Problems 15101 to 15200

Table 2.305: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	time (sec)

15101	$x y y^{'} = 2 x^{2} + 2 y^{2}$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓	79.286

15102	$y^{'} = \frac{x + 2 y}{x + 2 y + 3}$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	1.891

15103	$y^{'} = \frac{x + 2 y}{2 x - y}$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	40.450

15104	$y^{'} = \frac{y}{x} + \tan (\frac{y}{x})$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	4.048

15105	$y^{'} = x y^{2} + 3 y^{2} + x + 3$	[_separable]	✓	2.345

15106	$1 - (x + 2 y) y^{'} = 0$	[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert]	✓	1.819

15107	$\ln (y) + (\frac{x}{y} + 3) y^{'} = 0$	[_exact, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]	✓	1.424

15108	$y^{2} + 1 - y^{'} = 0$	[_quadrature]	✓	3.569

15109	$y^{'} - 3 y = 12 e^{2 x}$	[[_linear, ‘class A‘]]	✓	1.443

15110	$x y y^{'} = y^{2} + x y + x^{2}$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	7.619

15111	$(x + 2) y^{'} - x^{3} = 0$	[_quadrature]	✓	0.594

15112	$x y^{3} y^{'} = y^{4} - x^{2}$	[[_homogeneous, ‘class D‘], _rational, _Bernoulli]	✓	4.332

15113	$y^{'} = 4 y - \frac{16 e^{4 x}}{y^{2}}$	[[_1st_order, _with_linear_symmetries], _Bernoulli]	✓	2.748

15114	$2 y - 6 x + (x + 1) y^{'} = 0$	[_linear]	✓	1.881

15115	$x y^{2} + (x^{2} y + 10 y^{4}) y^{'} = 0$	[[_homogeneous, ‘class G‘], _exact, _rational]	✓	2.288

15116	$y y^{'} - x y^{2} = 6 x e^{4 x^{2}}$	[_Bernoulli]	✓	2.988

15117	${(y - x + 3)}^{2} (y^{'} - 1) = 1$	[[_homogeneous, ‘class C‘], _exact, _rational, _dAlembert]	✓	4.184

15118	$x + y e^{x y} + x e^{x y} y^{'} = 0$	[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✓	1.551

15119	$y^{2} - y^{2} \cos (x) + y^{'} = 0$	[_separable]	✓	2.382

15120	$y^{'} + 2 y = \sin (x)$	[[_linear, ‘class A‘]]	✓	1.529

15121	$y^{'} + 2 x = \sin (x)$	[_quadrature]	✓	0.586

15122	$y^{'} = y^{3} - y^{3} \cos (x)$	[_separable]	✓	3.497

15123	$y^{2} e^{x y^{2}} - 2 x + 2 x y e^{x y^{2}} y^{'} = 0$	[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✓	2.138

15124	$y^{'} = e^{4 x + 3 y}$	[_separable]	✓	2.804

15125	$y^{'} = \tan (6 x + 3 y + 1) - 2$	[[_homogeneous, ‘class C‘], _dAlembert]	✓	354.445

15126	$y^{'} = e^{4 x + 3 y}$	[_separable]	✓	2.810

15127	$y^{'} = x (6 y + e^{x^{2}})$	[_linear]	✓	1.477

15128	$x (1 - 2 y) + (y - x^{2}) y^{'} = 0$	[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class A‘]]	✓	1.352

15129	$x^{2} y^{'} + 3 x y = 6 e^{- x^{2}}$	[_linear]	✓	1.480

15130	$x y^{''} + 4 y^{'} = 18 x^{2}$	[[_2nd_order, _missing_y]]	✓	1.132

15131	$x y^{''} = 2 y^{'}$	[[_2nd_order, _missing_y]]	✓	0.810

15132	$y^{''} = y^{'}$	[[_2nd_order, _missing_x]]	✓	1.623

15133	$y^{''} + 2 y^{'} = 8 e^{2 x}$	[[_2nd_order, _missing_y]]	✓	2.046

15134	$x y^{''} = y^{'} - 2 x^{2} y^{'}$	[[_2nd_order, _missing_y]]	✓	0.806

15135	$(x^{2} + 1) y^{''} + 2 x y^{'} = 0$	[[_2nd_order, _missing_y]]	✓	0.948

15136	$y^{''} = 4 x \sqrt{y^{'}}$	[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]]	✓	0.384

