Problems 3601 to 3700

Table 2.75: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	time (sec)

3601	$y^{'} = \frac{x (- 1 + y^{2})}{2 (x - 2) (x - 1)}$	[_separable]	✓	2.897

3602	$y^{'} = \frac{x^{2} y - 32}{- x^{2} + 16} + 2$	[_separable]	✓	1.494

3603	$(x - a) (x - b) y^{'} - y + c = 0$	[_separable]	✓	2.217

3604	$(x^{2} + 1) y^{'} + y^{2} = - 1$ i.c.	[_separable]	✓	2.128

3605	$(- x^{2} + 1) y^{'} + x y = a x$ i.c.	[_separable]	✓	1.332

3606	$y^{'} = 1 - \frac{\sin (x + y)}{\sin (y) \cos (x)}$ i.c.	[_separable]	✓	3.425

3607	$y^{'} = y^{3} \sin (x)$ i.c.	[_separable]	✓	2.800

3608	$y^{'} = \frac{2 \sqrt{- 1 + y}}{3}$ i.c.	[_quadrature]	✓	1.074

3609	$m v^{'} = m g - k v^{2}$ i.c.	[_quadrature]	✓	1.854

3610	$y^{'} + y = 4 e^{x}$	[[_linear, ‘class A‘]]	✓	0.203

3611	$y^{'} + \frac{2 y}{x} = 5 x^{2}$	[_linear]	✓	0.156

3612	$x^{2} y^{'} - 4 x y = x^{7} \sin (x)$	[_linear]	✓	0.225

3613	$y^{'} + 2 x y = 2 x^{3}$	[_linear]	✓	0.203

3614	$y^{'} + \frac{2 x y}{- x^{2} + 1} = 4 x$	[_linear]	✓	0.181

3615	$y^{'} + \frac{2 x y}{x^{2} + 1} = \frac{4}{{(x^{2} + 1)}^{2}}$	[_linear]	✓	0.205

3616	$2 \cos {(x)}^{2} y^{'} + y \sin (2 x) = 4 \cos {(x)}^{4}$	[_linear]	✓	0.262

3617	$y^{'} + \frac{y}{x \ln (x)} = 9 x^{2}$	[_linear]	✓	0.170

3618	$y^{'} - y \tan (x) = 8 \sin {(x)}^{3}$	[_linear]	✓	0.262

3619	$x^{'} t + 2 x = 4 e^{t}$	[_linear]	✓	0.197

3620	$y^{'} = \sin (x) (y \sec (x) - 2)$	[_linear]	✓	2.188

3621	$1 - y \sin (x) - \cos (x) y^{'} = 0$	[_linear]	✓	0.292

3622	$y^{'} - \frac{y}{x} = 2 x^{2} \ln (x)$	[_linear]	✓	0.177

3623	$y^{'} + α y = e^{β x}$	[[_linear, ‘class A‘]]	✓	0.175

3624	$y^{'} + \frac{m y}{x} = \ln (x)$	[_linear]	✓	0.204

3625	$y^{'} + \frac{2 y}{x} = 4 x$ i.c.	[_linear]	✓	0.338

3626	$y^{'} \sin (x) - \cos (x) y = \sin (2 x)$ i.c.	[_linear]	✓	3.091

3627	$x^{'} + \frac{2 x}{4 - t} = 5$ i.c.	[_linear]	✓	1.737

3628	$y - e^{x} + y^{'} = 0$ i.c.	[[_linear, ‘class A‘]]	✓	1.375

3629	$y^{'} - 2 y = {\begin{array}{cc} 1 & x \leq 1 \\ 0 & 1 < x \end{array}$ i.c.	[[_linear, ‘class A‘]]	✓	0.801

3630	$y^{'} - 2 y = {\begin{array}{cc} 1 - x & x < 1 \\ 0 & 1 \leq x \end{array}$ i.c.	[[_linear, ‘class A‘]]	✓	0.805

3631	$y^{''} + \frac{y^{'}}{x} = 9 x$	[[_2nd_order, _missing_y]]	✓	0.745

3632	$y^{'} + \frac{y}{x} = \cos (x)$	[_linear]	✓	1.334

3633	$y^{'} + y = e^{- 2 x}$	[[_linear, ‘class A‘]]	✓	1.093

3634	$y^{'} + \cot (x) y = 2 \cos (x)$	[_linear]	✓	1.935

3635	$y^{'} x - y = x^{2} \ln (x)$	[_linear]	✓	0.974

3636	$y^{'} = \frac{x^{2} + x y + y^{2}}{x^{2}}$	[[_homogeneous, ‘class A‘], _rational, _Riccati]	✓	2.004

