Problems 7401 to 7500

Table 2.151: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	time (sec)

7401	$y^{'} = (- 1 + y) (x + 1)$	[_separable]	✓	1.188

7402	$y^{'} = e^{x - y}$	[_separable]	✓	1.753

7403	$y^{'} = \frac{\sqrt{y}}{\sqrt{x}}$	[_separable]	✓	10.105

7404	$y^{'} = \frac{\sqrt{y}}{x}$	[_separable]	✓	1.995

7405	$z^{'} = 10^{x + z}$	[_separable]	✓	2.475

7406	$x^{'} + t = 1$	[_quadrature]	✓	0.290

7407	$y^{'} = \cos (x - y)$	[[_homogeneous, ‘class C‘], _dAlembert]	✓	2.267

7408	$y^{'} - y = 2 x - 3$	[[_linear, ‘class A‘]]	✓	0.929

7409	$(x + 2 y) y^{'} = 1$ i.c.	[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert]	✓	2.649

7410	$y^{'} + y = 2 x + 1$	[[_linear, ‘class A‘]]	✓	0.869

7411	$y^{'} = \cos (x - y - 1)$	[[_homogeneous, ‘class C‘], _dAlembert]	✓	2.493

7412	$y^{'} + \sin {(x + y)}^{2} = 0$	[[_homogeneous, ‘class C‘], _dAlembert]	✓	3.758

7413	$y^{'} = 2 \sqrt{2 x + y + 1}$	[[_homogeneous, ‘class C‘], _dAlembert]	✓	2.394

7414	$y^{'} = {(x + y + 1)}^{2}$	[[_homogeneous, ‘class C‘], _Riccati]	✓	5.204

7415	$y^{2} + x y^{2} + (x^{2} - x^{2} y) y^{'} = 0$	[_separable]	✓	1.769

7416	$(1 + y^{2}) (e^{2 x} - e^{y} y^{'}) - (1 + y) y^{'} = 0$	[_separable]	✓	2.266

7417	$(x + y) y^{'} + x - y = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	3.494

7418	$y - 2 x y + x^{2} y^{'} = 0$	[_separable]	✓	1.519

7419	$2 y^{'} x = (2 x^{2} - y^{2}) y$	[_rational, _Bernoulli]	✓	1.620

7420	$x^{2} y^{'} + y^{2} = x y^{'} y$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	109.071

7421	$(x^{2} + y^{2}) y^{'} = 2 x y$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	5.450

7422	$y^{'} x - y = x \tan (\frac{y}{x})$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	3.768

7423	$y^{'} x = y - e^{\frac{y}{x}} x$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	9.231

7424	$y^{'} x - y = (x + y) \ln (\frac{x + y}{x})$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	3.661

7425	$y^{'} x = y \cos (\frac{y}{x})$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	2.916

7426	$y + \sqrt{x y} - y^{'} x = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	6.194

7427	$y^{'} x - \sqrt{x^{2} - y^{2}} - y = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	128.603

7428	$x + y - (x - y) y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	3.528

7429	$x^{2} + 2 x y - y^{2} + (y^{2} + 2 x y - x^{2}) y^{'} = 0$ i.c.	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	4.861

7430	$y^{'} x - y = y y^{'}$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	2.698

7431	$y^{2} + (x^{2} - x y) y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	8.401

7432	$x^{2} + x y + y^{2} = x^{2} y^{'}$	[[_homogeneous, ‘class A‘], _rational, _Riccati]	✓	2.073

7433	$\frac{1}{x^{2} - x y + y^{2}} = \frac{y^{'}}{2 y^{2} - x y}$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	16.655

7434	$y^{'} = \frac{2 x y}{3 x^{2} - y^{2}}$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	3.477

7435	$y^{'} = \frac{x}{y} + \frac{y}{x}$ i.c.	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓	3.018

7436	$y^{'} x = y + \sqrt{y^{2} - x^{2}}$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	5.757

7437	$(2 \sqrt{x y} - x) y^{'} + y = 0$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	59.394

7438	$y^{'} x = y \ln (\frac{y}{x})$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	3.191

