems 18301 to 18400

Table 2.369: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	time (sec)

18301	$y^{''} - 4 y = e^{2 x}$	[[_2nd_order, _with_linear_symmetries]]	✓	1.197

18302	$y^{''} - y = x^{2} e^{2 x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.193

18303	$y^{''} + 4 y^{'} + 4 y = 10 x^{3} e^{- 2 x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.247

18304	$y^{''} - 2 y^{'} + y = e^{x}$	[[_2nd_order, _with_linear_symmetries]]	✓	1.166

18305	$y^{''} - y = e^{- x}$	[[_2nd_order, _with_linear_symmetries]]	✓	1.151

18306	$y^{''} - 2 y^{'} - 3 y = 6 e^{5 x}$	[[_2nd_order, _with_linear_symmetries]]	✓	1.135

18307	$y^{''} - y^{'} + y = x^{3} - 3 x^{2} + 1$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	32.030

18308	$y^{'''} - 2 y^{'} + y = 2 x^{3} - 3 x^{2} + 4 x + 5$	[[_3rd_order, _linear, _nonhomogeneous]]	✓	0.117

18309	$4 y^{''} + y = x^{4}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	2.556

18310	$y^{(5)} - y^{'''} = x^{2}$	[[_high_order, _missing_y]]	✓	0.111

18311	$y^{(6)} - y = x^{10}$	[[_high_order, _linear, _nonhomogeneous]]	✓	0.167

18312	$y^{''} + y^{'} - y = - x^{4} + 3 x$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.621

18313	$y^{''} + y = x^{4}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.985

18314	$y^{'''} - y^{''} = 12 x - 2$	[[_3rd_order, _missing_y]]	✓	0.094

18315	$y^{'''} + y^{''} = 9 x^{2} - 2 x + 1$	[[_3rd_order, _missing_y]]	✓	0.103

18316	$y^{''} - 4 y^{'} + 3 y = x^{3} e^{2 x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.226

18317	$y^{''} - 7 y^{'} + 12 y = e^{2 x} (x^{3} - 5 x^{2})$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.302

18318	$y^{''} + 2 y^{'} + y = 2 x^{2} e^{- 2 x} + 3 e^{2 x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.358

18319	$y^{'''} - 8 y = 16 x^{2}$	[[_3rd_order, _with_linear_symmetries]]	✓	0.105

18320	$y^{''''} - y = - x^{3} + 1$	[[_high_order, _linear, _nonhomogeneous]]	✓	0.107

18321	$y^{'''} - \frac{y^{'}}{4} = x$	[[_3rd_order, _missing_y]]	✓	0.090

18322	$y^{''''} = \frac{1}{x^{3}}$	[[_high_order, _quadrature]]	✓	0.175

18323	$y^{'''} - y^{''} + y^{'} = x + 1$	[[_3rd_order, _missing_y]]	✓	0.100

18324	$y^{'''} + 2 y^{''} = x$	[[_3rd_order, _missing_y]]	✓	0.094

18325	$y^{'''} - 6 y^{''} + 12 y^{'} - 8 y = e^{2 x}$	[[_3rd_order, _with_linear_symmetries]]	✓	0.113

18326	$y^{'''} + 3 y^{''} + 3 y^{'} + y = 12 e^{- x}$	[[_3rd_order, _with_linear_symmetries]]	✓	0.120

18327	$y^{''} - 4 y^{'} + 4 y = e^{2 x} \sin (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.392

18328	$y^{'} = 2 x y$	[_separable]	✓	0.365

18329	$y^{'} + y = 1$	[_quadrature]	✓	0.343

18330	$x y^{'} = y$	[_separable]	✓	0.273

18331	$x^{2} y^{'} = y$	[_separable]	✗	0.061

18332	$y^{'} = 1 + y^{2}$ i.c.	[_quadrature]	✓	0.293

18333	$y^{'} = x - y$ i.c.	[[_linear, ‘class A‘]]	✓	0.467

18334	$(x^{2} + 1) y^{''} + 2 x y^{'} - 2 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.358