3637	$(3 x - y) y^{'} = 3 y$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	2.864

3638	$y^{'} = \frac{{(x + y)}^{2}}{2 x^{2}}$	[[_homogeneous, ‘class A‘], _rational, _Riccati]	✓	2.107

3639	$\sin (\frac{y}{x}) (y^{'} x - y) = x \cos (\frac{y}{x})$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	6.212

3640	$y^{'} x = \sqrt{16 x^{2} - y^{2}} + y$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	119.772

3641	$y^{'} x - y = \sqrt{9 x^{2} + y^{2}}$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	5.804

3642	$y (x^{2} - y^{2}) - x (x^{2} - y^{2}) y^{'} = 0$	[_separable]	✓	1.536

3643	$y^{'} x + y \ln (x) = y \ln (y)$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	3.654

3644	$y^{'} = \frac{y^{2} + 2 x y - 2 x^{2}}{x^{2} - x y + y^{2}}$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	6.163

3645	$2 x y^{'} y - 2 y^{2} - x^{2} e^{- \frac{y^{2}}{x^{2}}} = 0$	[[_homogeneous, ‘class A‘]]	✓	4.697

3646	$x^{2} y^{'} = y^{2} + 3 x y + x^{2}$	[[_homogeneous, ‘class A‘], _rational, _Riccati]	✓	1.656

3647	$y y^{'} = \sqrt{x^{2} + y^{2}} - x$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	6.161

3648	$2 x (2 x + y) y^{'} = y (4 x - y)$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	3.816

3649	$y^{'} x = x \tan (\frac{y}{x}) + y$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	3.862

3650	$y^{'} = \frac{x \sqrt{x^{2} + y^{2}} + y^{2}}{x y}$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	30.165

3651	$y^{'} = \frac{- 2 x + 4 y}{x + y}$ i.c.	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	13.461

3652	$y^{'} = \frac{2 x - y}{x + 4 y}$ i.c.	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	4.257

3653	$y^{'} = \frac{y - \sqrt{x^{2} + y^{2}}}{x}$ i.c.	[[_homogeneous, ‘class A‘], _dAlembert]	✓	4.023

3654	$y^{'} x - y = \sqrt{4 x^{2} - y^{2}}$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	145.237

3655	$y^{'} = \frac{x + a y}{a x - y}$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	4.769

3656	$y^{'} = \frac{x + \frac{y}{2}}{\frac{x}{2} - y}$ i.c.	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	26.410

3657	$y^{'} - \frac{y}{x} = \frac{4 x^{2} \cos (x)}{y}$	[[_homogeneous, ‘class D‘], _Bernoulli]	✓	3.465

3658	$y^{'} + \frac{y \tan (x)}{2} = 2 y^{3} \sin (x)$	[_Bernoulli]	✓	10.848

3659	$y^{'} - \frac{3 y}{2 x} = 6 y^{1 / 3} x^{2} \ln (x)$	[_Bernoulli]	✓	2.478

3660	$y^{'} + \frac{2 y}{x} = 6 \sqrt{x^{2} + 1} \sqrt{y}$	[_Bernoulli]	✓	2.525

3661	$y^{'} + \frac{2 y}{x} = 6 x^{4} y^{2}$	[[_homogeneous, ‘class G‘], _rational, _Bernoulli]	✓	1.941

3662	$2 x (y^{'} + x^{2} y^{3}) + y = 0$	[[_homogeneous, ‘class G‘], _rational, _Bernoulli]	✓	3.037

3663	$(x - a) (x - b) (y^{'} - \sqrt{y}) = 2 (b - a) y$	[_rational, _Bernoulli]	✓	3.512

3664	$y^{'} + \frac{6 y}{x} = \frac{3 y^{2 / 3} \cos (x)}{x}$	[_Bernoulli]	✓	3.243

3665	$y^{'} + 4 x y = 4 x^{3} \sqrt{y}$	[_Bernoulli]	✓	1.551

3666	$y^{'} - \frac{y}{2 x \ln (x)} = 2 x y^{3}$	[_Bernoulli]	✓	1.907

3667	$y^{'} - \frac{y}{(π - 1) x} = \frac{3 x y^{π}}{1 - π}$	[[_homogeneous, ‘class G‘], _rational, _Bernoulli]	✓	3.798

3668	$2 y^{'} + \cot (x) y = \frac{8 \cos {(x)}^{3}}{y}$	[_Bernoulli]	✓	43.383

3669	$(1 - \sqrt{3}) y^{'} + y \sec (x) = y^{\sqrt{3}} \sec (x)$	[_separable]	✓	6.089

