Problems 19501 to 19571

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


#	ODE	CAS classiﬁcation	Solved?	time (sec)

19501	${y^{'}}^{2} + 2 y^{'} x - y = 0$	[[_1st_order, _with_linear_symmetries], _dAlembert]	✓	0.548

19502	$x^{3} {y^{'}}^{2} + x^{2} y y^{'} + a^{3} = 0$	[[_homogeneous, ‘class G‘]]	✓	2.947

19503	$x^{2} {y^{'}}^{3} + (2 x + y) y y^{'} + y^{2} = 0$	[[_1st_order, _with_linear_symmetries], _dAlembert]	✓	1.777

19504	$x {y^{'}}^{2} - 2 y y^{'} + x + 2 y = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	1.914

19505	${y^{'}}^{2} y^{2} \cos {(a)}^{2} - 2 y^{'} x y \sin {(a)}^{2} + y^{2} - x^{2} \sin {(a)}^{2} = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	53.275

19506	$(2 x^{2} + 1) {y^{'}}^{2} + (y^{2} + 2 x y + x^{2} + 2) y^{'} + 2 y^{2} + 1 = 0$	[_rational]	✗	68.690

19507	$x^{4} y^{'''} + 2 x^{3} y^{''} - x^{2} y^{'} + x y = 1$	[[_3rd_order, _with_linear_symmetries]]	✓	0.253

19508	$x^{2} y^{''} - 2 y = x^{2} + \frac{1}{x}$	[[_2nd_order, _exact, _linear, _nonhomogeneous]]	✓	0.890

19509	$x^{3} y^{'''} - x^{2} y^{''} + 2 y^{'} x - 2 y = x^{2} + 3 x$	[[_3rd_order, _with_linear_symmetries]]	✓	0.320

19510	$x^{3} y^{'''} + 6 x^{2} y^{''} + 4 y^{'} x - 4 y = 0$	[[_3rd_order, _with_linear_symmetries]]	✓	0.131

19511	$x^{3} y^{'''} + 3 x^{2} y^{''} + y^{'} x + y = 0$	[[_3rd_order, _exact, _linear, _homogeneous]]	✓	0.159

19512	$x^{2} y^{''} - 3 y^{'} x + 4 y = 2 x^{2}$	[[_2nd_order, _with_linear_symmetries]]	✓	1.485

19513	$x^{3} y^{'''} + 2 x^{2} y^{''} + 2 y = 10 x + \frac{10}{x}$	[[_3rd_order, _exact, _linear, _nonhomogeneous]]	✓	0.891

19514	$x^{2} y^{''} + 3 y^{'} x + y = \frac{1}{{(1 - x)}^{2}}$	[[_2nd_order, _exact, _linear, _nonhomogeneous]]	✓	1.653

19515	${(2 x - 1)}^{3} y^{'''} + (2 x - 1) y^{'} - 2 y = 0$	[[_3rd_order, _with_linear_symmetries]]	✗	0.072

19516	${(x + a)}^{2} y^{''} - 4 (x + a) y^{'} + 6 y = x$	[[_2nd_order, _with_linear_symmetries]]	✓	1.101

19517	$16 {(x + 1)}^{4} y^{''''} + 96 {(x + 1)}^{3} y^{'''} + 104 {(x + 1)}^{2} y^{''} + 8 (x + 1) y^{'} + y = x^{2} + 4 x + 3$	[[_high_order, _with_linear_symmetries]]	✗	0.097

19518	${(x + 1)}^{2} y^{''} + (x + 1) y^{'} + y = 4 \cos (\ln (x + 1))$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.542

19519	$2 x^{2} y y^{''} + 4 y^{2} = x^{2} {y^{'}}^{2} + 2 x y^{'} y$	[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]]	✗	0.350

19520	$x^{2} y^{''} - (2 m - 1) x y^{'} + (m^{2} + n^{2}) y = n^{2} x^{m} \ln (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	2.508

19521	$x^{2} y^{''} - 3 y^{'} x + y = \frac{\ln (x) \sin (\ln (x)) + 1}{x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	4.150

