Problems 7401 to 7500

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


#	ODE	CAS classiﬁcation	Solved?	time (sec)

7401	$y^{'} = (y - 1) (x + 1)$	[_separable]	✓	1.570

7402	$y^{'} = e^{x - y}$	[_separable]	✓	2.428

7403	$y^{'} = \frac{\sqrt{y}}{\sqrt{x}}$	[_separable]	✓	12.209

7404	$y^{'} = \frac{\sqrt{y}}{x}$	[_separable]	✓	3.366

7405	$z^{'} = 10^{x + z}$	[_separable]	✓	2.927

7406	$x^{'} + t = 1$	[_quadrature]	✓	0.458

7407	$y^{'} = \cos (x - y)$	[[_homogeneous, ‘class C‘], _dAlembert]	✓	2.374

7408	$y^{'} - y = 2 x - 3$	[[_linear, ‘class A‘]]	✓	1.316

7409	$(x + 2 y) y^{'} = 1$ i.c.	[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert]	✓	2.502

7410	$y^{'} + y = 2 x + 1$	[[_linear, ‘class A‘]]	✓	1.263

7411	$y^{'} = \cos (x - y - 1)$	[[_homogeneous, ‘class C‘], _dAlembert]	✓	2.822

7412	$y^{'} + \sin {(x + y)}^{2} = 0$	[[_homogeneous, ‘class C‘], _dAlembert]	✓	3.996

7413	$y^{'} = 2 \sqrt{2 x + y + 1}$	[[_homogeneous, ‘class C‘], _dAlembert]	✓	2.094

7414	$y^{'} = {(x + y + 1)}^{2}$	[[_homogeneous, ‘class C‘], _Riccati]	✓	4.098

7415	$y^{2} + x y^{2} + (x^{2} - x^{2} y) y^{'} = 0$	[_separable]	✓	1.658

7416	$(1 + y^{2}) (e^{2 x} - e^{y} y^{'}) - (y + 1) y^{'} = 0$	[_separable]	✓	2.358

7417	$x - y + (x + y) y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	38.392

7418	$y - 2 x y + x^{2} y^{'} = 0$	[_separable]	✓	1.924

7419	$2 x y^{'} = y (2 x^{2} - y^{2})$	[_rational, _Bernoulli]	✓	1.560

7420	$y^{2} + x^{2} y^{'} = x y y^{'}$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	72.921

7421	$(x^{2} + y^{2}) y^{'} = 2 x y$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	5.997

7422	$- y + x y^{'} = x \tan (\frac{y}{x})$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	3.925

7423	$x y^{'} = y - x e^{\frac{y}{x}}$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	18.777

7424	$- y + x y^{'} = (x + y) \ln (\frac{x + y}{x})$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	3.741

7425	$x y^{'} = y \cos (\frac{y}{x})$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	3.415

7426	$y + \sqrt{x y} - x y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	5.131

7427	$x y^{'} - \sqrt{x^{2} - y^{2}} - y = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	98.532

7428	$x + y - (x - y) y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	38.328

7429	$x^{2} + 2 x y - y^{2} + (y^{2} + 2 x y - x^{2}) y^{'} = 0$ i.c.	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	110.095

7430	$- y + x y^{'} = y y^{'}$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	3.138

7431	$y^{2} + (x^{2} - x y) y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	7.300

7432	$y^{2} + x y + x^{2} = x^{2} y^{'}$	[[_homogeneous, ‘class A‘], _rational, _Riccati]	✓	2.522

7433	$\frac{1}{x^{2} - x y + y^{2}} = \frac{y^{'}}{2 y^{2} - x y}$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	16.227

7434	$y^{'} = \frac{2 x y}{3 x^{2} - y^{2}}$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	35.079

7435	$y^{'} = \frac{x}{y} + \frac{y}{x}$ i.c.	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓	3.967

7436	$x y^{'} = y + \sqrt{y^{2} - x^{2}}$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	6.525

7437	$y + (2 \sqrt{x y} - x) y^{'} = 0$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	43.104

7438	$x y^{'} = y \ln (\frac{y}{x})$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	3.411

