Problems 8701 to 8800

Table 2.177: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	time (sec)

8701	$y^{'} = \frac{2 x - y}{x + 4 y}$ i.c.	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	5.102

8702	$y^{'} + \frac{2 y}{x} = 6 y^{2} x^{4}$	[[_homogeneous, ‘class G‘], _rational, _Bernoulli]	✓	2.401

8703	$y^{2} + \cos (x) + (2 x y + \sin (y)) y^{'} = 0$	[_exact]	✓	0.337

8704	$x y - 1 + x^{2} y^{'} = 0$	[_linear]	✓	0.275

8705	$y^{''} - y^{'} - 2 y = 5 e^{2 x}$	[[_2nd_order, _with_linear_symmetries]]	✓	1.200

8706	$y^{''} + 16 y = 4 \cos (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	3.526

8707	$y^{''} - 4 y^{'} + 3 y = 9 x^{2} + 4$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	1.260

8708	$y^{''} + y = \tan {(x)}^{2}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	3.579

8709	$[\begin{matrix} x^{'} = - 2 x + 3 y \\ y^{'} = - 2 x + 5 y \end{matrix}]$ i.c.	system_of_ODEs	✓	0.586

8710	$[\begin{matrix} x^{'} = - x + 4 y \\ y^{'} = 2 x - 3 y \end{matrix}]$ i.c.	system_of_ODEs	✓	0.590

8711	$[\begin{matrix} x^{'} = 2 x - y \\ y^{'} = - x + 2 y + 4 e^{t} \end{matrix}]$	system_of_ODEs	✓	0.448

8712	$[\begin{matrix} x^{'} = 6 x - 7 y + 10 \\ y^{'} = x - 2 y - 2 e^{t} \end{matrix}]$	system_of_ODEs	✓	0.516

8713	$y^{'} = \frac{\cos (y) \sec (x)}{x}$	[_separable]	✓	3.084

8714	$y^{'} = x (\cos (y) + y)$	[_separable]	✓	1.924

8715	$y^{'} = \frac{\sec (x) (\sin (y) + y)}{x}$	[_separable]	✓	3.716

8716	$y^{'} = (5 + \frac{\sec (x)}{x}) (\sin (y) + y)$	[_separable]	✓	13.742

8717	$y^{'} = y + 1$	[_quadrature]	✓	1.374

8718	$y^{'} = x + 1$	[_quadrature]	✓	0.452

8719	$y^{'} = x$	[_quadrature]	✓	0.450

8720	$y^{'} = y$	[_quadrature]	✓	1.563

8721	$y^{'} = 0$	[_quadrature]	✓	0.440

8722	$y^{'} = 1 + \frac{\sec (x)}{x}$	[_quadrature]	✓	0.761

8723	$y^{'} = x + \frac{\sec (x) y}{x}$	[_linear]	✓	6.469

8724	$y^{'} = \frac{2 y}{x}$ i.c.	[_separable]	✓	2.639

8725	$y^{'} = \frac{2 y}{x}$	[_separable]	✓	2.267

8726	$y^{'} = \frac{\ln (1 + y^{2})}{\ln (x^{2} + 1)}$	[_separable]	✓	2.018

8727	$y^{'} = \frac{1}{x}$	[_quadrature]	✓	0.441

8728	$y^{'} = \frac{- x y - 1}{4 x^{3} y - 2 x^{2}}$	[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	2.786

8729	$\frac{{y^{'}}^{2}}{4} - x y^{'} + y = 0$	[[_1st_order, _with_linear_symmetries], _Clairaut]	✓	0.411

8730	$y^{'} = \sqrt{\frac{y + 1}{y^{2}}}$ i.c.	[_quadrature]	✓	1687.005

8731	$y^{'} = \sqrt{1 - x^{2} - y^{2}}$	[‘y=_G(x,y’)‘]	✗	1.580

8732	$y^{'} + \frac{y}{3} = \frac{(1 - 2 x) y^{4}}{3}$	[_Bernoulli]	✓	2.260

8733	$y^{'} = \sqrt{y} + x$	[[_1st_order, _with_linear_symmetries], _Chini]	✓	10.400