3670	$y^{'} + \frac{2 x y}{x^{2} + 1} = x y^{2}$ i.c.	[_rational, _Bernoulli]	✓	2.160

3671	$y^{'} + \cot (x) y = y^{3} \sin {(x)}^{3}$ i.c.	[_Bernoulli]	✓	6.067

3672	$y^{'} = {(9 x - y)}^{2}$ i.c.	[[_homogeneous, ‘class C‘], _Riccati]	✓	2.268

3673	$y^{'} = {(4 x + y + 2)}^{2}$	[[_homogeneous, ‘class C‘], _Riccati]	✓	15.074

3674	$y^{'} = \sin {(3 x - 3 y + 1)}^{2}$	[[_homogeneous, ‘class C‘], _dAlembert]	✓	26.065

3675	$y^{'} = \frac{y (\ln (x y) - 1)}{x}$	[[_homogeneous, ‘class G‘]]	✓	1.878

3676	$y^{'} = 2 x {(x + y)}^{2} - 1$ i.c.	[[_1st_order, _with_linear_symmetries], _Riccati]	✓	2.051

3677	$y^{'} = \frac{x + 2 y - 1}{2 x - y + 3}$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	2.583

3678	$y^{'} + p (x) y + q (x) y^{2} = r (x)$	[_Riccati]	✗	2.959

3679	$y^{'} + \frac{2 y}{x} - y^{2} = - \frac{2}{x^{2}}$	[[_homogeneous, ‘class G‘], _rational, _Riccati]	✓	2.063

3680	$y^{'} + \frac{7 y}{x} - 3 y^{2} = \frac{3}{x^{2}}$	[[_homogeneous, ‘class G‘], _rational, _Riccati]	✓	1.507

3681	$\frac{y^{'}}{y} + p (x) \ln (y) = q (x)$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✓	1.953

3682	$\frac{y^{'}}{y} - \frac{2 \ln (y)}{x} = \frac{1 - 2 \ln (x)}{x}$ i.c.	[[_homogeneous, ‘class A‘], _dAlembert]	✓	4.051

3683	$\sec {(y)}^{2} y^{'} + \frac{\tan (y)}{2 \sqrt{x + 1}} = \frac{1}{2 \sqrt{x + 1}}$	[_separable]	✓	26.081

3684	$y e^{x y} + (2 y - x e^{x y}) y^{'} = 0$	[‘x=_G(y,y’)‘]	✗	1.704

3685	$\cos (x y) - x y \sin (x y) - x^{2} \sin (x y) y^{'} = 0$	[[_homogeneous, ‘class G‘], _exact]	✓	0.427

3686	$y + 3 x^{2} + y^{'} x = 0$	[_linear]	✓	0.194

3687	$2 x e^{y} + (3 y^{2} + x^{2} e^{y}) y^{'} = 0$	[_exact, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]	✓	0.302

3688	$(x^{2} + 1) y^{'} + 2 x y = 0$	[_separable]	✓	0.191

3689	$y^{2} - 2 x + 2 x y^{'} y = 0$	[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli]	✓	0.408

3690	$4 e^{2 x} + 2 x y - y^{2} + {(x - y)}^{2} y^{'} = 0$	[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]]	✓	0.634

3691	$\frac{1}{x} - \frac{y}{x^{2} + y^{2}} + \frac{x y^{'}}{x^{2} + y^{2}} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, _Riccati]	✓	0.339

3692	$y \cos (x y) - \sin (x) + x \cos (x y) y^{'} = 0$	[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✓	0.283

3693	$2 y^{2} e^{2 x} + 3 x^{2} + 2 y e^{2 x} y^{'} = 0$	[_exact, _Bernoulli]	✓	0.593

3694	$y^{2} + \cos (x) + (2 x y + \sin (y)) y^{'} = 0$	[_exact]	✓	0.315

3695	$\sin (y) + \cos (x) y + (x \cos (y) + \sin (x)) y^{'} = 0$	[_exact]	✓	0.293

3696	$y^{''} - 2 y^{'} - 3 y = 0$	[[_2nd_order, _missing_x]]	✓	0.325

3697	$y^{''} + 7 y^{'} + 10 y = 0$	[[_2nd_order, _missing_x]]	✓	0.342

3698	$y^{''} - 36 y = 0$	[[_2nd_order, _missing_x]]	✓	1.522

3699	$y^{''} + 4 y^{'} = 0$	[[_2nd_order, _missing_x]]	✓	1.063

3700	$y^{'''} - 3 y^{''} - y^{'} + 3 y = 0$	[[_3rd_order, _missing_x]]	✓	0.082

2.2.37 Problems 3601 to 3700