Problems 7701 to 7800

Table 2.157: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	time (sec)

7701	$x^{2} y^{''} + y^{'} x - 4 y = 0$	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	0.804

7702	$x^{2} y^{''} - 5 y^{'} x + 9 y = x^{2}$	[[_2nd_order, _with_linear_symmetries]]	✓	1.266

7703	$x^{3} y^{'''} + 2 x^{2} y^{''} - y^{'} x + y = 0$	[[_3rd_order, _exact, _linear, _homogeneous]]	✓	0.138

7704	$x^{2} y^{''} + y^{'} x + 4 y = 1$	[[_2nd_order, _with_linear_symmetries]]	✓	1.404

7705	$x^{2} y^{''} - 3 y^{'} x + 5 y = 0$	[[_Emden, _Fowler]]	✓	1.034

7706	$x^{2} y^{''} + (- 2 - i) x y^{'} + 3 i y = 0$	[[_Emden, _Fowler]]	✓	1.376

7707	$x^{2} y^{''} + y^{'} x - 4 π y = x$	[[_2nd_order, _with_linear_symmetries]]	✓	1.504

7708	$x^{2} y^{''} + (x^{2} + x) y^{'} - y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.875

7709	$3 x^{2} y^{''} + x^{6} y^{'} + 2 x y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	1.539

7710	$x^{2} y^{''} - 5 y^{'} + 3 x^{2} y = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	0.200

7711	$x y^{''} + 4 y = 0$	[[_Emden, _Fowler]]	✓	1.237

7712	$(- x^{2} + 1) y^{''} - 2 y^{'} x + 2 y = 0$	[_Gegenbauer]	✓	0.830

7713	${(x^{2} + x - 2)}^{2} y^{''} + 3 (x + 2) y^{'} + (x - 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	1.290

7714	$x^{2} y^{''} + y^{'} \sin (x) + \cos (x) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.766

7715	$x^{2} y^{''} + y^{'} x + (x^{2} - \frac{1}{4}) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.845

7716	$4 x^{2} y^{''} + (4 x^{4} - 5 x) y^{'} + (x^{2} + 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.965

7717	$x^{2} y^{''} + (- 3 x^{2} + x) y^{'} + y e^{x} = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.854

7718	$3 x^{2} y^{''} + 5 y^{'} x + 3 x y = 0$	[[_Emden, _Fowler]]	✓	0.895

7719	$x^{2} y^{''} + y^{'} x + x^{2} y = 0$	[_Lienard]	✓	0.534

7720	$x^{2} y^{''} + x e^{x} y^{'} + y = 0$	[[_Emden, _Fowler]]	✓	0.902

7721	$2 x^{2} y^{''} + (x^{2} + 5 x) y^{'} + (x^{2} - 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	1.024

7722	$4 x^{2} y^{''} - 4 x e^{x} y^{'} + 3 \cos (x) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	1.953

7723	$x^{2} (- x^{2} + 1) y^{''} + 3 (x^{2} + x) y^{'} + y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.988

7724	$x^{2} y^{''} + 3 y^{'} x + (x + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.821

7725	$x^{2} y^{''} + 2 x^{2} y^{'} - 2 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.880

7726	$x^{2} y^{''} + 5 y^{'} x + (- x^{3} + 3) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.844

7727	$x^{2} y^{''} - 2 x (x + 1) y^{'} + 2 (x + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.959

7728	$x^{2} y^{''} + y^{'} x + (x^{2} - 1) y = 0$	[_Bessel]	✓	1.355

7729	$x^{2} y^{''} - 2 x^{2} y^{'} + (4 x - 2) y = 0$	[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	1.437