19522	$(x^{2} + x + 1) y^{'''} + (3 + 6 x) y^{''} + 6 y^{'} = 0$	[[_3rd_order, _missing_y]]	✓	0.992

19523	$(x^{3} - x) y^{'''} + (8 x^{2} - 3) y^{''} + 14 y^{'} x + 4 y = \frac{2}{x^{3}}$	[[_3rd_order, _fully, _exact, _linear]]	✓	1.418

19524	$y^{'''} + \cos (x) y^{''} - 2 y^{'} \sin (x) - \cos (x) y = \sin (2 x)$	[[_3rd_order, _fully, _exact, _linear]]	✓	1.429

19525	$\sqrt{x} y^{''} + 2 y^{'} x + 3 y = x$	[[_2nd_order, _with_linear_symmetries]]	✗	1.066

19526	$2 x^{2} (x + 1) y^{''} + x (3 + 7 x) y^{'} - 3 y = x^{2}$	[[_2nd_order, _with_linear_symmetries]]	✓	0.588

19527	$2 x^{2} \cos (y) y^{''} - 2 x^{2} \sin (y) {y^{'}}^{2} + x \cos (y) y^{'} - \sin (y) = \ln (x)$	[[_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]]	✗	1.870

19528	$x^{2} y y^{''} + {(y^{'} x - y)}^{2} - 3 y^{2} = 0$	[[_2nd_order, _exact, _nonlinear], [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]]	✓	1.096

19529	$y + 3 y^{'} x + 2 y {y^{'}}^{2} + (2 y^{2} y^{'} + x^{2}) y^{''} = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	0.303

19530	$(y^{2} + 2 x^{2} y^{'}) y^{''} + 2 (x + y) {y^{'}}^{2} + y^{'} x + y = 0$	[[_2nd_order, _exact, _nonlinear], [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_poly_yn]]	✗	161.518

19531	$y^{'''} = x e^{x}$	[[_3rd_order, _quadrature]]	✓	0.150

19532	$y^{''} = x^{2} \sin (x)$	[[_2nd_order, _quadrature]]	✓	1.250

19533	$y^{''} = \sec {(x)}^{2}$	[[_2nd_order, _quadrature]]	✓	1.152

19534	$y^{''} + y^{'} + {y^{'}}^{3} = 0$	[[_2nd_order, _missing_x]]	✓	3.104

19535	$(x^{2} + 1) y^{''} + 1 + {y^{'}}^{2} = 0$	[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]]	✓	0.860

19536	$y (1 - \ln (y)) y^{''} + (1 + \ln (y)) {y^{'}}^{2} = 0$	[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]	✓	0.953

19537	$y y^{''} - {y^{'}}^{2} = y^{2} \ln (y)$	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]]	✓	4.243

19538	$y^{'} - y y^{''} = n \sqrt{{y^{'}}^{2} + a^{2} y^{''}}$	[[_2nd_order, _missing_x]]	✗	18.850

19539	$x y^{''} + y^{'} = 0$	[[_2nd_order, _missing_y]]	✓	0.829

19540	$y^{''''} - a^{2} y^{''} = 0$	[[_high_order, _missing_x]]	✓	0.072

19541	$x^{4} y^{''} = {(y - y^{'} x)}^{3}$	[[_2nd_order, _with_linear_symmetries]]	✗	0.294

19542	$x y^{''} + 2 y^{'} = - y^{2} + x^{2} y^{'}$	[NONE]	✗	0.280

19543	$x y^{''} - (2 x - 1) y^{'} + (x - 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.394

19544	$\sin {(x)}^{2} y^{''} = 2 y$	[[_2nd_order, _with_linear_symmetries]]	✗	1.088

19545	$(- x^{2} + 1) y^{''} + y^{'} x - y = x {(- x^{2} + 1)}^{3 / 2}$	[[_2nd_order, _with_linear_symmetries]]	✓	1.981

19546	$(x + 2) y^{''} - (5 + 2 x) y^{'} + 2 y = e^{x} (x + 1)$	[[_2nd_order, _with_linear_symmetries]]	✓	0.743

