Problems 17401 to 17500

Table 2.351: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	time (sec)

17401	$[\begin{matrix} x^{'} = x + y - 3 \\ y^{'} = - x + y + 1 \end{matrix}]$	system_of_ODEs	✓	0.647

17402	$[\begin{matrix} x^{'} = - 5 x + 4 y - 35 \\ y^{'} = - 2 x + y - 11 \end{matrix}]$	system_of_ODEs	✓	0.774

17403	$[\begin{matrix} x^{'} = 3 x - 2 y \\ y^{'} = 2 x - 2 y \end{matrix}]$	system_of_ODEs	✓	0.355

17404	$[\begin{matrix} x^{'} = x - 2 y \\ y^{'} = 3 x - 4 y \end{matrix}]$	system_of_ODEs	✓	0.323

17405	$[\begin{matrix} x^{'} = 2 x - y \\ y^{'} = 3 x - 2 y \end{matrix}]$	system_of_ODEs	✓	0.402

17406	$[\begin{matrix} x^{'} = x + y \\ y^{'} = 4 x - 2 y \end{matrix}]$	system_of_ODEs	✓	0.387

17407	$[\begin{matrix} x^{'} = 4 x - 3 y \\ y^{'} = 8 x - 6 y \end{matrix}]$	system_of_ODEs	✓	0.378

17408	$[\begin{matrix} x^{'} = - 2 x + y \\ y^{'} = x - 2 y \end{matrix}]$	system_of_ODEs	✓	0.309

17409	$[\begin{matrix} x^{'} = \frac{5 x}{4} + \frac{3 y}{4} \\ y^{'} = \frac{3 x}{4} + \frac{5 y}{4} \end{matrix}]$	system_of_ODEs	✓	0.335

17410	$[\begin{matrix} x^{'} = - \frac{3 x}{4} - \frac{7 y}{4} \\ y^{'} = \frac{x}{4} + \frac{5 y}{4} \end{matrix}]$	system_of_ODEs	✓	0.352

17411	$[\begin{matrix} x^{'} = - \frac{x}{4} - \frac{3 y}{4} \\ y^{'} = \frac{x}{2} + y \end{matrix}]$	system_of_ODEs	✓	0.333

17412	$[\begin{matrix} x^{'} = 5 x - y \\ y^{'} = 3 x + y \end{matrix}]$	system_of_ODEs	✓	0.334

17413	$[\begin{matrix} x^{'} = - 2 x + y \\ y^{'} = - 5 x + 4 y \end{matrix}]$	system_of_ODEs	✓	0.345

17414	$[\begin{matrix} x^{'} = 3 x + 6 y \\ y^{'} = - x - 2 y \end{matrix}]$	system_of_ODEs	✓	0.321

17415	$[\begin{matrix} x^{'} = x - 2 y \\ y^{'} = 3 x - 4 y \end{matrix}]$ i.c.	system_of_ODEs	✓	0.480

17416	$[\begin{matrix} x^{'} = 2 x - y \\ y^{'} = 3 x - 2 y \end{matrix}]$ i.c.	system_of_ODEs	✓	0.495

17417	$[\begin{matrix} x^{'} = 5 x - y \\ y^{'} = 3 x + y \end{matrix}]$ i.c.	system_of_ODEs	✓	0.539

17418	$[\begin{matrix} x^{'} = - 2 x + y \\ y^{'} = - 5 x + 4 y \end{matrix}]$ i.c.	system_of_ODEs	✓	0.513

17419	$[\begin{matrix} x^{'} = 3 x - 2 y \\ y^{'} = 4 x - y \end{matrix}]$	system_of_ODEs	✓	0.554

17420	$[\begin{matrix} x^{'} = - x - 4 y \\ y^{'} = x - y \end{matrix}]$	system_of_ODEs	✓	0.364

17421	$[\begin{matrix} x^{'} = 2 x - 5 y \\ y^{'} = x - 2 y \end{matrix}]$	system_of_ODEs	✓	0.447

17422	$[\begin{matrix} x^{'} = 2 x - \frac{5 y}{2} \\ y^{'} = \frac{9 x}{5} - y \end{matrix}]$	system_of_ODEs	✓	0.508

