Problems 9101 to 9200

Table 2.185: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	time (sec)

9101	$y^{''} + y^{'} + y = \cos (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.746

9102	$y^{''} + y^{'} = 1$	[[_2nd_order, _missing_x]]	✓	1.098

9103	$y^{''} + y^{'} = x$	[[_2nd_order, _missing_y]]	✓	0.959

9104	$y^{''} + y^{'} = x + 1$	[[_2nd_order, _missing_y]]	✓	0.960

9105	$y^{''} + y^{'} = x^{2} + x + 1$	[[_2nd_order, _missing_y]]	✓	1.079

9106	$y^{''} + y^{'} = x^{3} + x^{2} + x + 1$	[[_2nd_order, _missing_y]]	✓	1.112

9107	$y^{''} + y^{'} = \sin (x)$	[[_2nd_order, _missing_y]]	✓	1.198

9108	$y^{''} + y^{'} = \cos (x)$	[[_2nd_order, _missing_y]]	✓	1.259

9109	$y^{''} + y = 1$	[[_2nd_order, _missing_x]]	✓	1.610

9110	$y^{''} + y = x$	[[_2nd_order, _with_linear_symmetries]]	✓	0.603

9111	$y^{''} + y = x + 1$	[[_2nd_order, _with_linear_symmetries]]	✓	0.598

9112	$y^{''} + y = x^{2} + x + 1$	[[_2nd_order, _with_linear_symmetries]]	✓	0.610

9113	$y^{''} + y = x^{3} + x^{2} + x + 1$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.605

9114	$y^{''} + y = \sin (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.690

9115	$y^{''} + y = \cos (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.739

9116	$y {y^{''}}^{2} + y^{'} = 0$	[[_2nd_order, _missing_x]]	✓	6.921

9117	$y {y^{''}}^{2} + {y^{'}}^{3} = 0$	[[_2nd_order, _missing_x]]	✓	3.077

9118	$y^{2} {y^{''}}^{2} + y^{'} = 0$	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	1.901

9119	$y {y^{''}}^{4} + {y^{'}}^{2} = 0$	[[_2nd_order, _missing_x]]	✓	14.684

9120	$y^{3} {y^{''}}^{2} + y y^{'} = 0$	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	2.078

9121	$y y^{''} + {y^{'}}^{3} = 0$	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]]	✓	0.641

9122	$y {y^{''}}^{3} + y^{3} y^{'} = 0$	[[_2nd_order, _missing_x]]	✓	92.879

9123	$y {y^{''}}^{3} + y^{3} {y^{'}}^{5} = 0$	[[_2nd_order, _missing_x]]	✓	440.728

9124	$y^{''} + y^{'} x + y {y^{'}}^{2} = 0$	[_Liouville, [_2nd_order, _reducible, _mu_xy]]	✓	0.420

9125	$y^{''} + y^{'} \sin (x) + y {y^{'}}^{2} = 0$	[_Liouville, [_2nd_order, _reducible, _mu_xy]]	✓	0.658

9126	$y^{''} + (1 - x) y^{'} + y^{2} {y^{'}}^{2} = 0$	[_Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]	✗	0.269

9127	$y^{''} + (\sin (x) + 2 x) y^{'} + \cos (y) y {y^{'}}^{2} = 0$	[_Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]	✗	0.864

9128	$y^{'} y^{''} + y^{2} = 0$	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	4.634

9129	$y^{'} y^{''} + y^{n} = 0$	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	4.237

9130	$y^{'} = {(x + y)}^{4}$	[[_homogeneous, ‘class C‘], _dAlembert]	✓	340.056

9131	$y^{''} + (3 + x) y^{'} + (3 + y^{2}) {y^{'}}^{2} = 0$	[_Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]	✗	0.287

9132	$y^{''} + y^{'} x + y {y^{'}}^{2} = 0$	[_Liouville, [_2nd_order, _reducible, _mu_xy]]	✓	0.513

