Problems 10401 to 10500

Table 2.211: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	time (sec)

10401	${y^{'}}^{2} - 3 x y^{2 / 3} y^{'} + 9 y^{5 / 3} = 0$	[[_1st_order, _with_linear_symmetries]]	✓	4.338

10402	$2 {y^{'}}^{2} + (- 1 + x) y^{'} - y = 0$	[[_1st_order, _with_linear_symmetries], _Clairaut]	✓	0.432

10403	$2 {y^{'}}^{2} - 2 x^{2} y^{'} + 3 x y = 0$	[[_homogeneous, ‘class G‘]]	✓	2.174

10404	$3 {y^{'}}^{2} - 2 x y^{'} + y = 0$	[[_1st_order, _with_linear_symmetries], _dAlembert]	✓	0.423

10405	$3 {y^{'}}^{2} + 4 x y^{'} - y + x^{2} = 0$	[[_homogeneous, ‘class G‘]]	✓	1.754

10406	$a {y^{'}}^{2} + b y^{'} - y = 0$	[_quadrature]	✓	0.510

10407	$a {y^{'}}^{2} + b x^{2} y^{'} + c x y = 0$	[[_homogeneous, ‘class G‘]]	✓	2.996

10408	$a {y^{'}}^{2} + y y^{'} - x = 0$	[_dAlembert]	✓	73.217

10409	$a {y^{'}}^{2} - y y^{'} - x = 0$	[_dAlembert]	✓	46.317

10410	$x {y^{'}}^{2} - y = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	2.414

10411	$x {y^{'}}^{2} - 2 y + x = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	1.867

10412	$x {y^{'}}^{2} - 2 y^{'} - y = 0$	[_rational, _dAlembert]	✓	0.972

10413	$x {y^{'}}^{2} + 4 y^{'} - 2 y = 0$	[_rational, _dAlembert]	✓	1.154

10414	$x {y^{'}}^{2} + x y^{'} - y = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	1.785

10415	$x {y^{'}}^{2} + y y^{'} + a = 0$	[[_homogeneous, ‘class G‘], _dAlembert]	✓	0.490

10416	$x {y^{'}}^{2} + y y^{'} - x^{2} = 0$	[[_homogeneous, ‘class G‘]]	✓	2.773

10417	$x {y^{'}}^{2} + y y^{'} + x^{3} = 0$	[[_homogeneous, ‘class G‘]]	✓	3.249

10418	$x {y^{'}}^{2} + y y^{'} - y^{4} = 0$	[[_homogeneous, ‘class G‘]]	✓	2.469

10419	$x {y^{'}}^{2} + (y - 3 x) y^{'} + y = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	3.831

10420	$x {y^{'}}^{2} - y y^{'} + a = 0$	[[_homogeneous, ‘class G‘], _rational, _Clairaut]	✓	0.432

10421	$x {y^{'}}^{2} - y y^{'} + a y = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	2.375

10422	$x {y^{'}}^{2} + 2 y y^{'} - x = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	1.276

10423	$x {y^{'}}^{2} - 2 y y^{'} + a = 0$	[[_homogeneous, ‘class G‘], _rational, _dAlembert]	✓	0.490

10424	$x {y^{'}}^{2} - 2 y y^{'} - x = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	0.950

10425	$x {y^{'}}^{2} - 2 y y^{'} + 4 x = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	1.338

10426	$x {y^{'}}^{2} - 2 y y^{'} + 2 y + x = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	1.584

10427	$x {y^{'}}^{2} + a y y^{'} + b x = 0$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	1.453

10428	$(x + 1) {y^{'}}^{2} - (x + y) y^{'} + y = 0$	[[_1st_order, _with_linear_symmetries], _rational, _dAlembert]	✓	0.617

10429	$(3 x + 1) {y^{'}}^{2} - 3 (y + 2) y^{'} + 9 = 0$	[[_1st_order, _with_linear_symmetries], _Clairaut]	✓	0.616

10430	$(3 x + 5) {y^{'}}^{2} - (3 y + x) y^{'} + y = 0$	[[_1st_order, _with_linear_symmetries], _rational, _dAlembert]	✓	0.654

10431	$a x {y^{'}}^{2} + (b x - a y + c) y^{'} - b y = 0$	[[_1st_order, _with_linear_symmetries], _rational, _dAlembert]	✓	0.713

10432	$a x {y^{'}}^{2} - (a y + b x - a - b) y^{'} + b y = 0$	[[_1st_order, _with_linear_symmetries], _rational, _dAlembert]	✓	0.815

10433	$(a 2 x + c 2) {y^{'}}^{2} + (a 1 x + b 1 y + c 1) y^{'} + a 0 x + b 0 y + c 0 = 0$	[_rational, _dAlembert]	✓	1.532

10434	$x^{2} {y^{'}}^{2} - y^{4} + y^{2} = 0$	[_separable]	✓	2.746

10435	${(x y^{'} + a)}^{2} - 2 a y + x^{2} = 0$	[_rational]	✓	70.193

10436	${(x y^{'} + y + 2 x)}^{2} - 4 x y - 4 x^{2} - 4 a = 0$	[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✓	4.450