18335	$y^{''} + x y^{'} + y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	1.059

18336	$y^{''} + x y^{'} + y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.335

18337	$y^{''} + y^{'} - x y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.368

18338	$y^{''} + x y = 0$	[[_Emden, _Fowler]]	✓	0.236

18339	$(- x^{2} + 1) y^{''} - x y^{'} + n^{2} y = 0$	[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	0.476

18340	$y^{''} - 2 x y^{'} + 2 n y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.390

18341	$x^{3} (- 1 + x) y^{''} - 2 (- 1 + x) y^{'} + 3 x y = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	0.110

18342	$x^{2} {(x^{2} - 1)}^{2} y^{''} - x (1 - x) y^{'} + 2 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.634

18343	$x^{2} y^{''} + (2 - x) y^{'} = 0$	[[_2nd_order, _missing_y]]	✗	0.145

18344	$(3 x + 1) x y^{''} - (x + 1) y^{'} + 2 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	1.444

18345	$y^{''} + y \sin (x) = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.470

18346	$x y^{''} + y \sin (x) = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	1.018

18347	$x^{2} y^{''} + y \sin (x) = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	1.171

18348	$x^{3} y^{''} + y \sin (x) = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.542

18349	$x^{4} y^{''} + y \sin (x) = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	0.112

18350	$x^{3} y^{''} + (\cos (2 x) - 1) y^{'} + 2 x y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.724

18351	$4 x^{2} y^{''} + (2 x^{4} - 5 x) y^{'} + (3 x^{2} + 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.723

18352	$4 x y^{''} + 2 y^{'} + y = 0$	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	0.684

18353	$2 x y^{''} + (3 - x) y^{'} - y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.655

18354	$2 x y^{''} + (x + 1) y^{'} + 3 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.708

18355	$2 x^{2} y^{''} + x y^{'} - (x + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.720

18356	$x^{2} y^{''} + x y^{'} + x^{2} y = 0$	[_Lienard]	✓	0.434

18357	$y^{''} + \frac{y^{'}}{x^{2}} - \frac{y}{x^{3}} = 0$	[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✗	0.102

18358	$y^{''} + \frac{n y^{'}}{x^{2}} + \frac{q y}{x^{3}} = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	0.104

18359	$x^{2} y^{''} - 3 x y^{'} + (4 x + 4) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.666

18360	$4 x^{2} y^{''} - 8 x^{2} y^{'} + (4 x^{2} + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.717

18361	$x y^{''} + 2 y^{'} + x y = 0$	[_Lienard]	✓	0.588

18362	$x^{2} y^{''} - x^{2} y^{'} + (x^{2} - 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.741

18363	$x y^{''} - y^{'} + 4 x^{3} y = 0$	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	0.504

18364	$x^{2} y^{''} + x y^{'} + (x^{2} - 1) y = 0$	[_Bessel]	✓	1.211

18365	$x^{2} y^{''} + x y^{'} + (x^{2} - \frac{1}{4}) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.668

18366	$x (1 - x) y^{''} + (\frac{3}{2} - 2 x) y^{'} + 2 y = 0$	[_Jacobi]	✓	0.732

18367	$(2 x^{2} + 2 x) y^{''} + (1 + 5 x) y^{'} + y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.596

18368	$(x^{2} - 1) y^{''} + (5 x + 4) y^{'} + 4 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.768

18369	$(x^{2} - x - 6) y^{''} + (5 + 3 x) y^{'} + y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.748

18370	$x (1 - x) y^{''} + (1 - 3 x) y^{'} - y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.469

18371	$(- x^{2} + 1) y^{''} - 2 x y^{'} + n (n + 1) y = 0$	[_Gegenbauer]	✓	0.807

18372	$x^{2} y^{''} + x y^{'} + (- n^{2} + x^{2}) y = 0$	[_Bessel]	✗	0.180

18373	$y^{'} + y = 3 e^{2 x}$ i.c.	[[_linear, ‘class A‘]]	✓	0.381

18374	$y^{''} - 4 y^{'} + 4 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.204