15137	$y^{'} y^{''} = 1$	[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_poly_yn]]	✓	1.909

15138	$y y^{''} = - {y^{'}}^{2}$	[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]	✓	1.705

15139	$x y^{''} = {y^{'}}^{2} - y^{'}$	[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]]	✓	0.312

15140	$x y^{''} - {y^{'}}^{2} = 6 x^{5}$	[[_2nd_order, _missing_y]]	✓	1.506

15141	$y y^{''} - {y^{'}}^{2} = y^{'}$	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]	✓	0.348

15142	$y^{''} = 2 y^{'} - 6$	[[_2nd_order, _missing_x]]	✓	2.042

15143	$(y - 3) y^{''} = 2 {y^{'}}^{2}$	[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]	✓	0.215

15144	$y^{''} + 4 y^{'} = 9 e^{- 3 x}$	[[_2nd_order, _missing_y]]	✓	1.983

15145	$y^{'''} = y^{''}$	[[_3rd_order, _missing_x]]	✓	0.045

15146	$x y^{'''} + 2 y^{''} = 6 x$	[[_3rd_order, _missing_y]]	✓	0.127

15147	$y^{'''} = 2 \sqrt{y^{''}}$	[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]]	✓	0.998

15148	$y^{''''} = - 2 y^{'''}$	[[_high_order, _missing_x]]	✓	0.053

15149	$y y^{''} = {y^{'}}^{2}$ i.c.	[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]	✓	0.584

15150	$3 y y^{''} = 2 {y^{'}}^{2}$ i.c.	[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]	✓	0.552

15151	$\sin (y) y^{''} + \cos (y) {y^{'}}^{2} = 0$	[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]	✓	0.717

15152	$y^{''} = y^{'}$	[[_2nd_order, _missing_x]]	✓	1.622

15153	${y^{'}}^{2} + y y^{''} = 2 y y^{'}$	[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]	✓	2.039

15154	$y^{2} y^{''} + y^{''} + 2 y {y^{'}}^{2} = 0$	[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]	✓	0.472

15155	$y^{''} = 4 x \sqrt{y^{'}}$	[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]]	✓	0.369

15156	$y^{'} y^{''} = 1$	[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_poly_yn]]	✓	1.924

15157	$x y^{''} = {y^{'}}^{2} - y^{'}$	[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]]	✓	0.308

15158	$x y^{''} - y^{'} = 6 x^{5}$	[[_2nd_order, _missing_y]]	✓	1.043

15159	$y y^{''} - {y^{'}}^{2} = y^{'}$	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]	✓	0.346

15160	$y y^{''} = 2 {y^{'}}^{2}$	[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]	✓	0.270

15161	$(y - 3) y^{''} = {y^{'}}^{2}$	[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]	✓	0.279

15162	$y^{''} + 4 y^{'} = 9 e^{- 3 x}$	[[_2nd_order, _missing_y]]	✓	2.081

15163	$y^{''} = y^{'} (y^{'} - 2)$	[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]]	✓	0.971

15164	$x y^{''} + 4 y^{'} = 18 x^{2}$ i.c.	[[_2nd_order, _missing_y]]	✓	1.617

15165	$x y^{''} = 2 y^{'}$ i.c.	[[_2nd_order, _missing_y]]	✓	1.112

15166	$y^{''} = y^{'}$ i.c.	[[_2nd_order, _missing_x]]	✓	2.134

15167	$y^{''} + 2 y^{'} = 8 e^{2 x}$ i.c.	[[_2nd_order, _missing_y]]	✓	1.964

15168	$y^{'''} = y^{''}$ i.c.	[[_3rd_order, _missing_x]]	✓	0.120

15169	$x y^{'''} + 2 y^{''} = 6 x$ i.c.	[[_3rd_order, _missing_y]]	✓	0.210

15170	$x y^{''} + 2 y^{'} = 6$ i.c.	[[_2nd_order, _missing_y]]	✓	1.413

15171	$2 x y^{'} y^{''} = {y^{'}}^{2} - 1$ i.c.	[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_poly_yn]]	✓	0.747

