Problems 3201 to 3300

Table 2.67: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	time (sec)

3201	$y^{'''} + 4 y^{''} + 5 y^{'} = e^{- 2 x} \cos (x)$	[[_3rd_order, _missing_y]]	✓	0.701

3202	$y^{'''} + y^{''} - 2 y^{'} = e^{- 2 x} \cos (2 x)$	[[_3rd_order, _missing_y]]	✓	0.230

3203	$y^{'''} + 2 y^{'} = x^{2} \sin (x)$	[[_3rd_order, _missing_y]]	✓	0.240

3204	$y^{''''} - y = x^{2} \cos (x)$	[[_high_order, _linear, _nonhomogeneous]]	✓	0.754

3205	$y^{''} + 4 y = x \sin (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.781

3206	$y^{''} + y = x^{2} \cos (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.890

3207	$y^{''} - y = x^{2} \cos (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.852

3208	$y^{'''} + 4 y^{'} = e^{x} + \sin (x)$	[[_3rd_order, _missing_y]]	✓	0.213

3209	$y^{(5)} + y^{''''} = x^{2}$	[[_high_order, _missing_y]]	✓	0.163

3210	$2 y^{''} + 3 y^{'} - 2 y = x^{2} e^{x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.540

3211	$y^{'''} + y^{'} = \sin (x)$	[[_3rd_order, _missing_y]]	✓	0.471

3212	$y^{'''} - y^{'} = x \sin (x)$	[[_3rd_order, _missing_y]]	✓	0.191

3213	$y^{'''} + 2 y^{''} = x \cos (2 x)$	[[_3rd_order, _missing_y]]	✓	0.243

3214	$y^{''} + 3 y^{'} + 2 y = x^{2} \cos (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.782

3215	$y^{''} - 4 y^{'} + 3 y = x^{2} \sin (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.786

3216	$y^{''} - y = x \sin (2 x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.789

3217	$y^{''} + 2 y^{'} = x^{3} \sin (2 x)$	[[_2nd_order, _missing_y]]	✓	3.081

3218	$y^{''} - y^{'} = x e^{2 x} \sin (x)$	[[_2nd_order, _missing_y]]	✓	2.287

3219	$y^{''} - 4 y = x e^{2 x} \cos (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.908

3220	$y^{''} + 2 y^{'} = x^{2} e^{- x} \sin (x)$	[[_2nd_order, _missing_y]]	✓	2.155

3221	$x^{2} y^{''} - 4 y^{'} x + y = 0$	[[_Emden, _Fowler]]	✓	1.110

3222	$x^{2} y^{''} + y^{'} x + 16 y = 0$	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	1.010

3223	$4 x^{2} y^{''} - 16 y^{'} x + 25 y = 0$	[[_Emden, _Fowler]]	✓	0.957

3224	$x^{2} y^{''} + 5 y^{'} x + 10 y = 0$	[[_Emden, _Fowler]]	✓	1.137

3225	$2 x^{2} y^{''} - 3 y^{'} x - 18 y = \ln (x)$	[[_2nd_order, _with_linear_symmetries]]	✓	1.290

3226	$2 x^{2} y^{''} - 3 y^{'} x + 2 y = \ln (x^{2})$	[[_2nd_order, _with_linear_symmetries]]	✓	2.230

3227	$x^{2} y^{''} - 3 y^{'} x + 4 y = x^{3}$	[[_2nd_order, _with_linear_symmetries]]	✓	1.447

3228	$x^{2} y^{''} + 3 y^{'} x + y = 1 - x$	[[_2nd_order, _exact, _linear, _nonhomogeneous]]	✓	1.579

3229	$x^{3} y^{'''} + 2 x^{2} y^{''} - y^{'} x + y = \frac{1}{x}$	[[_3rd_order, _exact, _linear, _nonhomogeneous]]	✓	0.300

3230	$x^{2} y^{''} - 2 y^{'} x + 2 y = 4 x + \sin (\ln (x))$	[[_2nd_order, _with_linear_symmetries]]	✓	2.999

3231	$x^{2} y^{''} - y^{'} x + 2 y = x^{2} \ln (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	2.461

3232	$x^{2} y^{''} + 4 y^{'} x + 3 y = (x - 1) \ln (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	75.797

3233	$4 x^{3} y^{'''} + 8 x^{2} y^{''} - y^{'} x + y = x + \ln (x)$	[[_3rd_order, _with_linear_symmetries]]	✓	0.397