7439	$y^{'} (y^{'} + y) = (x + y) x$ i.c.	[_quadrature]	✓	0.442

7440	${(y^{'} x + y)}^{2} = y^{2} y^{'}$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	85.777

7441	$x^{2} {y^{'}}^{2} - 3 x y^{'} y + 2 y^{2} = 0$	[_separable]	✓	0.717

7442	$y^{'} x - y = \sqrt{x^{2} + y^{2}}$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	5.360

7443	$y {y^{'}}^{2} + 2 y^{'} x - y = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	1.820

7444	$y^{'} + \frac{x + 2 y}{x} = 0$	[_linear]	✓	2.147

7445	$y^{'} = \frac{y}{x + y}$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	2.548

7446	$y^{'} x = x + \frac{y}{2}$ i.c.	[_linear]	✓	3.277

7447	$y^{'} = \frac{x + y - 2}{y - x - 4}$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	3.043

7448	$2 x - 4 y + 6 + (x + y - 2) y^{'} = 0$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	3.621

7449	$y^{'} = \frac{2 y - x + 5}{2 x - y - 4}$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	3.222

7450	$y^{'} = - \frac{4 x + 3 y + 15}{2 x + y + 7}$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	3.263

7451	$y^{'} = \frac{x + 3 y - 5}{x - y - 1}$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	2.330

7452	$y^{'} = \frac{2 {(y + 2)}^{2}}{{(x + y + 1)}^{2}}$	[[_homogeneous, ‘class C‘], _rational]	✓	2.029

7453	$2 x + y + 1 - (4 x + 2 y - 3) y^{'} = 0$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	2.066

7454	$x - y - 1 + (y - x + 2) y^{'} = 0$	[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	1.673

7455	$(x + 4 y) y^{'} = 2 x + 3 y - 5$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	3.338

7456	$y + 2 = (2 x + y - 4) y^{'}$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	4.539

7457	$(y^{'} + 1) \ln (\frac{x + y}{3 + x}) = \frac{x + y}{3 + x}$	[[_homogeneous, ‘class C‘], _exact, _dAlembert]	✓	10.532

7458	$y^{'} = \frac{x - 2 y + 5}{y - 2 x - 4}$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	3.388

7459	$y^{'} = \frac{3 x - y + 1}{2 x + y + 4}$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	81.632

7460	$2 y^{'} x + (x^{2} y^{4} + 1) y = 0$	[[_homogeneous, ‘class G‘], _rational, _Bernoulli]	✓	2.967

7461	$2 x (x - y^{2}) y^{'} + y^{3} = 0$	[[_homogeneous, ‘class G‘], _rational]	✓	0.787

7462	$x^{3} (y^{'} - x) = y^{2}$	[[_homogeneous, ‘class G‘], _rational, _Riccati]	✓	0.319

7463	$2 x^{2} y^{'} = y^{3} + x y$	[[_homogeneous, ‘class G‘], _rational, _Bernoulli]	✓	0.565

7464	$y + x (1 + 2 x y) y^{'} = 0$	[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	0.672

7465	$2 y^{'} + x = 4 \sqrt{y}$	[[_1st_order, _with_linear_symmetries], _Chini]	✓	1.206

7466	$y^{'} = y^{2} - \frac{2}{x^{2}}$	[[_homogeneous, ‘class G‘], _rational, [_Riccati, _special]]	✓	0.510

7467	$2 y^{'} x + y = y^{2} \sqrt{x - x^{2} y^{2}}$	[[_homogeneous, ‘class G‘]]	✓	3.030

7468	$\frac{2 x y^{'} y}{3} = \sqrt{x^{6} - y^{4}} + y^{2}$	[[_homogeneous, ‘class G‘]]	✓	4.033

7469	$2 y + (x^{2} y + 1) x y^{'} = 0$	[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	0.619

7470	$x (1 - x y) y^{'} + (x y + 1) y = 0$	[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	0.606

7471	$(1 + x^{2} y^{2}) y + (x^{2} y^{2} - 1) x y^{'} = 0$	[[_homogeneous, ‘class G‘], _rational]	✓	0.774