17423	$[\begin{matrix} x^{'} = x - y \\ y^{'} = 5 x - 3 y \end{matrix}]$	system_of_ODEs	✓	0.552

17424	$[\begin{matrix} x^{'} = x + 2 y \\ y^{'} = - 5 x - y \end{matrix}]$	system_of_ODEs	✓	0.459

17425	$[\begin{matrix} x^{'} = - x - 4 y \\ y^{'} = x - y \end{matrix}]$ i.c.	system_of_ODEs	✓	0.489

17426	$[\begin{matrix} x^{'} = 2 x - 5 y \\ y^{'} = x - 2 y \end{matrix}]$ i.c.	system_of_ODEs	✓	0.496

17427	$[\begin{matrix} x^{'} = x - 5 y \\ y^{'} = x - 3 y \end{matrix}]$ i.c.	system_of_ODEs	✓	0.526

17428	$[\begin{matrix} x^{'} = - 3 x + 2 y \\ y^{'} = - x - y \end{matrix}]$ i.c.	system_of_ODEs	✓	0.622

17429	$[\begin{matrix} x^{'} = \frac{3 x}{4} - 2 y \\ y^{'} = x - \frac{5 y}{4} \end{matrix}]$	system_of_ODEs	✓	0.495

17430	$[\begin{matrix} x^{'} = - \frac{4 x}{5} + 2 y \\ y^{'} = - x + \frac{6 y}{5} \end{matrix}]$	system_of_ODEs	✓	0.467

17431	$[\begin{matrix} x^{'} = a x + y \\ y^{'} = - x + a y \end{matrix}]$	system_of_ODEs	✓	0.409

17432	$[\begin{matrix} x^{'} = - 5 y \\ y^{'} = x + a y \end{matrix}]$	system_of_ODEs	✓	0.675

17433	$[\begin{matrix} x^{'} = 2 x - 5 y \\ y^{'} = a x - 2 y \end{matrix}]$	system_of_ODEs	✓	0.553

17434	$[\begin{matrix} x^{'} = \frac{5 x}{4} + \frac{3 y}{4} \\ y^{'} = a x + \frac{5 y}{4} \end{matrix}]$	system_of_ODEs	✓	0.515

17435	$[\begin{matrix} x^{'} = - x + a y \\ y^{'} = - x - y \end{matrix}]$	system_of_ODEs	✓	0.482

17436	$[\begin{matrix} x^{'} = 3 x + a y \\ y^{'} = - 6 x - 4 y \end{matrix}]$	system_of_ODEs	✓	0.559

17437	$[\begin{matrix} x^{'} = a x + 10 y \\ y^{'} = - x - 4 y \end{matrix}]$	system_of_ODEs	✓	0.701

17438	$[\begin{matrix} x^{'} = 4 x + a y \\ y^{'} = 8 x - 6 y \end{matrix}]$	system_of_ODEs	✓	0.559

17439	$[\begin{matrix} i^{'} = \frac{i}{2} - \frac{v}{8} \\ v^{'} = 2 i - \frac{v}{2} \end{matrix}]$	system_of_ODEs	✓	0.345

17440	$[\begin{matrix} x^{'} = 3 x - 4 y \\ y^{'} = x - y \end{matrix}]$	system_of_ODEs	✓	0.327

17441	$[\begin{matrix} x^{'} = \frac{5 x}{4} + \frac{3 y}{4} \\ y^{'} = - \frac{3 x}{4} - \frac{y}{4} \end{matrix}]$	system_of_ODEs	✓	0.374

17442	$[\begin{matrix} x^{'} = - \frac{3 x}{2} + y \\ y^{'} = - \frac{x}{4} - \frac{y}{2} \end{matrix}]$	system_of_ODEs	✓	0.341

17443	$[\begin{matrix} x^{'} = - 3 x + \frac{5 y}{2} \\ y^{'} = - \frac{5 x}{2} + 2 y \end{matrix}]$	system_of_ODEs	✓	0.309

17444	$[\begin{matrix} x^{'} = - x - \frac{y}{2} \\ y^{'} = 2 x - 3 y \end{matrix}]$	system_of_ODEs	✓	0.311