7730	$(- x^{2} + 1) y^{''} - 2 y^{'} x + 2 y = 0$	[_Gegenbauer]	✓	0.509

7731	$y^{'} = x^{2} y$	[_separable]	✓	1.117

7732	$y y^{'} = x$	[_separable]	✓	3.714

7733	$y^{'} = \frac{x^{2} + x}{y - y^{2}}$	[_separable]	✓	1.493

7734	$y^{'} = \frac{e^{x - y}}{e^{x} + 1}$	[_separable]	✓	1.562

7735	$y^{'} = x^{2} y^{2} - 4 x^{2}$	[_separable]	✓	2.741

7736	$y^{'} = y^{2}$ i.c.	[_quadrature]	✓	1.616

7737	$y^{'} = 2 \sqrt{y}$ i.c.	[_quadrature]	✓	4.039

7738	$y^{'} = 2 \sqrt{y}$ i.c.	[_quadrature]	✓	1.299

7739	$y^{'} = \frac{x + y}{x - y}$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	3.433

7740	$y^{'} = \frac{y^{2}}{x^{2} + x y}$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	76.215

7741	$y^{'} = \frac{x^{2} + x y + y^{2}}{x^{2}}$	[[_homogeneous, ‘class A‘], _rational, _Riccati]	✓	2.064

7742	$y^{'} = \frac{y + x e^{- \frac{2 y}{x}}}{x}$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	14.258

7743	$y^{'} = \frac{x - y + 2}{x + y - 1}$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	2.878

7744	$y^{'} = \frac{2 x + 3 y + 1}{x - 2 y - 1}$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	4.220

7745	$y^{'} = \frac{x + y + 1}{2 x + 2 y - 1}$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	1.830

7746	$y^{'} = \frac{{(x + y - 1)}^{2}}{2 {(x + 2)}^{2}}$	[[_homogeneous, ‘class C‘], _rational, _Riccati]	✓	2.374

7747	$2 x y + (x^{2} + 3 y^{2}) y^{'} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert]	✓	0.227

7748	$x^{2} + x y + (x + y) y^{'} = 0$	[_quadrature]	✓	0.159

7749	$e^{x} + e^{y} (1 + y) y^{'} = 0$	[_separable]	✓	0.294

7750	$\cos (x) \cos {(y)}^{2} - \sin (x) \sin (2 y) y^{'} = 0$	[_separable]	✓	0.693

7751	$x^{2} y^{3} - x^{3} y^{2} y^{'} = 0$	[_separable]	✓	0.710

7752	$x + y + (x - y) y^{'} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	0.351

7753	$2 e^{2 x} y + 2 x \cos (y) + (e^{2 x} - x^{2} \sin (y)) y^{'} = 0$	[_exact]	✓	0.329

7754	$3 x^{2} \ln (x) + x^{2} + y + y^{'} x = 0$	[_linear]	✓	0.222

7755	$2 y^{3} + 2 + 3 x y^{2} y^{'} = 0$	[_separable]	✓	0.668

7756	$\cos (x) \cos (y) - 2 \sin (x) \sin (y) y^{'} = 0$	[_separable]	✓	0.372

7757	$5 x^{3} y^{2} + 2 y + (3 y x^{4} + 2 x) y^{'} = 0$	[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	0.393

7758	$e^{y} + x e^{y} + x e^{y} y^{'} = 0$	[_quadrature]	✓	0.316

7759	$y^{''} + y^{'} = 1$	[[_2nd_order, _missing_x]]	✓	1.079

7760	$y^{''} + e^{x} y^{'} = e^{x}$	[[_2nd_order, _missing_y]]	✓	0.565

7761	$y y^{''} + 4 {y^{'}}^{2} = 0$	[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]	✓	0.316

7762	$y^{''} + k^{2} y = 0$	[[_2nd_order, _missing_x]]	✓	1.381

7763	$y^{''} = y y^{'}$	[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Lagerstrom, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]	✓	0.969

7764	$x y^{''} - 2 y^{'} = x^{3}$	[[_2nd_order, _missing_y]]	✓	1.011

7765	$y^{''} = 1 + {y^{'}}^{2}$ i.c.	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]]	✓	1.624

7766	$y^{''} = - \frac{1}{2 {y^{'}}^{2}}$ i.c.	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_poly_yn]]	✗	2.906

7767	$y^{''} + \sin (y) = 0$ i.c.	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	21.421