10437	$y^{'} - 1 = 0$	[_quadrature]	✓	0.784

10438	$x^{2} {y^{'}}^{2} - 2 x y y^{'} + y (y + 1) - x = 0$	[[_1st_order, _with_linear_symmetries], _rational]	✓	3.437

10439	$x^{2} {y^{'}}^{2} - 2 x y y^{'} + y^{2} (- x^{2} + 1) - x^{4} = 0$	[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✓	9.569

10440	$x^{2} {y^{'}}^{2} - (2 x y + a) y^{'} + y^{2} = 0$	[[_homogeneous, ‘class G‘], _rational, _Clairaut]	✓	0.713

10441	$x^{2} {y^{'}}^{2} + 3 x y y^{'} + 2 y^{2} = 0$	[_separable]	✓	1.049

10442	$x^{2} {y^{'}}^{2} + 3 x y y^{'} + 3 y^{2} = 0$	[_separable]	✓	0.461

10443	$x^{2} {y^{'}}^{2} + 4 x y y^{'} - 5 y^{2} = 0$	[_separable]	✓	0.942

10444	$x^{2} {y^{'}}^{2} - 4 x (y + 2) y^{'} + 4 y (y + 2) = 0$	[_separable]	✓	0.474

10445	$x^{2} {y^{'}}^{2} + (x^{2} y - 2 x y + x^{3}) y^{'} + (y^{2} - x^{2} y) (1 - x) = 0$	[_linear]	✓	0.805

10446	$x^{2} {y^{'}}^{2} - y (y - 2 x) y^{'} + y^{2} = 0$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	70.548

10447	$x^{2} {y^{'}}^{2} + (a x^{2} y^{3} + b) y^{'} + a b y^{3} = 0$	[_quadrature]	✓	7.958

10448	$(x^{2} + 1) {y^{'}}^{2} - 2 x y y^{'} + y^{2} - 1 = 0$	[[_1st_order, _with_linear_symmetries], _rational, _Clairaut]	✓	0.634

10449	$(x^{2} - 1) {y^{'}}^{2} - 1 = 0$	[_quadrature]	✓	0.343

10450	$(x^{2} - 1) {y^{'}}^{2} - y^{2} + 1 = 0$	[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✓	1.024

10451	$(- a^{2} + x^{2}) {y^{'}}^{2} + 2 x y y^{'} + y^{2} = 0$	[_separable]	✓	0.855

10452	$(- a^{2} + x^{2}) {y^{'}}^{2} - 2 x y y^{'} - x^{2} = 0$	[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✓	31.458

10453	$(x^{2} + a) {y^{'}}^{2} - 2 x y y^{'} + y^{2} + b = 0$	[[_1st_order, _with_linear_symmetries], _rational, _Clairaut]	✓	0.726

10454	$(2 x^{2} + 1) {y^{'}}^{2} + (y^{2} + 2 x y + x^{2} + 2) y^{'} + 2 y^{2} + 1 = 0$	[‘y=_G(x,y’)‘]	✓	70.017

10455	$(a^{2} - 1) x^{2} {y^{'}}^{2} + 2 x y y^{'} - y^{2} + a^{2} x^{2} = 0$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	69.131

10456	$a x^{2} {y^{'}}^{2} - 2 a x y y^{'} + y^{2} - a (a - 1) x^{2} = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	3.524

10457	$x^{3} {y^{'}}^{2} + x^{2} y y^{'} + a = 0$	[[_homogeneous, ‘class G‘]]	✓	2.999

10458	$x (x^{2} - 1) {y^{'}}^{2} + 2 (- x^{2} + 1) y y^{'} + x y^{2} - x = 0$	[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✓	12.290

10459	$x^{4} {y^{'}}^{2} - x y^{'} - y = 0$	[[_homogeneous, ‘class G‘], _rational]	✓	1.714

10460	$x^{2} (- a^{2} + x^{2}) {y^{'}}^{2} - 1 = 0$	[_quadrature]	✓	0.625

10461	$e^{- 2 x} {y^{'}}^{2} - {(y^{'} - 1)}^{2} + e^{- 2 y} = 0$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✓	17.540

10462	$({y^{'}}^{2} + y^{2}) \cos {(x)}^{4} - a^{2} = 0$	[‘y=_G(x,y’)‘]	✓	28.306

10463	$y {y^{'}}^{2} - 1 = 0$	[_quadrature]	✓	0.364

10464	$y {y^{'}}^{2} - e^{2 x} = 0$	[[_1st_order, _with_linear_symmetries]]	✓	1.171

10465	$y {y^{'}}^{2} + 2 x y^{'} - y = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	1.636

10466	$y {y^{'}}^{2} + 2 x y^{'} - 9 y = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	1.747

10467	$y {y^{'}}^{2} - 2 x y^{'} + y = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	1.617

10468	$y {y^{'}}^{2} - 4 x y^{'} + y = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	1.578

10469	$y {y^{'}}^{2} - 4 a^{2} x y^{'} + a^{2} y = 0$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	1.858