17445	$[\begin{matrix} x^{'} = 2 x + \frac{y}{2} \\ y^{'} = - \frac{x}{2} + y \end{matrix}]$	system_of_ODEs	✓	0.394

17446	$[\begin{matrix} x^{'} = x - 4 y \\ y^{'} = 4 x - 7 y \end{matrix}]$ i.c.	system_of_ODEs	✓	0.685

17447	$[\begin{matrix} x^{'} = - \frac{5 x}{2} + \frac{3 y}{2} \\ y^{'} = - \frac{3 x}{2} + \frac{y}{2} \end{matrix}]$ i.c.	system_of_ODEs	✓	0.477

17448	$[\begin{matrix} x^{'} = 2 x + \frac{3 y}{2} \\ y^{'} = - \frac{3 x}{2} - y \end{matrix}]$ i.c.	system_of_ODEs	✓	0.479

17449	$[\begin{matrix} x^{'} = \frac{5 x}{4} + \frac{3 y}{4} \\ y^{'} = - \frac{3 x}{4} - \frac{y}{4} \end{matrix}]$ i.c.	system_of_ODEs	✓	0.501

17450	$[\begin{matrix} x^{'} = - 3 x + \frac{5 y}{2} \\ y^{'} = - \frac{5 x}{2} + 2 y \end{matrix}]$ i.c.	system_of_ODEs	✓	0.486

17451	$[\begin{matrix} x^{'} = 2 x + \frac{y}{2} \\ y^{'} = - \frac{x}{2} + y \end{matrix}]$ i.c.	system_of_ODEs	✓	0.519

17452	$[\begin{matrix} x^{'} = - x \\ y^{'} = - 2 y \end{matrix}]$ i.c.	system_of_ODEs	✓	0.444

17453	$[\begin{matrix} x^{'} = - x \\ y^{'} = 2 y \end{matrix}]$ i.c.	system_of_ODEs	✓	0.439

17454	$[\begin{matrix} x^{'} = - x \\ y^{'} = - 2 y \end{matrix}]$ i.c.	system_of_ODEs	✓	0.480

17455	$[\begin{matrix} x^{'} = 2 y \\ y^{'} = 8 x \end{matrix}]$ i.c.	system_of_ODEs	✓	0.531

17456	$[\begin{matrix} x^{'} = 2 y \\ y^{'} = 8 x \end{matrix}]$ i.c.	system_of_ODEs	✓	0.532

17457	$[\begin{matrix} x^{'} = 2 y \\ y^{'} = - 8 x \end{matrix}]$ i.c.	system_of_ODEs	✓	0.705

17458	$[\begin{matrix} x^{'} = 2 x - y \\ y^{'} = x - 2 y \end{matrix}]$	system_of_ODEs	✓	0.515

17459	$[\begin{matrix} x^{'} = - x + y \\ y^{'} = x + y \end{matrix}]$	system_of_ODEs	✓	0.533

17460	$[\begin{matrix} x^{'} = 2 x - 4 y \\ y^{'} = 2 x - 2 y \end{matrix}]$	system_of_ODEs	✓	0.446

17461	$[\begin{matrix} x^{'} = - x + y + x^{2} \\ y^{'} = y - 2 x y \end{matrix}]$	system_of_ODEs	✓	0.057

17462	$[\begin{matrix} x^{'} = 2 y x^{2} - 3 x^{2} - 4 y \\ y^{'} = - 2 x y^{2} + 6 x y \end{matrix}]$	system_of_ODEs	✓	0.062

17463	$[\begin{matrix} x^{'} = 3 x - x^{2} \\ y^{'} = 2 x y - 3 y + 2 \end{matrix}]$	system_of_ODEs	✓	0.062

17464	$[\begin{matrix} x^{'} = x - x y \\ y^{'} = y + 2 x y \end{matrix}]$	system_of_ODEs	✓	0.058

17465	$[\begin{matrix} x^{'} = 2 - y \\ y^{'} = y - x^{2} \end{matrix}]$	system_of_ODEs	✓	0.053

17466	$[\begin{matrix} x^{'} = x - x^{2} - x y \\ y^{'} = \frac{y}{2} - \frac{y^{2}}{4} - \frac{3 x y}{4} \end{matrix}]$	system_of_ODEs	✓	0.065