18375	$y^{''} + 2 y^{'} + 2 y = 2$ i.c.	[[_2nd_order, _missing_x]]	✓	0.340

18376	$y^{''} + y^{'} = 3 x^{2}$ i.c.	[[_2nd_order, _missing_y]]	✓	0.321

18377	$y^{''} + 2 y^{'} + 5 y = 3 e^{- x} \sin (x)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.409

18378	$y^{''} - 2 a y^{'} + a^{2} y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.181

18379	$x y^{''} + (3 x - 1) y^{'} - (4 x + 9) y = 0$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.215

18380	$x y^{''} + (2 x + 3) y^{'} + (x + 3) y = 3 e^{- x}$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✗	0.361

18381	$y^{''} + x^{2} y = 0$ i.c.	[[_Emden, _Fowler]]	✗	1.633

18382	$y^{''} + a^{2} y = f (x)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.445

18383	$y^{''} + 5 y^{'} + 6 y = 4 e^{3 t}$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.414

18384	$y^{''} + y^{'} - 6 y = t$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.332

18385	$y^{''} - y^{'} = t^{2}$ i.c.	[[_2nd_order, _missing_y]]	✓	0.320

18386	$y^{''} + 3 y^{'} + 2 y = f (t)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.413

18387	$[\begin{matrix} x^{'} = x + 3 y \\ y^{'} = 3 x + y \end{matrix}]$ i.c.	system_of_ODEs	✓	0.559

18388	$[\begin{matrix} x^{'} = x + 2 y \\ y^{'} = 3 x + 2 y \end{matrix}]$	system_of_ODEs	✓	0.463

18389	$[\begin{matrix} x^{'} = x + 2 y + t - 1 \\ y^{'} = 3 x + 2 y - 5 t - 2 \end{matrix}]$	system_of_ODEs	✓	0.588

18390	$[\begin{matrix} x^{'} = x + y \\ y^{'} = y \end{matrix}]$	system_of_ODEs	✓	0.405

18391	$[\begin{matrix} x^{'} = x \\ y^{'} = y \end{matrix}]$	system_of_ODEs	✓	0.297

18392	$[\begin{matrix} x^{'} = - 3 x + 4 y \\ y^{'} = - 2 x + 3 y \end{matrix}]$	system_of_ODEs	✓	0.442

18393	$[\begin{matrix} x^{'} = 4 x - 2 y \\ y^{'} = 5 x + 2 y \end{matrix}]$	system_of_ODEs	✓	0.581

18394	$[\begin{matrix} x^{'} = 5 x + 4 y \\ y^{'} = y - x \end{matrix}]$	system_of_ODEs	✓	0.457

18395	$[\begin{matrix} x^{'} = 4 x - 3 y \\ y^{'} = 8 x - 6 y \end{matrix}]$	system_of_ODEs	✓	0.461

18396	$[\begin{matrix} x^{'} = 2 x \\ y^{'} = 3 y \end{matrix}]$	system_of_ODEs	✓	0.407

18397	$[\begin{matrix} x^{'} = - 4 x - y \\ y^{'} = x - 2 y \end{matrix}]$	system_of_ODEs	✓	0.431

18398	$[\begin{matrix} x^{'} = 7 x + 6 y \\ y^{'} = 2 x + 6 y \end{matrix}]$	system_of_ODEs	✓	0.485

18399	$[\begin{matrix} x^{'} = x - 2 y \\ y^{'} = 4 x + 5 y \end{matrix}]$	system_of_ODEs	✓	0.571

18400	$[\begin{matrix} x^{'} = x + y - 5 t + 2 \\ y^{'} = 4 x - 2 y - 8 t - 8 \end{matrix}]$	system_of_ODEs	✓	0.540

2.2.184 Problems 18301 to 18400