9133	$y^{''} + y^{'} \sin (x) + {y^{'}}^{2} = 0$	[[_2nd_order, _missing_y], _Liouville, [_2nd_order, _reducible, _mu_xy]]	✓	1.113

9134	$3 y^{''} + \cos (x) y^{'} + \sin (y) {y^{'}}^{2} = 0$	[_Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]	✓	0.916

9135	$10 y^{''} + x^{2} y^{'} + \frac{3 {y^{'}}^{2}}{y} = 0$	[_Liouville, [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]	✓	0.393

9136	$10 y^{''} + (e^{x} + 3 x) y^{'} + \frac{3 e^{y} {y^{'}}^{2}}{\sin (y)} = 0$	[_Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]	✗	1.261

9137	$y^{''} - \frac{2 y}{x^{2}} = x e^{- \sqrt{x}}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.710

9138	$y^{''} - \frac{y^{'}}{\sqrt{x}} + \frac{(x + \sqrt{x} - 8) y}{4 x^{2}} = x$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.672

9139	$y^{''} + \frac{2 y^{'}}{x} + \frac{a^{2} y}{x^{4}} = 0$	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	0.901

9140	$(- x^{2} + 1) y^{''} - y^{'} x - c^{2} y = 0$	[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	1.286

9141	$x^{6} y^{''} + 3 x^{5} y^{'} + a^{2} y = \frac{1}{x^{2}}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	2.006

9142	$x^{2} y^{''} - 3 y^{'} x + 3 y = 2 x^{3} - x^{2}$	[[_2nd_order, _with_linear_symmetries]]	✓	1.786

9143	$y^{''} + \cot (x) y^{'} + 4 y \csc {(x)}^{2} = 0$	[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	1.282

9144	$(x^{2} + 1) y^{''} + (x + 1) y^{'} + y = 4 \cos (\ln (x + 1))$	[[_2nd_order, _linear, _nonhomogeneous]]	✗	1.944

9145	$y^{''} + y^{'} \tan (x) + \cos {(x)}^{2} y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	1.082

9146	$x y^{''} - y^{'} + 4 x^{3} y = 8 x^{3} \sin {(x)}^{2}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	19.309

9147	$x y^{''} - y^{'} + 4 x^{3} y = x^{5}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.622

9148	$\cos (x) y^{''} + y^{'} \sin (x) - 2 \cos {(x)}^{3} y = 2 \cos {(x)}^{5}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	3.282

9149	$y^{''} + (1 - \frac{1}{x}) y^{'} + 4 x^{2} y e^{- 2 x} = 4 (x^{3} + x^{2}) e^{- 3 x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	2.369

9150	$y^{''} - x^{2} y^{'} + x y = x^{m + 1}$	[[_2nd_order, _with_linear_symmetries]]	✓	1.632

9151	$y^{''} - \frac{y^{'}}{\sqrt{x}} + \frac{(x + \sqrt{x} - 8) y}{4 x^{2}} = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.575

9152	$\cos {(x)}^{2} y^{''} - 2 \cos (x) \sin (x) y^{'} + \cos {(x)}^{2} y = 0$	[_Lienard]	✓	0.908

9153	$y^{''} - 4 y^{'} x + (4 x^{2} - 1) y = - 3 e^{x^{2}} \sin (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.974

9154	$y^{''} - 2 b x y^{'} + b^{2} x^{2} y = x$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	6.532

9155	$y^{''} - 4 y^{'} x + (4 x^{2} - 3) y = e^{x^{2}}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.744

9156	$y^{''} - 2 y^{'} \tan (x) + 5 y = e^{x^{2}} \sec (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.502

9157	$x^{2} y^{''} - 2 y^{'} x + 2 (x^{2} + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.774

9158	$4 x^{2} y^{''} + 4 x^{5} y^{'} + (x^{8} + 6 x^{4} + 4) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.701

9159	$x^{2} y^{''} + {(y^{'} x - y)}^{2} = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	0.288

9160	$x y^{''} + 2 y^{'} - x y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.557

