Problems 19501 to 19563

Table 2.393: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	time (sec)

19501	$x^{3} y^{'''} - x^{2} y^{''} + 2 x y^{'} - 2 y = x^{2} + 3 x$	[[_3rd_order, _with_linear_symmetries]]	✓	0.304

19502	$x^{3} y^{'''} + 6 x^{2} y^{''} + 4 x y^{'} - 4 y = 0$	[[_3rd_order, _with_linear_symmetries]]	✓	0.101

19503	$x^{3} y^{'''} + 3 x^{2} y^{''} + x y^{'} + y = 0$	[[_3rd_order, _exact, _linear, _homogeneous]]	✓	0.115

19504	$x^{2} y^{''} - 3 x y^{'} + 4 y = 2 x^{2}$	[[_2nd_order, _with_linear_symmetries]]	✓	1.401

19505	$x^{3} y^{'''} + 2 x^{2} y^{''} + 2 y = 10 x + \frac{10}{x}$	[[_3rd_order, _exact, _linear, _nonhomogeneous]]	✓	0.770

19506	$x^{2} y^{''} + 3 x y^{'} + y = \frac{1}{{(1 - x)}^{2}}$	[[_2nd_order, _exact, _linear, _nonhomogeneous]]	✓	1.921

19507	${(2 x - 1)}^{3} y^{'''} + (2 x - 1) y^{'} - 2 y = 0$	[[_3rd_order, _with_linear_symmetries]]	✗	0.040

19508	${(x + a)}^{2} y^{''} - 4 (x + a) y^{'} + 6 y = x$	[[_2nd_order, _with_linear_symmetries]]	✓	1.191

19509	$16 {(x + 1)}^{4} y^{''''} + 96 {(x + 1)}^{3} y^{'''} + 104 {(x + 1)}^{2} y^{''} + 8 (x + 1) y^{'} + y = x^{2} + 4 x + 3$	[[_high_order, _with_linear_symmetries]]	✗	0.053

19510	${(x + 1)}^{2} y^{''} + (x + 1) y^{'} + y = 4 \cos (\ln (x + 1))$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	5.056

19511	$2 x^{2} y y^{''} + 4 y^{2} = x^{2} {y^{'}}^{2} + 2 x y y^{'}$	[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]]	✗	0.139

19512	$x^{2} y^{''} - (2 m - 1) x y^{'} + (m^{2} + n^{2}) y = n^{2} x^{m} \ln (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	57.691

19513	$x^{2} y^{''} - 3 x y^{'} + y = \frac{\ln (x) \sin (\ln (x)) + 1}{x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	8.834

19514	$(x^{2} + x + 1) y^{'''} + (3 + 6 x) y^{''} + 6 y^{'} = 0$	[[_3rd_order, _missing_y]]	✓	0.163

19515	$(x^{3} - x) y^{'''} + (8 x^{2} - 3) y^{''} + 14 x y^{'} + 4 y = \frac{2}{x^{3}}$	[[_3rd_order, _fully, _exact, _linear]]	✓	0.383

19516	$y^{'''} + \cos (x) y^{''} - 2 \sin (x) y^{'} - y \cos (x) = \sin (2 x)$	[[_3rd_order, _fully, _exact, _linear]]	✓	0.660

19517	$\sqrt{x} y^{''} + 2 x y^{'} + 3 y = x$	[[_2nd_order, _with_linear_symmetries]]	✗	0.840

19518	$2 x^{2} (x + 1) y^{''} + x (7 x + 3) y^{'} - 3 y = x^{2}$	[[_2nd_order, _with_linear_symmetries]]	✓	0.969

19519	$2 x^{2} \cos (y) y^{''} - 2 x^{2} \sin (y) {y^{'}}^{2} + x \cos (y) y^{'} - \sin (y) = \ln (x)$	[[_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]]	✗	1.758

19520	$x^{2} y y^{''} + {(- y + x y^{'})}^{2} - 3 y^{2} = 0$	[[_2nd_order, _exact, _nonlinear], [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]]	✓	0.922

19521	$y + 3 x y^{'} + 2 y {y^{'}}^{2} + (x^{2} + 2 y^{2} y^{'}) y^{''} = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	0.145

19522	$(y^{2} + 2 x^{2} y^{'}) y^{''} + 2 {y^{'}}^{2} (x + y) + x y^{'} + y = 0$	[[_2nd_order, _exact, _nonlinear], [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_poly_yn]]	✗	151.255

19523	$y^{'''} = x e^{x}$	[[_3rd_order, _quadrature]]	✓	0.101

19524	$y^{''} = x^{2} \sin (x)$	[[_2nd_order, _quadrature]]	✓	36.177

19525	$y^{''} = \sec {(x)}^{2}$	[[_2nd_order, _quadrature]]	✓	2.416

19526	$y^{''} + y^{'} + {y^{'}}^{3} = 0$	[[_2nd_order, _missing_x]]	✓	3.117

19527	$(x^{2} + 1) y^{''} + 1 + {y^{'}}^{2} = 0$	[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]]	✓	0.798

19528	$y (1 - \ln (y)) y^{''} + (1 + \ln (y)) {y^{'}}^{2} = 0$	[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]	✓	0.526

19529	$y y^{''} - {y^{'}}^{2} = y^{2} \ln (y)$	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]]	✓	2.030