7439	$y^{'} (y^{'} + y) = (x + y) x$ i.c.	[_quadrature]	✓	0.531

7440	${(x y^{'} + y)}^{2} = y^{2} y^{'}$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	66.839

7441	$x^{2} {y^{'}}^{2} - 3 x y y^{'} + 2 y^{2} = 0$	[_separable]	✓	0.972

7442	$- y + x y^{'} = \sqrt{x^{2} + y^{2}}$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	8.358

7443	$y {y^{'}}^{2} + 2 x y^{'} - y = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	1.721

7444	$y^{'} + \frac{x + 2 y}{x} = 0$	[_linear]	✓	2.682

7445	$y^{'} = \frac{y}{x + y}$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	3.200

7446	$x y^{'} = x + \frac{y}{2}$ i.c.	[_linear]	✓	4.207

7447	$y^{'} = \frac{x + y - 2}{y - x - 4}$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	3.370

7448	$2 x - 4 y + 6 + (x + y - 2) y^{'} = 0$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	3.820

7449	$y^{'} = \frac{2 y - x + 5}{2 x - y - 4}$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	3.653

7450	$y^{'} = - \frac{4 x + 3 y + 15}{2 x + y + 7}$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	3.838

7451	$y^{'} = \frac{x + 3 y - 5}{x - y - 1}$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	2.813

7452	$y^{'} = \frac{2 {(y + 2)}^{2}}{{(x + y + 1)}^{2}}$	[[_homogeneous, ‘class C‘], _rational]	✓	1.898

7453	$2 x + y + 1 - (4 x + 2 y - 3) y^{'} = 0$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	1.950

7454	$x - y - 1 + (y - x + 2) y^{'} = 0$	[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	1.910

7455	$(x + 4 y) y^{'} = 2 x + 3 y - 5$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	3.799

7456	$y + 2 = (2 x + y - 4) y^{'}$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	4.150

7457	$(y^{'} + 1) \ln (\frac{x + y}{x + 3}) = \frac{x + y}{x + 3}$	[[_homogeneous, ‘class C‘], _exact, _dAlembert]	✓	7.585

7458	$y^{'} = \frac{x - 2 y + 5}{y - 2 x - 4}$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	3.579

7459	$y^{'} = \frac{3 x - y + 1}{2 x + y + 4}$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	7.480

7460	$2 x y^{'} + (x^{2} y^{4} + 1) y = 0$	[[_homogeneous, ‘class G‘], _rational, _Bernoulli]	✓	3.529

7461	$2 x y^{'} (x - y^{2}) + y^{3} = 0$	[[_homogeneous, ‘class G‘], _rational]	✓	0.618

7462	$x^{3} (y^{'} - x) = y^{2}$	[[_homogeneous, ‘class G‘], _rational, _Riccati]	✓	0.396

7463	$2 x^{2} y^{'} = y^{3} + x y$	[[_homogeneous, ‘class G‘], _rational, _Bernoulli]	✓	0.621

7464	$y + x (2 x y + 1) y^{'} = 0$	[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	0.612

7465	$2 y^{'} + x = 4 \sqrt{y}$	[[_1st_order, _with_linear_symmetries], _Chini]	✓	0.995

7466	$y^{'} = y^{2} - \frac{2}{x^{2}}$	[[_homogeneous, ‘class G‘], _rational, [_Riccati, _special]]	✓	0.565

7467	$2 x y^{'} + y = y^{2} \sqrt{x - y^{2} x^{2}}$	[[_homogeneous, ‘class G‘]]	✓	5.743

7468	$\frac{2 x y y^{'}}{3} = \sqrt{x^{6} - y^{4}} + y^{2}$	[[_homogeneous, ‘class G‘]]	✓	4.505

7469	$2 y + (x^{2} y + 1) x y^{'} = 0$	[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	0.576

7470	$y (1 + x y) + (1 - x y) x y^{'} = 0$	[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	0.609

7471	$y (1 + y^{2} x^{2}) + (y^{2} x^{2} - 1) x y^{'} = 0$	[[_homogeneous, ‘class G‘], _rational]	✓	0.673