9161	$x y^{''} + 2 y^{'} + x y = 0$	[_Lienard]	✓	0.633

9162	$y^{'} + \cot (x) y = 2 \cos (x)$	[_linear]	✓	2.103

9163	$2 x y^{2} - y + (y^{2} + x + y) y^{'} = 0$	[_rational]	✓	1.643

9164	$y^{'} = x - y^{2}$	[[_Riccati, _special]]	✓	1.445

9165	$y^{''''} - y^{'''} - 3 y^{''} + 5 y^{'} - 2 y = x e^{x} + 3 e^{- 2 x}$	[[_high_order, _linear, _nonhomogeneous]]	✓	0.260

9166	$x^{2} y^{''} - x (6 + x) y^{'} + 10 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	1.476

9167	$x^{2} y^{''} + y^{'} x + (x^{2} - 5) y = 0$	[_Bessel]	✓	0.735

9168	$x^{2} y^{''} + y^{'} x + (x^{2} - 5) y = 0$	[_Bessel]	✓	0.593

9169	$x^{2} y^{''} - 4 y^{'} x + 6 y = 0$	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	1.057

9170	$y^{'''} - x y = 0$	[[_3rd_order, _with_linear_symmetries]]	✗	0.072

9171	$y^{'} = y^{1 / 3}$ i.c.	[_quadrature]	✓	1.340

9172	$[\begin{matrix} x^{'} = 3 x + y \\ y^{'} = - x + y \end{matrix}]$	system_of_ODEs	✓	0.326

9173	$(x^{2} - 1) y^{''} - 2 y^{'} x + 2 y = 0$	[_Gegenbauer]	✓	0.322

9174	$(x^{2} - 1) y^{''} - 6 y^{'} x + 12 y = 0$	[_Gegenbauer]	✓	0.329

9175	$(x^{2} + 3) y^{''} - 7 y^{'} x + 16 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.611

9176	$(x^{2} - 1) y^{''} + 8 y^{'} x + 12 y = 0$	[_Gegenbauer]	✓	0.305

9177	$3 y^{''} + y^{'} x - 4 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.363

9178	$5 y^{''} - 2 y^{'} x + 10 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.428

9179	$y^{''} - x^{2} y^{'} - 3 x y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.424

9180	$(x^{2} + 1) y^{''} + 2 y^{'} x - 2 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.456

9181	$y^{''} + y^{'} x - 2 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.365

9182	$(x^{2} - 6 x + 10) y^{''} - 4 (x - 3) y^{'} + 6 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.442

9183	$(x^{2} + 6 x) y^{''} + (3 x + 9) y^{'} - 3 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.331

9184	$t y^{''} + (t^{2} - 1) y^{'} + t^{2} y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.542

9185	$t^{2} y^{''} - t (t + 2) y^{'} + (t + 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.195

9186	$t y^{''} - (1 + t) y^{'} + y = 0$	[_Laguerre]	✓	0.347

9187	$(1 - t) y^{''} + y^{'} t - y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.358

9188	$x^{2} y^{''} + y^{'} x + (x^{2} - \frac{1}{4}) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.265

9189	$t y^{''} - (1 + t) y^{'} + y = 0$	[_Laguerre]	✓	0.357

9190	$(1 - t) y^{''} + y^{'} t - y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.393

9191	$y^{''} + y^{'} x + 2 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.372

9192	$(x^{2} + 1) y^{''} - 4 y^{'} x + 6 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.411

9193	$(1 - x) y^{''} + y^{'} x - y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.380

9194	$2 y^{''} + y^{'} x + 3 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.459

9195	$y^{''} + y^{'} x + 2 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.338

9196	$(1 - x) y^{''} + y^{'} x - y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.388

9197	$y^{''} + y^{'} x + 2 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.362

9198	$(- x^{2} + 4) y^{''} + y^{'} x + 2 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	1.384

9199	$4 x^{2} y^{''} - 4 y^{'} x + (- 16 x^{2} + 3) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.197

9200	$(x - 1) y^{''} - y^{'} x + y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.360

2.2.92 Problems 9101 to 9200