19547	$y^{''} - \cot (x) y^{'} - (1 - \cot (x)) y = e^{x} \sin (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✗	2.333

19548	$(x \sin (x) + \cos (x)) y^{''} - x \cos (x) y^{'} + \cos (x) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	1.445

19549	$y^{''} + (1 + \frac{2 \cot (x)}{x} - \frac{2}{x^{2}}) y = x \cos (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✗	1.826

19550	$x^{2} y^{''} - 2 (x^{2} + x) y^{'} + (x^{2} + 2 x + 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.531

19551	$x^{2} y^{''} - 2 y^{'} x + (x^{2} + 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.655

19552	$y^{''} + \frac{y^{'}}{x^{1 / 3}} + (\frac{1}{4 x^{2 / 3}} - \frac{1}{6 x^{4 / 3}} - \frac{6}{x^{2}}) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.587

19553	$y^{''} - 2 y^{'} \tan (x) + y = 0$	[_Lienard]	✓	0.780

19554	$y^{''} - 4 y^{'} x + (4 x^{2} - 1) y = - 3 e^{x^{2}} \sin (2 x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.866

19555	$y^{''} - (8 e^{2 x} + 2) y^{'} + 4 e^{4 x} y = e^{6 x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.342

19556	$y^{''} + \cot (x) y^{'} + \frac{y \csc {(x)}^{2}}{2} = 0$	[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	1.227

19557	$x^{6} y^{''} + 3 x^{5} y^{'} + a^{2} y = \frac{1}{x^{2}}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.674

19558	$x y^{''} - y^{'} - 4 x^{3} y = 8 x^{3} \sin (x^{2})$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	2.347

19559	$\cos (x) y^{''} + y^{'} \sin (x) - 2 \cos {(x)}^{3} y = 2 \cos {(x)}^{5}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	2.960

19560	${(x + 1)}^{2} y^{''} + (x + 1) y^{'} + y = 4 \cos (\ln (x + 1))$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.589

19561	$x y^{''} + (x - 1) y^{'} - y = x^{2}$	[[_2nd_order, _with_linear_symmetries]]	✓	0.732

19562	$3 x^{2} y^{''} + (- 6 x^{2} + 6 x + 2) y^{'} - 4 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.742

19563	$y^{''} + a^{2} y = \sec (a x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.020

19564	$x^{2} y^{''} + y^{'} x - y = x^{2} e^{x}$	[[_2nd_order, _exact, _linear, _nonhomogeneous]]	✓	2.287

19565	$x^{2} y^{''} - 2 x (x + 1) y^{'} + 2 (x + 1) y = x^{3}$	[[_2nd_order, _with_linear_symmetries]]	✓	0.883

19566	$y^{''} + (1 - \cot (x)) y^{'} - \cot (x) y = \sin {(x)}^{2}$	[[_2nd_order, _linear, _nonhomogeneous]]	✗	2.644

19567	$y^{'''} - 6 y^{''} + 11 y^{'} - 6 y = e^{2 x}$	[[_3rd_order, _with_linear_symmetries]]	✓	0.149

19568	$[\begin{matrix} x^{'} - 7 x + y = 0 \\ y^{'} - 2 x - 5 y = 0 \end{matrix}]$	system_of_ODEs	✓	0.484

19569	$[\begin{matrix} x^{'} + 5 x + y = e^{t} \\ y^{'} - x + 3 y = e^{2 t} \end{matrix}]$	system_of_ODEs	✓	0.576

19570	$[\begin{matrix} 4 x^{'} + 9 y^{'} + 11 x + 31 y = e^{t} \\ 3 x^{'} + 7 y^{'} + 8 x + 24 y = e^{2 t} \end{matrix}]$	system_of_ODEs	✓	0.629

19571	$[\begin{matrix} x^{'} t = t - 2 x \\ y^{'} t = t x + t y + 2 x - t \end{matrix}]$	system_of_ODEs	✓	0.061

2.2.196 Problems 19501 to 19571