7472	$(x^{2} - y^{4}) y^{'} - x y = 0$	[[_homogeneous, ‘class G‘], _rational]	✓	2.314

7473	$y (1 + \sqrt{x^{2} y^{4} - 1}) + 2 x y^{'} = 0$	[[_homogeneous, ‘class G‘]]	✓	0.815

7474	$x (2 - 9 x y^{2}) + y (4 y^{2} - 6 x^{3}) y^{'} = 0$	[_exact, _rational]	✓	2.128

7475	$\frac{y}{x} + (y^{3} + \ln (x)) y^{'} = 0$	[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✓	1.544

7476	$2 x + 3 + (2 y - 2) y^{'} = 0$	[_separable]	✓	3.155

7477	$2 x + 4 y + (2 x - 2 y) y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	5.980

7478	$y^{''} + 2 y^{'} - y = 0$	[[_2nd_order, _missing_x]]	✓	1.142

7479	$y^{''} + \frac{y^{'}}{x} - \frac{y}{x^{2}} = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	1.309

7480	$(x^{2} + 1) y^{''} + x y^{'} + y = 0$	[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	2.521

7481	$y^{''} - \cot (x) y^{'} + \cos (x) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	2.382

7482	$y^{''} + \frac{y^{'}}{x} + x^{2} y = 0$	[[_Emden, _Fowler]]	✓	0.829

7483	$x^{2} (- x^{2} + 1) y^{''} + 2 x (- x^{2} + 1) y^{'} - 2 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	1.044

7484	$(- x^{2} + 1) y^{''} - x y^{'} + y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	2.010

7485	$y^{'''} - 2 x y^{''} + 4 x^{2} y^{'} + 8 x^{3} y = 0$	[[_3rd_order, _with_linear_symmetries]]	✗	0.048

7486	$y^{''} + x (1 - x) y^{'} + y e^{x} = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	0.532

7487	$x^{2} y^{''} + 2 x y^{'} + 4 y = 0$	[[_Emden, _Fowler]]	✓	2.758

7488	$x^{4} y^{''''} - x^{2} y^{''} + y = 0$	[[_high_order, _with_linear_symmetries]]	✓	0.332

7489	$(x^{2} + 1) y^{''} + x y^{'} + y = 0$	[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	2.433

7490	$y^{''} + x y^{'} + y = 2 x e^{x} - 1$	[[_2nd_order, _exact, _linear, _nonhomogeneous]]	✓	2.345

7491	$x y^{''} + x y^{'} - y = x^{2} + 2 x$	[[_2nd_order, _with_linear_symmetries]]	✓	1.485

7492	$x^{2} y^{''} + x y^{'} - y = x^{2} + 2 x$	[[_2nd_order, _exact, _linear, _nonhomogeneous]]	✓	2.432

7493	$x^{3} y^{''} + x y^{'} - y = \cos (\frac{1}{x})$	[[_2nd_order, _with_linear_symmetries]]	✓	2.426

7494	$x (x + 1) y^{''} + (x + 2) y^{'} - y = x + \frac{1}{x}$	[[_2nd_order, _exact, _linear, _nonhomogeneous]]	✓	1.853

7495	$2 x y^{''} + (- 2 + x) y^{'} - y = x^{2} - 1$	[[_2nd_order, _with_linear_symmetries]]	✓	1.396

7496	$x^{2} (x + 1) y^{''} + x (4 x + 3) y^{'} - y = x + \frac{1}{x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✗	1.991

7497	$x^{2} (\ln (x) - 1) y^{''} - x y^{'} + y = x {(1 - \ln (x))}^{2}$	[[_2nd_order, _with_linear_symmetries]]	✓	1.045

7498	$x y^{''} + 2 y^{'} + x y = \sec (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	4.419

7499	$(- x^{2} + 1) y^{''} - x y^{'} + \frac{y}{4} = - \frac{x^{2}}{2} + \frac{1}{2}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.743

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]]	✗	268.212

2.2.75 Problems 7401 to 7500