8734	$x^{2} y^{'} + y^{2} = x y y^{'}$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	40.740

8735	$y = x y^{'} + x^{2} {y^{'}}^{2}$	[_separable]	✓	0.436

8736	$(x + y) y^{'} = 0$	[_quadrature]	✓	0.524

8737	$x y^{'} = 0$	[_quadrature]	✓	0.443

8738	$\frac{y^{'}}{x + y} = 0$	[_quadrature]	✓	0.496

8739	$\frac{y^{'}}{x} = 0$	[_quadrature]	✓	0.449

8740	$y^{'} = 0$	[_quadrature]	✓	0.439

8741	$y = x {y^{'}}^{2} + {y^{'}}^{2}$	[[_homogeneous, ‘class C‘], _rational, _dAlembert]	✓	0.508

8742	$y^{'} = \frac{5 x^{2} - x y + y^{2}}{x^{2}}$	[[_homogeneous, ‘class A‘], _rational, _Riccati]	✓	2.816

8743	$2 t + 3 x + (x + 2) x^{'} = 0$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	3.546

8744	$y^{'} = \frac{1}{1 - y}$ i.c.	[_quadrature]	✓	2.230

8745	$p^{'} = a p - b p^{2}$ i.c.	[_quadrature]	✓	5.109

8746	$y^{2} + \frac{2}{x} + 2 x y y^{'} = 0$	[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli]	✓	2.407

8747	$x f^{'} - f = \frac{{f^{'}}^{2} {(1 - {f^{'}}^{λ})}^{2}}{λ^{2}}$	[_Clairaut]	✓	5.423

8748	$x y^{'} - 2 y + b y^{2} = c x^{4}$	[_rational, _Riccati]	✓	2.250

8749	$x y^{'} - y + y^{2} = x^{2 / 3}$	[_rational, _Riccati]	✓	11.816

8750	$u^{'} + u^{2} = \frac{1}{x^{4 / 5}}$	[_rational, _Riccati]	✓	0.439

8751	$y y^{'} - y = x$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	3.945

8752	$y^{''} + 2 y^{'} + y = 0$	[[_2nd_order, _missing_x]]	✓	0.947

8753	$5 y^{''} + 2 y^{'} + 4 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	2.777

8754	$y^{''} + y^{'} + 4 y = 1$	[[_2nd_order, _missing_x]]	✓	14.192

8755	$y^{''} + y^{'} + 4 y = \sin (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	75.832

8756	$y = x {y^{'}}^{2}$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	2.406

8757	$y y^{'} = 1 - x {y^{'}}^{3}$	[_dAlembert]	✓	0.300

8758	$f^{'} = \frac{1}{f}$	[_quadrature]	✓	1.826

8759	$t y^{''} + 4 y^{'} = t^{2}$	[[_2nd_order, _missing_y]]	✓	1.108

8760	$(t^{2} + 9) y^{''} + 2 t y^{'} = 0$ i.c.	[[_2nd_order, _missing_y]]	✓	1.335

8761	$t^{2} y^{''} - 3 t y^{'} + 5 y = 0$	[[_Emden, _Fowler]]	✓	3.406

8762	$t y^{''} + y^{'} = 0$	[[_2nd_order, _missing_y]]	✓	0.722

8763	$t^{2} y^{''} - 2 y^{'} = 0$	[[_2nd_order, _missing_y]]	✓	0.834

8764	$y^{''} + \frac{(t^{2} - 1) y^{'}}{t} + \frac{t^{2} y}{{(1 + e^{\frac{t^{2}}{2}})}^{2}} = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	0.867

8765	$t y^{''} - y^{'} + 4 t^{3} y = 0$	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	1.141

8766	$y^{''} = 0$	[[_2nd_order, _quadrature]]	✓	1.894

8767	$y^{''} = 1$	[[_2nd_order, _quadrature]]	✓	2.096

8768	$y^{''} = f (t)$	[[_2nd_order, _quadrature]]	✓	0.482

8769	$y^{''} = k$	[[_2nd_order, _quadrature]]	✓	2.152

8770	$y^{'} = - 4 \sin (x - y) - 4$	[[_homogeneous, ‘class C‘], _dAlembert]	✓	73.916