3234	$3 x^{3} y^{'''} + 4 x^{2} y^{''} - 10 y^{'} x + 10 y = \frac{4}{x^{2}}$	[[_3rd_order, _with_linear_symmetries]]	✓	0.515

3235	$x^{4} y^{''''} + 7 x^{3} y^{'''} + 9 x^{2} y^{''} - 6 y^{'} x - 6 y = \cos (\ln (x))$	[[_high_order, _exact, _linear, _nonhomogeneous]]	✓	1.455

3236	$x^{3} y^{'''} - 2 x^{2} y^{''} - y^{'} x + 4 y = \sin (\ln (x))$	[[_3rd_order, _linear, _nonhomogeneous]]	✓	1.021

3237	$[\begin{matrix} x^{'} - x = \cos (t) \\ y + y^{'} = 4 t \end{matrix}]$	system_of_ODEs	✓	0.503

3238	$[\begin{matrix} x^{'} + 5 x = 3 t^{2} \\ y + y^{'} = e^{3 t} \end{matrix}]$	system_of_ODEs	✓	0.440

3239	$[\begin{matrix} x^{'} + 2 x = 3 t \\ x^{'} + 2 y^{'} + y = \cos (2 t) \end{matrix}]$	system_of_ODEs	✓	0.934

3240	$[\begin{matrix} x^{'} - x + y = 2 \sin (t) \\ x^{'} + y^{'} = 3 y - 3 x \end{matrix}]$	system_of_ODEs	✓	0.665

3241	$[\begin{matrix} 2 x^{'} + 3 x - y = e^{t} \\ 5 x - 3 y^{'} = y + 2 t \end{matrix}]$	system_of_ODEs	✓	1.243

3242	$[\begin{matrix} 5 y^{'} - 3 x^{'} - 5 y = 5 t \\ 3 x^{'} - 5 y^{'} - 2 x = 0 \end{matrix}]$	system_of_ODEs	✓	0.275

3243	$[\begin{matrix} x^{'} = 3 x \\ y^{'} = 2 x + 3 y \\ z^{'} = 3 y - 2 z \end{matrix}]$	system_of_ODEs	✓	0.493

3244	$y^{''} = \cos (t)$	[[_2nd_order, _quadrature]]	✓	0.935

3245	$y^{''} = k^{2} y$	[[_2nd_order, _missing_x]]	✓	1.714

3246	$x^{''} + k^{2} x = 0$	[[_2nd_order, _missing_x]]	✓	1.546

3247	$y^{3} y^{''} + 4 = 0$	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	2.392

3248	$x^{''} = \frac{k^{2}}{x^{2}}$	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	68.608

3249	$x y^{''} = x^{2} + 1$	[[_2nd_order, _quadrature]]	✓	0.765

3250	$(1 - x) y^{''} = y^{'}$	[[_2nd_order, _missing_y]]	✓	0.956

3251	$(x^{2} + 1) y^{''} + 2 x (y^{'} + 1) = 0$	[[_2nd_order, _missing_y]]	✓	1.229

3252	$y^{''} = {y^{'}}^{3} + y^{'}$	[[_2nd_order, _missing_x]]	✓	1.625

3253	$x y^{''} + x = y^{'}$	[[_2nd_order, _missing_y]]	✓	1.161

3254	$x^{''} + t x^{'} = t^{3}$	[[_2nd_order, _missing_y]]	✓	1.022

3255	$x^{2} y^{''} = y^{'} x + 1$	[[_2nd_order, _missing_y]]	✓	0.752

3256	$y^{''} = 1 + {y^{'}}^{2}$	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]]	✓	1.932

3257	$(- x^{2} + 1) y^{''} + y^{'} x = 1$	[[_2nd_order, _missing_y]]	✓	1.250

3258	$y^{''} = \sqrt{1 + {y^{'}}^{2}}$	[[_2nd_order, _missing_x]]	✓	3.864

3259	$y^{''} = {y^{'}}^{2} + y^{'}$	[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]]	✓	1.358

3260	$y^{''} = y y^{'}$	[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Lagerstrom, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]	✓	1.125

3261	$(x^{2} + 1) y^{''} + 1 + {y^{'}}^{2} = 0$	[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]]	✓	1.065

3262	$y^{''} + y y^{'} = 0$	[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Lagerstrom, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]	✓	1.281

3263	$y^{''} + 2 {y^{'}}^{2} = 0$	[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]]	✓	0.710

3264	$y y^{''} + {y^{'}}^{2} = 0$	[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]	✓	1.400