15172	$3 y y^{''} = 2 {y^{'}}^{2}$ i.c.	[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]	✓	0.476

15173	$y y^{''} + 2 {y^{'}}^{2} = 3 y y^{'}$ i.c.	[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]	✓	2.056

15174	$y^{''} = - y^{'} e^{- y}$ i.c.	[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_xy]]	✓	2.388

15175	$y^{''} = - 2 x {y^{'}}^{2}$ i.c.	[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]]	✓	0.425

15176	$y^{''} = - 2 x {y^{'}}^{2}$ i.c.	[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]]	✗	0.536

15177	$y^{''} = - 2 x {y^{'}}^{2}$ i.c.	[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]]	✓	1.132

15178	$y^{''} = - 2 x {y^{'}}^{2}$ i.c.	[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]]	✓	0.547

15179	$y^{''} = 2 y y^{'}$ i.c.	[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Lagerstrom, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]	✓	1.116

15180	$y^{''} = 2 y y^{'}$ i.c.	[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Lagerstrom, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]	✓	15.660

15181	$y^{''} = 2 y y^{'}$ i.c.	[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Lagerstrom, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]	✓	0.923

15182	$y^{''} = 2 y y^{'}$ i.c.	[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Lagerstrom, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]	✓	1.066

15183	$y^{''} + x^{2} y^{'} - 4 y = x^{3}$	[[_2nd_order, _linear, _nonhomogeneous]]	✗	0.695

15184	$y^{''} + x^{2} y^{'} - 4 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	0.685

15185	$y^{''} + x^{2} y^{'} = 4 y$	[[_2nd_order, _with_linear_symmetries]]	✗	0.685

15186	$y^{''} + x^{2} y^{'} + 4 y = y^{3}$	[NONE]	✗	0.132

15187	$x y^{'} + 3 y = e^{2 x}$	[_linear]	✓	1.385

15188	$y^{'''} + y = 0$	[[_3rd_order, _missing_x]]	✓	0.058

15189	$(y + 1) y^{''} = {y^{'}}^{3}$	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]]	✓	0.429

15190	$y^{''} = 2 y^{'} - 5 y + 30 e^{3 x}$	[[_2nd_order, _with_linear_symmetries]]	✓	13.451

15191	$y^{''''} + 6 y^{''} + 3 y^{'} - 83 y - 25 = 0$	[[_high_order, _missing_x]]	✓	0.138

15192	$y y^{'''} + 6 y^{''} + 3 y^{'} = y$	[[_3rd_order, _missing_x], [_3rd_order, _with_linear_symmetries]]	✗	0.035

15193	$y^{''} - 5 y^{'} + 6 y = 0$	[[_2nd_order, _missing_x]]	✓	0.271

15194	$y^{''} - 10 y^{'} + 25 y = 0$	[[_2nd_order, _missing_x]]	✓	0.254

15195	$x^{2} y^{''} - 6 x y^{'} + 12 y = 0$	[[_Emden, _Fowler]]	✓	0.085

15196	$2 x^{2} y^{''} - x y^{'} + y = 0$	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	0.101

15197	$4 x^{2} y^{''} + y = 0$	[[_Emden, _Fowler]]	✓	0.082

15198	$y^{''} - (4 + \frac{2}{x}) y^{'} + (4 + \frac{4}{x}) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.104

15199	$(x + 1) y^{''} + x y^{'} - y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.109

15200	$y^{''} - \frac{y^{'}}{x} - 4 x^{2} y = 0$	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	0.111

2.2.152 Problems 15101 to 15200