10470	$y {y^{'}}^{2} + a x y^{'} + b y = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	1.500

10471	$y {y^{'}}^{2} + x^{3} y^{'} - x^{2} y = 0$	[[_1st_order, _with_linear_symmetries]]	✓	2.768

10472	$y {y^{'}}^{2} - (y - x) y^{'} - x = 0$	[_quadrature]	✓	0.458

10473	$(x + y) {y^{'}}^{2} + 2 x y^{'} - y = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	1.696

10474	$(y - 2 x) {y^{'}}^{2} - 2 (- 1 + x) y^{'} + y - 2 = 0$	[[_homogeneous, ‘class C‘], _dAlembert]	✓	0.763

10475	$2 y {y^{'}}^{2} - (4 x - 5) y^{'} + 2 y = 0$	[[_homogeneous, ‘class C‘], _rational, _dAlembert]	✓	0.769

10476	$4 y {y^{'}}^{2} + 2 x y^{'} - y = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	1.493

10477	$9 y {y^{'}}^{2} + 4 x^{3} y^{'} - 4 x^{2} y = 0$	[[_1st_order, _with_linear_symmetries]]	✓	2.802

10478	$a y {y^{'}}^{2} + (2 x - b) y^{'} - y = 0$	[[_homogeneous, ‘class C‘], _rational, _dAlembert]	✓	0.858

10479	$(a y + b) (1 + {y^{'}}^{2}) - c = 0$	[_quadrature]	✓	0.552

10480	$(b_{2} y + a_{2} x + c_{2}) {y^{'}}^{2} + (a_{1} x + b_{1} y + c_{1}) y^{'} + a_{0} x + b_{0} y + c_{0} = 0$	[_rational, _dAlembert]	✓	282.755

10481	$(a y - x^{2}) {y^{'}}^{2} + 2 x y {y^{'}}^{2} - y^{2} = 0$	[_rational]	✓	3.678

10482	$x y {y^{'}}^{2} + (x^{2} + y^{2}) y^{'} + x y = 0$	[_separable]	✓	1.369

10483	$x y {y^{'}}^{2} + (x^{22} - y^{2} + a) y^{'} - x y = 0$	[_rational]	✓	37.145

10484	$(2 x y - x^{2}) {y^{'}}^{2} + 2 x y y^{'} + 2 x y - y^{2} = 0$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	147.797

10485	$(2 x y - x^{2}) {y^{'}}^{2} - 6 x y y^{'} - y^{2} + 2 x y = 0$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	73.017

10486	$a x y {y^{'}}^{2} - (a y^{2} + b x^{2} + c) y^{'} + b x y = 0$	[_rational]	✓	56.085

10487	$y^{2} {y^{'}}^{2} + y^{2} - a^{2} = 0$	[_quadrature]	✓	0.512

10488	$y^{2} {y^{'}}^{2} - 6 x^{3} y^{'} + 4 x^{2} y = 0$	[[_1st_order, _with_linear_symmetries]]	✓	2.861

10489	$y^{2} {y^{'}}^{2} - 4 a y y^{'} + y^{2} - 4 a x + 4 a^{2} = 0$	[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✓	72.013

10490	$y^{2} {y^{'}}^{2} + 2 x y y^{'} + a y^{2} + b x + c = 0$	[_rational]	✓	9.119

10491	$y^{2} {y^{'}}^{2} - 2 x y y^{'} + 2 y^{2} - x^{2} + a = 0$	[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✓	79.845

10492	$y^{2} {y^{'}}^{2} + 2 a x y y^{'} + (1 - a) y^{2} + a x^{2} + (a - 1) b = 0$	[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✓	10.167

10493	$(y^{2} - a^{2}) {y^{'}}^{2} + y^{2} = 0$	[_quadrature]	✓	0.647

10494	$(y^{2} - 2 a x + a^{2}) {y^{'}}^{2} + 2 a y y^{'} + y^{2} = 0$	[‘y=_G(x,y’)‘]	✓	78.706

10495	$(y^{2} - a^{2} x^{2}) {y^{'}}^{2} + 2 x y y^{'} + (- a^{2} + 1) x^{2} = 0$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	2.653

10496	$(y^{2} + (1 - a) x^{2}) {y^{'}}^{2} + 2 a x y y^{'} + (1 - a) y^{2} + x^{2} = 0$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	310.007

10497	${(y - x)}^{2} (1 + {y^{'}}^{2}) - a^{2} {(y^{'} + 1)}^{2} = 0$	[[_homogeneous, ‘class C‘], _dAlembert]	✓	7.282

10498	$3 y^{2} {y^{'}}^{2} - 2 x y y^{'} + 4 y^{2} - x^{2} = 0$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	3.274

10499	$(3 y - 2) {y^{'}}^{2} - 4 + 4 y = 0$	[_quadrature]	✓	0.615

10500	$(- a^{2} + 1) y^{2} {y^{'}}^{2} - 2 a^{2} x y y^{'} + y^{2} - a^{2} x^{2} = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	292.509

2.2.105 Problems 10401 to 10500