17467	$[\begin{matrix} x^{'} = - (x - y) (1 - x - y) \\ y^{'} = x (y + 2) \end{matrix}]$	system_of_ODEs	✓	0.067

17468	$[\begin{matrix} x^{'} = y (2 - x - y) \\ y^{'} = - x - y - 2 x y \end{matrix}]$	system_of_ODEs	✓	0.061

17469	$[\begin{matrix} x^{'} = (x + 2) (- x + y) \\ y^{'} = y - x^{2} - y^{2} \end{matrix}]$	system_of_ODEs	✓	0.066

17470	$[\begin{matrix} x^{'} = - x + 2 x y \\ y^{'} = y - x^{2} - y^{2} \end{matrix}]$	system_of_ODEs	✓	0.064

17471	$[\begin{matrix} x^{'} = y \\ y^{'} = x - \frac{x^{3}}{5} - \frac{y}{5} \end{matrix}]$	system_of_ODEs	✓	0.060

17472	$x^{'} = \frac{x \sqrt{6 x - 9}}{3}$ i.c.	[_quadrature]	✓	2.434

17473	$[\begin{matrix} x^{'} = x (1 - x - y) \\ y^{'} = y (\frac{3}{4} - y - \frac{x}{2}) \end{matrix}]$	system_of_ODEs	✓	0.058

17474	$y^{''} + t y = 0$	[[_Emden, _Fowler]]	✓	0.298

17475	$y^{''} + y^{'} + y + y^{3} = 0$	[[_2nd_order, _missing_x]]	✗	2.217

17476	$(- x^{2} + 1) y^{''} - 2 y^{'} x + α (α + 1) y = 0$	[_Gegenbauer]	✗	1.411

17477	$x^{2} y^{''} + y^{'} x + (- ν^{2} + x^{2}) y = 0$	[_Bessel]	✓	0.664

17478	$y^{''} + μ (1 - y^{2}) y^{'} + y = 0$	[[_2nd_order, _missing_x], _Van_der_Pol]	✗	2.821

17479	$y^{''} - t y = \frac{1}{π}$	unknown	✓	0.927

17480	$a x^{2} y^{''} + b x y^{'} + c y = d$	[[_2nd_order, _with_linear_symmetries]]	✓	2.780

17481	$y^{''} + y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	1.756

17482	$y^{''} + 9 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	1.805

17483	$y^{''} + y^{'} + 16 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.910

17484	$y^{''} + 3 y^{'} + 4 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.871

17485	$y^{''} - y^{'} + 4 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.902

17486	$t y^{''} + 3 y = t$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.914

17487	$(t - 1) y^{''} - 3 y^{'} t + 4 y = \sin (t)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✗	1.441

17488	$t (t - 4) y^{''} + 3 y^{'} t + 4 y = 2$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✗	25.696

17489	$y^{''} + \cos (t) y^{'} + 3 \ln (t) y = 0$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✗	1.587

17490	$(3 + x) y^{''} + y^{'} x + y \ln (x) = 0$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✗	0.933

17491	$(x - 2) y^{''} + y^{'} + (x - 2) \tan (x) y = 0$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✗	1.891

17492	$(- x^{2} + 1) y^{''} - 2 y^{'} x + \frac{α (α + 1) μ^{2} y}{- x^{2} + 1} = 0$ i.c.	[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	2.667

17493	$y^{''} - \frac{t}{y} = \frac{1}{π}$ i.c.	[NONE]	✗	0.303

17494	$t^{2} y^{''} - 2 y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.593

17495	$y y^{''} + {y^{'}}^{2} = 0$	[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]	✓	1.245

17496	$y^{''} + 4 y = 0$	[[_2nd_order, _missing_x]]	✓	1.413

17497	$y^{''} - 2 y^{'} + y = 0$	[[_2nd_order, _missing_x]]	✓	0.401

17498	$x^{2} y^{''} - x (x + 2) y^{'} + (x + 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.644

17499	$(1 - x \cot (x)) y^{''} - y^{'} x + y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	1.995

17500	$y^{''} - y^{'} - 2 y = 0$	[[_2nd_order, _missing_x]]	✓	0.351

2.2.175 Problems 17401 to 17500