3265	$y y^{''} + 1 = {y^{'}}^{2}$	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	1.609

3266	$y^{''} = y$	[[_2nd_order, _missing_x]]	✓	1.708

3267	$y y^{''} + {y^{'}}^{2} = y y^{'}$	[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]	✓	1.825

3268	$2 y y^{''} - {y^{'}}^{2} = 0$	[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]	✓	0.589

3269	$y^{''} + 2 {y^{'}}^{2} = 2$	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]]	✓	2.020

3270	$y^{''} + y^{'} = {y^{'}}^{3}$	[[_2nd_order, _missing_x]]	✓	3.950

3271	$(1 + y) y^{''} = 3 {y^{'}}^{2}$	[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]	✓	0.936

3272	$y^{''} = \sec (x) \tan (x)$ i.c.	[[_2nd_order, _quadrature]]	✓	3.899

3273	$2 y^{''} = e^{y}$ i.c.	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	1.595

3274	$y^{''} = y^{3}$ i.c.	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	1.802

3275	$y^{''} = {y^{'}}^{2} \cos (x)$ i.c.	[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]]	✗	2.263

3276	$y y^{''} - y^{2} y^{'} = {y^{'}}^{2}$ i.c.	[[_2nd_order, _missing_x], [_2nd_order, _with_potential_symmetries], [_2nd_order, _reducible, _mu_xy]]	✓	0.998

3277	$(x^{2} + 1) y^{''} + 1 + {y^{'}}^{2} = 0$ i.c.	[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]]	✓	1.174

3278	$y y^{''} = y^{3} + {y^{'}}^{2}$ i.c.	[[_2nd_order, _missing_x]]	✗	156.037

3279	${(1 + {y^{'}}^{2})}^{2} = y^{2} y^{''}$ i.c.	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✗	49.789

3280	$y^{''} = {y^{'}}^{2} \sin (x)$ i.c.	[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]]	✗	1.673

3281	$2 y y^{''} = y^{3} + 2 {y^{'}}^{2}$ i.c.	[[_2nd_order, _missing_x]]	✗	84.617

3282	$x^{''} - k^{2} x = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	1.677

3283	$y y^{''} = 2 {y^{'}}^{2} + y^{2}$ i.c.	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]]	✓	3.397

3284	$(1 - e^{x}) y^{''} = e^{x} y^{'}$ i.c.	[[_2nd_order, _missing_y]]	✓	2.113

3285	$4 y^{2} = x^{2} {y^{'}}^{2}$	[_separable]	✓	1.575

3286	$x y {y^{'}}^{2} + (x + y) y^{'} + 1 = 0$	[_quadrature]	✓	0.454

3287	$1 + (2 y - x^{2}) {y^{'}}^{2} - 2 x^{2} y {y^{'}}^{2} = 0$	[‘y=_G(x,y’)‘]	✗	3.519

3288	$x ({y^{'}}^{2} - 1) = 2 y y^{'}$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	1.331

3289	$(1 - y^{2}) {y^{'}}^{2} = 1$	[_quadrature]	✓	59.707

3290	$x y {y^{'}}^{2} + (x y - 1) y^{'} = y$	[_rational]	✗	11.259

3291	$y^{2} {y^{'}}^{2} + x y^{'} y - 2 x^{2} = 0$	[_separable]	✓	1.108

3292	$y^{2} {y^{'}}^{2} - 2 x y^{'} y + 2 y^{2} = x^{2}$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	3.276

3293	${y^{'}}^{3} + (x + y - 2 x y) {y^{'}}^{2} - 2 y^{'} x y (x + y) = 0$	[_quadrature]	✓	0.633

3294	$y {y^{'}}^{2} + (y^{2} - x^{3} - x y^{2}) y^{'} - x y (x^{2} + y^{2}) = 0$	[_quadrature]	✓	0.753

3295	$y = y^{'} x (y^{'} + 1)$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	2.420

3296	$y = x + 3 \ln (y^{'})$	[_separable]	✓	3.549

3297	$y (1 + {y^{'}}^{2}) = 2$	[_quadrature]	✓	0.607

3298	$y {y^{'}}^{2} - 2 y^{'} x + y = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	2.058

3299	${y^{'}}^{2} + y^{2} = 1$	[_quadrature]	✓	0.989

3300	$x ({y^{'}}^{2} - 1) = 2 y y^{'}$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	1.267

2.2.33 Problems 3201 to 3300