Problems 3301 to 3400

Table 2.69: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	time (sec)

3301	$4 x - 2 y y^{'} + x {y^{'}}^{2} = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	1.913

3302	$2 x^{2} y + {y^{'}}^{2} = x^{3} y^{'}$	[[_1st_order, _with_linear_symmetries]]	✓	2.175

3303	$y {y^{'}}^{2} = 3 y^{'} x + y$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	51.696

3304	$8 x + 1 = y {y^{'}}^{2}$	[[_homogeneous, ‘class C‘], _rational, _dAlembert]	✓	1.316

3305	$y {y^{'}}^{2} + 2 y^{'} + 1 = 0$	[_quadrature]	✓	2.807

3306	$(1 + {y^{'}}^{2}) x = (x + y) y^{'}$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	3.120

3307	$x^{2} - 3 y y^{'} + x {y^{'}}^{2} = 0$	[[_homogeneous, ‘class G‘], _rational]	✓	4.736

3308	$2 y^{'} x + y = x {y^{'}}^{2}$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	2.588

3309	$x = {y^{'}}^{2} + y^{'}$	[_quadrature]	✓	0.323

3310	$x = y - {y^{'}}^{3}$	[[_homogeneous, ‘class C‘], _dAlembert]	✓	0.637

3311	$x + 2 y y^{'} = x {y^{'}}^{2}$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	1.266

3312	$4 x - 2 y y^{'} + x {y^{'}}^{2} = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	1.684

3313	$x {y^{'}}^{3} = y y^{'} + 1$	[_dAlembert]	✓	0.317

3314	$y (1 + {y^{'}}^{2}) = 2 y^{'} x$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	1.989

3315	$2 x + x {y^{'}}^{2} = 2 y y^{'}$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	1.782

3316	$x = y y^{'} + {y^{'}}^{2}$	[_dAlembert]	✓	1.733

3317	$4 x {y^{'}}^{2} + 2 y^{'} x = y$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	36.821

3318	$y = y^{'} x (y^{'} + 1)$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	2.234

3319	$2 x {y^{'}}^{3} + 1 = y {y^{'}}^{2}$	[[_1st_order, _with_linear_symmetries], _dAlembert]	✓	0.643

3320	${y^{'}}^{3} + x y^{'} y = 2 y^{2}$	[[_1st_order, _with_linear_symmetries]]	✓	8.780

3321	$3 {y^{'}}^{4} x = y {y^{'}}^{3} + 1$	[[_1st_order, _with_linear_symmetries], _dAlembert]	✓	2.681

3322	$2 {y^{'}}^{5} + 2 y^{'} x = y$	[_dAlembert]	✓	0.908

3323	$\frac{1}{{y^{'}}^{2}} + y^{'} x = 2 y$	[[_1st_order, _with_linear_symmetries], _dAlembert]	✓	23.898

3324	$2 y = 3 y^{'} x + 4 + 2 \ln (y^{'})$	[[_1st_order, _with_linear_symmetries], _dAlembert]	✓	45.154

3325	$y = y^{'} x + {y^{'}}^{2}$	[[_1st_order, _with_linear_symmetries], _Clairaut]	✓	0.493

3326	$y = y^{'} x + \frac{1}{y^{'}}$	[[_homogeneous, ‘class G‘], _rational, _Clairaut]	✓	0.541

3327	$y = y^{'} x - \sqrt{y^{'}}$	[[_homogeneous, ‘class G‘], _Clairaut]	✓	0.988

3328	$y = y^{'} x + \ln (y^{'})$	[[_1st_order, _with_linear_symmetries], _Clairaut]	✓	2.252

3329	$y = y^{'} x + \frac{3}{{y^{'}}^{2}}$	[[_1st_order, _with_linear_symmetries], _Clairaut]	✓	0.686

3330	$y = y^{'} x - {y^{'}}^{2 / 3}$	[[_1st_order, _with_linear_symmetries], _Clairaut]	✓	1.555