7768	$y^{''} + \sin (y) = 0$ i.c.	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✗	4.819

7769	$[\begin{matrix} y_{1}^{'} = y_{1} \\ y_{2}^{'} = y_{1} + y_{2} \end{matrix}]$ i.c.	system_of_ODEs	✓	0.430

7770	$[\begin{matrix} y_{1}^{'} = y_{2} \\ y_{2}^{'} = 6 y_{1} + y_{2} \end{matrix}]$ i.c.	system_of_ODEs	✓	0.519

7771	$[\begin{matrix} y_{1}^{'} = y_{1} + y_{2} \\ y_{2}^{'} = y_{1} + y_{2} + e^{3 x} \end{matrix}]$ i.c.	system_of_ODEs	✓	0.723

7772	$[\begin{matrix} y_{1}^{'} = 3 y_{1} + x y_{3} \\ y_{2}^{'} = y_{2} + x^{3} y_{3} \\ y_{3}^{'} = 2 y_{1} x - y_{2} + e^{x} y_{3} \end{matrix}]$	system_of_ODEs	✓	0.071

7773	$y^{'} = 2 x$	[_quadrature]	✓	0.292

7774	$y^{'} x = 2 y$	[_separable]	✓	1.551

7775	$y y^{'} = e^{2 x}$	[_separable]	✓	1.793

7776	$y^{'} = k y$	[_quadrature]	✓	0.734

7777	$y^{''} + 4 y = 0$	[[_2nd_order, _missing_x]]	✓	1.405

7778	$y^{''} - 4 y = 0$	[[_2nd_order, _missing_x]]	✓	1.551

7779	$y^{'} x + y = y^{'} \sqrt{1 - x^{2} y^{2}}$	[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✓	46.061

7780	$y^{'} x = y + x^{2} + y^{2}$	[[_homogeneous, ‘class D‘], _rational, _Riccati]	✓	1.452

7781	$y^{'} = \frac{x y}{x^{2} + y^{2}}$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	3.128

7782	$2 x y^{'} y = x^{2} + y^{2}$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓	7.535

7783	$y^{'} x + y = x^{4} {y^{'}}^{2}$	[[_homogeneous, ‘class G‘], _rational]	✓	1.734

7784	$y^{'} = \frac{y^{2}}{x y - x^{2}}$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	92.051

7785	$(y \cos (y) - \sin (y) + x) y^{'} = y$	[[_1st_order, _with_linear_symmetries]]	✓	1.793

7786	$1 + y^{2} + y^{2} y^{'} = 0$	[_quadrature]	✓	0.610

7787	$y^{'} = e^{3 x} - x$	[_quadrature]	✓	0.339

7788	$y^{'} = x e^{x^{2}}$	[_quadrature]	✓	0.336

7789	$(x + 1) y^{'} = x$	[_quadrature]	✓	0.372

7790	$(x^{2} + 1) y^{'} = x$	[_quadrature]	✓	0.374

7791	$(x^{2} + 1) y^{'} = \arctan (x)$	[_quadrature]	✓	0.448

7792	$y^{'} x = 1$	[_quadrature]	✓	0.330

7793	$y^{'} = \arcsin (x)$	[_quadrature]	✓	0.372

7794	$y^{'} \sin (x) = 1$	[_quadrature]	✓	0.542

7795	$(x^{3} + 1) y^{'} = x$	[_quadrature]	✓	0.598

7796	$(x^{2} - 3 x + 2) y^{'} = x$	[_quadrature]	✓	0.408

7797	$y^{'} = x e^{x}$ i.c.	[_quadrature]	✓	0.556

7798	$y^{'} = 2 \sin (x) \cos (x)$ i.c.	[_quadrature]	✓	0.676

7799	$y^{'} = \ln (x)$ i.c.	[_quadrature]	✓	0.580

7800	$(x^{2} - 1) y^{'} = 1$ i.c.	[_quadrature]	✓	0.611

2.2.78 Problems 7701 to 7800