7472	$(x^{2} - y^{4}) y^{'} - x y = 0$	[[_homogeneous, ‘class G‘], _rational]	✓	1.713

7473	$y (1 + \sqrt{x^{2} y^{4} - 1}) + 2 y^{'} x = 0$	[[_homogeneous, ‘class G‘]]	✓	0.823

7474	$x (2 - 9 x y^{2}) + y (4 y^{2} - 6 x^{3}) y^{'} = 0$	[_exact, _rational]	✓	2.120

7475	$\frac{y}{x} + (y^{3} + \ln (x)) y^{'} = 0$	[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✓	1.464

7476	$3 + 2 x + (- 2 + 2 y) y^{'} = 0$	[_separable]	✓	2.575

7477	$2 x + 4 y + (2 x - 2 y) y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	6.489

7478	$y^{''} + 2 y^{'} - y = 0$	[[_2nd_order, _missing_x]]	✓	0.493

7479	$y^{''} + \frac{y^{'}}{x} - \frac{y}{x^{2}} = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	1.132

7480	$(x^{2} + 1) y^{''} + y^{'} x + y = 0$	[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	0.969

7481	$y^{''} - \cot (x) y^{'} + \cos (x) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	2.526

7482	$y^{''} + \frac{y^{'}}{x} + x^{2} y = 0$	[[_Emden, _Fowler]]	✓	0.555

7483	$x^{2} (- x^{2} + 1) y^{''} + 2 x (- x^{2} + 1) y^{'} - 2 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.570

7484	$(- x^{2} + 1) y^{''} - y^{'} x + y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	1.540

7485	$y^{'''} - 2 x y^{''} + 4 x^{2} y^{'} + 8 x^{3} y = 0$	[[_3rd_order, _with_linear_symmetries]]	✗	0.080

7486	$y^{''} + x (1 - x) y^{'} + y e^{x} = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	0.762

7487	$x^{2} y^{''} + 2 y^{'} x + 4 y = 0$	[[_Emden, _Fowler]]	✓	1.034

7488	$x^{4} y^{''''} - x^{2} y^{''} + y = 0$	[[_high_order, _with_linear_symmetries]]	✓	0.289

7489	$(x^{2} + 1) y^{''} + y^{'} x + y = 0$	[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	1.002

7490	$y^{''} + y^{'} x + y = 2 x e^{x} - 1$	[[_2nd_order, _exact, _linear, _nonhomogeneous]]	✓	1.221

7491	$x y^{''} + y^{'} x - y = x^{2} + 2 x$	[[_2nd_order, _with_linear_symmetries]]	✓	0.976

7492	$x^{2} y^{''} + y^{'} x - y = x^{2} + 2 x$	[[_2nd_order, _exact, _linear, _nonhomogeneous]]	✓	2.150

7493	$x^{3} y^{''} + y^{'} x - y = \cos (\frac{1}{x})$	[[_2nd_order, _with_linear_symmetries]]	✓	0.977

7494	$x (x + 1) y^{''} + (x + 2) y^{'} - y = x + \frac{1}{x}$	[[_2nd_order, _exact, _linear, _nonhomogeneous]]	✓	1.388

7495	$2 x y^{''} + (x - 2) y^{'} - y = x^{2} - 1$	[[_2nd_order, _with_linear_symmetries]]	✓	0.682

7496	$x^{2} (x + 1) y^{''} + x (4 x + 3) y^{'} - y = x + \frac{1}{x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✗	2.372

7497	$x^{2} (\ln (x) - 1) y^{''} - y^{'} x + y = x {(1 - \ln (x))}^{2}$	[[_2nd_order, _with_linear_symmetries]]	✓	0.885

7498	$x y^{''} + 2 y^{'} + x y = \sec (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.917

7499	$(- x^{2} + 1) y^{''} - y^{'} x + \frac{y}{4} = - \frac{x^{2}}{2} + \frac{1}{2}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.103

7500	$(\cos (x) + \sin (x)) y^{''} - 2 \cos (x) y^{'} + (\cos (x) - \sin (x)) y = {(\cos (x) + \sin (x))}^{2} e^{2 x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✗	8.380

2.2.75 Problems 7401 to 7500