3331	$y = y^{'} x + e^{y^{'}}$	[[_1st_order, _with_linear_symmetries], _Clairaut]	✓	1.404

3332	${(y - y^{'} x)}^{2} = 1 + {y^{'}}^{2}$	[[_1st_order, _with_linear_symmetries], _rational, _Clairaut]	✓	0.693

3333	$x {y^{'}}^{2} - y y^{'} - 2 = 0$	[[_homogeneous, ‘class G‘], _rational, _Clairaut]	✓	0.545

3334	$y^{2} - 2 x y^{'} y + {y^{'}}^{2} (x^{2} - 1) = 0$	[_separable]	✓	0.548

3335	$y^{'} = \sqrt{1 - y}$ i.c.	[_quadrature]	✓	0.214

3336	$y^{'} = x y - x^{2}$ i.c.	[_linear]	✓	0.431

3337	$y^{'} = x^{2} y^{2}$ i.c.	[_separable]	✓	0.250

3338	$y^{'} = 3 x + \frac{y}{x}$ i.c.	[_linear]	✓	0.432

3339	$y^{'} = \ln (x y)$ i.c.	[‘y=_G(x,y’)‘]	✓	0.368

3340	$y^{'} = 1 + y^{2}$ i.c.	[_quadrature]	✓	0.325

3341	$y^{'} = x^{2} + y^{2}$ i.c.	[[_Riccati, _special]]	✓	0.375

3342	$y^{'} = \sqrt{x y + 1}$ i.c.	[‘y=_G(x,y’)‘]	✓	0.283

3343	$y^{'} = \cos (x) + \sin (y)$ i.c.	[‘y=_G(x,y’)‘]	✓	0.367

3344	$y^{''} - y = \sin (x)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.538

3345	$y^{''} - 2 y = e^{2 x}$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.566

3346	$y^{''} + 2 y y^{'} = 0$ i.c.	[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Lagerstrom, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]	✓	0.292

3347	$y^{''} = \sin (y)$ i.c.	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	0.615

3348	$y^{''} + \frac{{y^{'}}^{2}}{2} - y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.348

3349	$y^{''} = \sin (x y)$ i.c.	[NONE]	✓	0.922

3350	$y^{''} = \cos (x y)$ i.c.	[NONE]	✓	0.986

3351	$2 x y^{''} + 5 y^{'} + x y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.617

3352	$3 x (3 x + 2) y^{''} - 4 y^{'} + 4 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.909

3353	$x^{2} (x + 4) y^{''} + 7 y^{'} x - y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.886

3354	$2 x^{2} y^{''} + (- x^{2} + x) y^{'} - y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.740

3355	$2 x^{2} y^{''} + 5 y^{'} x + (x + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.807

3356	$9 x^{2} y^{''} + (3 x + 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.821

3357	$(x^{3} + 2 x^{2}) y^{''} - y^{'} x + (1 - x) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.900

3358	$2 x^{2} y^{''} - 3 (x^{2} + x) y^{'} + (3 x + 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.775

3359	$3 x^{2} y^{''} + (- x^{2} + 5 x) y^{'} + (2 x^{2} - 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.918

3360	$4 x^{2} y^{''} + x (x^{2} - 4) y^{'} + 3 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.788

3361	$4 x^{2} y^{''} - 3 (x^{2} + x) y^{'} + 2 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	1.152

3362	$9 x^{2} y^{''} + 9 (- x^{2} + x) y^{'} + (x - 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.882

3363	$4 x^{2} (1 - x) y^{''} + 3 x (2 x + 1) y^{'} - 3 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.878

3364	$2 x^{2} (1 - 3 x) y^{''} + 5 y^{'} x - 2 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.873

3365	$4 x^{2} (x + 1) y^{''} - 5 y^{'} x + 2 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.870

3366	$x^{2} (x + 4) y^{''} + x (x - 1) y^{'} + y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.875

3367	$(8 - x) x^{2} y^{''} + 6 y^{'} x - y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.900