8771	$y^{'} + \sin (x - y) = 0$	[[_homogeneous, ‘class C‘], _dAlembert]	✓	2.297

8772	$y^{''} = 4 \sin (x) - 4$	[[_2nd_order, _quadrature]]	✓	2.196

8773	$y y^{''} = 0$	[[_2nd_order, _quadrature]]	✓	0.148

8774	$y y^{''} = 1$	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	0.724

8775	$y y^{''} = x$	[[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]]	✗	0.103

8776	$y^{2} y^{''} = x$	[[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]]	✗	0.107

8777	$y^{2} y^{''} = 0$	[[_2nd_order, _quadrature]]	✓	0.158

8778	$3 y y^{''} = \sin (x)$	[NONE]	✗	0.300

8779	$3 y y^{''} + y = 5$	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	32.918

8780	$a y y^{''} + b y = c$	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	1.676

8781	$a y^{2} y^{''} + b y^{2} = c$	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	1.796

8782	$a y y^{''} + b y = 0$	[[_2nd_order, _quadrature]]	✓	0.622

8783	$[\begin{matrix} x^{'} = 9 x + 4 y \\ y^{'} = - 6 x - y \\ z^{'} = 6 x + 4 y + 3 z \end{matrix}]$	system_of_ODEs	✓	0.392

8784	$[\begin{matrix} x^{'} = x - 3 y \\ y^{'} = 3 x + 7 y \end{matrix}]$	system_of_ODEs	✓	0.438

8785	$[\begin{matrix} x^{'} = x - 2 y \\ y^{'} = 2 x + 5 y \end{matrix}]$	system_of_ODEs	✓	0.427

8786	$[\begin{matrix} x^{'} = 7 x + y \\ y^{'} = - 4 x + 3 y \end{matrix}]$	system_of_ODEs	✓	0.441

8787	$[\begin{matrix} x^{'} = x + y \\ y^{'} = y \\ z^{'} = z \end{matrix}]$	system_of_ODEs	✓	0.328

8788	$[\begin{matrix} x^{'} = 2 x + y - z \\ y^{'} = - x + 2 z \\ z^{'} = - x - 2 y + 4 z \end{matrix}]$	system_of_ODEs	✓	0.375

8789	$x^{'} = 4 A k {(\frac{x}{A})}^{3 / 4} - 3 k x$	[_quadrature]	✓	10.339

8790	$\frac{y^{'} y}{1 + \frac{\sqrt{1 + {y^{'}}^{2}}}{2}} = - x$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	0.836

8791	$\frac{y^{'} y}{1 + \frac{\sqrt{1 + {y^{'}}^{2}}}{2}} = - x$ i.c.	[[_homogeneous, ‘class A‘], _dAlembert]	✓	0.851

8792	$y^{'} = \frac{y (1 + \frac{a^{2} x}{\sqrt{a^{2} (x^{2} + 1)}})}{\sqrt{a^{2} (x^{2} + 1)}}$	[_separable]	✓	38.539

8793	$y^{'} = x^{2} + y^{2}$	[[_Riccati, _special]]	✓	1.151

8794	$y^{'} = 2 \sqrt{y}$ i.c.	[_quadrature]	✓	1.669

8795	$z^{''} + 3 z^{'} + 2 z = 24 e^{- 3 t} - 24 e^{- 4 t}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.120

8796	$y^{'} = \sqrt{1 - y^{2}}$	[_quadrature]	✓	41.197

8797	$y^{'} = x^{2} + y^{2} - 1$	[_Riccati]	✓	1.949

8798	$y^{'} = 2 y (x \sqrt{y} - 1)$ i.c.	[_Bernoulli]	✓	1.569

8799	$y^{''} = \frac{1}{y} - \frac{x y^{'}}{y^{2}}$	[[_2nd_order, _exact, _nonlinear], [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]]	✓	67.281

8800	$y^{''} + y^{'} + y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	2.162

2.2.88 Problems 8701 to 8800