19530	$y^{'} - y y^{''} = n \sqrt{{y^{'}}^{2} + a^{2} y^{''}}$	[[_2nd_order, _missing_x]]	✗	21.150

19531	$x y^{''} + y^{'} = 0$	[[_2nd_order, _missing_y]]	✓	0.715

19532	$y^{''''} - a^{2} y^{''} = 0$	[[_high_order, _missing_x]]	✓	0.056

19533	$x^{4} y^{''} = {(y - x y^{'})}^{3}$	[[_2nd_order, _with_linear_symmetries]]	✗	0.128

19534	$x y^{''} + 2 y^{'} = x^{2} y^{'} - y^{2}$	[NONE]	✗	0.139

19535	$x y^{''} - (2 x - 1) y^{'} + (- 1 + x) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.752

19536	$y^{''} \sin {(x)}^{2} = 2 y$	[[_2nd_order, _with_linear_symmetries]]	✗	0.862

19537	$(- x^{2} + 1) y^{''} + x y^{'} - y = x {(- x^{2} + 1)}^{3 / 2}$	[[_2nd_order, _with_linear_symmetries]]	✓	2.240

19538	$(x + 2) y^{''} - (5 + 2 x) y^{'} + 2 y = (x + 1) e^{x}$	[[_2nd_order, _with_linear_symmetries]]	✓	1.414

19539	$y^{''} - \cot (x) y^{'} - (1 - \cot (x)) y = e^{x} \sin (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✗	2.196

19540	$(x \sin (x) + \cos (x)) y^{''} - x \cos (x) y^{'} + y \cos (x) = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	10.308

19541	$y^{''} + (1 + \frac{2 \cot (x)}{x} - \frac{2}{x^{2}}) y = x \cos (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✗	1.566

19542	$x^{2} y^{''} - 2 (x^{2} + x) y^{'} + (x^{2} + 2 x + 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.547

19543	$x^{2} y^{''} - 2 x y^{'} + (x^{2} + 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	1.264

19544	$y^{''} + \frac{y^{'}}{x^{1 / 3}} + (\frac{1}{4 x^{2 / 3}} - \frac{1}{6 x^{4 / 3}} - \frac{6}{x^{2}}) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.935

19545	$y^{''} - 2 \tan (x) y^{'} + y = 0$	[_Lienard]	✓	4.830

19546	$y^{''} - 4 x y^{'} + (4 x^{2} - 1) y = - 3 e^{x^{2}} \sin (2 x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	3.763

19547	$y^{''} - (8 e^{2 x} + 2) y^{'} + 4 e^{4 x} y = e^{6 x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	4.021

19548	$y^{''} + \cot (x) y^{'} + \frac{\csc {(x)}^{2} y}{2} = 0$	[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	1.810

19549	$x^{6} y^{''} + 3 x^{5} y^{'} + a^{2} y = \frac{1}{x^{2}}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	4.251

19550	$x y^{''} - y^{'} - 4 x^{3} y = 8 x^{3} \sin (x^{2})$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	2.438

19551	$\cos (x) y^{''} + \sin (x) y^{'} - 2 y \cos {(x)}^{3} = 2 \cos {(x)}^{5}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	4.875

19552	${(x + 1)}^{2} y^{''} + (x + 1) y^{'} + y = 4 \cos (\ln (x + 1))$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	5.058

19553	$x y^{''} + (- 1 + x) y^{'} - y = x^{2}$	[[_2nd_order, _with_linear_symmetries]]	✓	1.124

19554	$3 x^{2} y^{''} + (- 6 x^{2} + 6 x + 2) y^{'} - 4 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	1.234

19555	$y^{''} + a^{2} y = \sec (a x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	2.972

19556	$x^{2} y^{''} + x y^{'} - y = x^{2} e^{x}$	[[_2nd_order, _exact, _linear, _nonhomogeneous]]	✓	2.205

19557	$x^{2} y^{''} - 2 x (x + 1) y^{'} + 2 (x + 1) y = x^{3}$	[[_2nd_order, _with_linear_symmetries]]	✓	1.450

19558	$y^{''} + (1 - \cot (x)) y^{'} - y \cot (x) = \sin {(x)}^{2}$	[[_2nd_order, _linear, _nonhomogeneous]]	✗	2.536

19559	$y^{'''} - 6 y^{''} + 11 y^{'} - 6 y = e^{2 x}$	[[_3rd_order, _with_linear_symmetries]]	✓	0.102

19560	$[\begin{matrix} x^{'} - 7 x + y = 0 \\ y^{'} - 2 x - 5 y = 0 \end{matrix}]$	system_of_ODEs	✓	0.543

19561	$[\begin{matrix} x^{'} + 5 x + y = e^{t} \\ y^{'} - x + 3 y = e^{2 t} \end{matrix}]$	system_of_ODEs	✓	0.477

19562	$[\begin{matrix} 4 x^{'} + 9 y^{'} + 11 x + 31 y = e^{t} \\ 3 x^{'} + 7 y^{'} + 8 x + 24 y = e^{2 t} \end{matrix}]$	system_of_ODEs	✓	0.585

19563	$[\begin{matrix} t x^{'} = t - 2 x \\ t y^{'} = t x + t y + 2 x - t \end{matrix}]$	system_of_ODEs	✗	0.033

2.2.196 Problems 19501 to 19563