3368	$2 x^{2} y^{''} + x (x^{2} + 1) y^{'} - (x + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.862

3369	$2 x^{2} y^{''} - y^{'} x + (x^{2} + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.704

3370	$3 x^{2} y^{''} + 2 y^{'} x + (x^{2} - 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.697

3371	$x^{3} (x^{2} + 3) y^{''} + 5 y^{'} x - (x + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	0.203

3372	$2 x y^{''} - (x^{3} + 1) y^{'} + y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.822

3373	$x y^{''} + y^{'} + 2 y = 0$	[[_Emden, _Fowler]]	✓	0.595

3374	$x y^{''} + y^{'} + 2 x y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.599

3375	$x^{2} y^{''} - 3 y^{'} x + 4 (x + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.698

3376	$x^{2} y^{''} - x (x + 1) y^{'} + y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.695

3377	$x^{2} y^{''} - x (2 x + 3) y^{'} + 4 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.741

3378	$x^{2} (- x^{2} + 1) y^{''} - 5 y^{'} x + 9 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.651

3379	$x^{2} y^{''} + x (x^{2} - 1) y^{'} + (- x^{2} + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.699

3380	$x^{2} y^{''} + x (2 x - 1) y^{'} + x (x - 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.962

3381	$x^{2} y^{''} - x^{2} y^{'} + (x^{2} - 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.792

3382	$x^{2} y^{''} + 2 x^{2} y^{'} - (3 x^{2} + 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.845

3383	$x^{2} (1 - x) y^{''} + x (x + 1) y^{'} - 9 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.933

3384	$(- x^{2} + x) y^{''} - 3 y^{'} + 2 y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.750

3385	$x^{2} y^{''} + x (x - 7) y^{'} + (x + 12) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	1.628

3386	$x^{2} (x + 1) y^{''} + x (x - 4) y^{'} + 4 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	1.498

3387	$x^{2} y^{''} + x (- x^{2} + 3) y^{'} - 3 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	1.531

3388	$x y^{''} + 3 y^{'} - y = x$	[[_2nd_order, _with_linear_symmetries]]	✓	1.497

3389	$x y^{''} + 3 y^{'} - y = x$	[[_2nd_order, _with_linear_symmetries]]	✓	1.480

3390	$x y^{''} + y^{'} - 2 x y = x^{2}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.661

3391	$x y^{''} - y^{'} x + y = x^{3}$	[[_2nd_order, _with_linear_symmetries]]	✓	1.516

3392	$(- 2 x + 1) y^{''} + 4 y^{'} x - 4 y = x^{2} - x$	[[_2nd_order, _with_linear_symmetries]]	✓	0.538

3393	$x^{2} y^{''} + y^{'} x + (x + 12) y = x^{2} + x$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.119

3394	$x^{2} (x + 1) y^{''} + x (x^{2} + 3) y^{'} + y = - 2 x^{2} + x$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.046

3395	$3 x^{2} (x + 1) y^{''} + x (5 - x) y^{'} + (2 x^{2} - 1) y = - x^{3} + x$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.260

3396	$9 x^{2} y^{''} + (3 x + 2) y = x^{4} + x^{2}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.045

3397	$9 x^{2} y^{''} + 10 y^{'} x + y = x - 1$	[[_2nd_order, _with_linear_symmetries]]	✓	0.711

3398	$2 x^{2} y^{''} + (- x^{2} + x) y^{'} - y = x^{3} + 1$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.013

3399	$(- x^{2} + 1) y^{''} + 2 y^{'} x - 2 y = 6 {(- x^{2} + 1)}^{2}$	[[_2nd_order, _with_linear_symmetries]]	✓	0.365

3400	$(x^{2} + 2 x) y^{''} - (2 x + 2) y^{'} + 2 y = x^{2} {(x + 2)}^{2}$	[[_2nd_order, _with_linear_symmetries]]	✓	1.062

2.2.34 Problems 3301 to 3400