Problems 701 to 800

Table 2.17: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	time (sec)

701	$y^{'} = 2 x y^{2} + 3 y^{2} x^{2}$ i.c.	[_separable]	✓	2.225

702	$y^{'} = 6 e^{2 x - y}$ i.c.	[_separable]	✓	4.343

703	$2 \sqrt{x} y^{'} = \cos {(y)}^{2}$ i.c.	[_separable]	✓	2.010

704	$y + y^{'} = 2$ i.c.	[_quadrature]	✓	1.848

705	$- 2 y + y^{'} = 3 e^{2 x}$ i.c.	[[_linear, ‘class A‘]]	✓	1.619

706	$y^{'} + 3 y = 2 x e^{- 3 x}$	[[_linear, ‘class A‘]]	✓	1.829

707	$y^{'} - 2 x y = e^{x^{2}}$	[_linear]	✓	1.684

708	$2 y + x y^{'} = 3 x$ i.c.	[_linear]	✓	3.157

709	$y + 2 x y^{'} = 10 \sqrt{x}$ i.c.	[_linear]	✓	5.052

710	$y + 2 x y^{'} = 10 \sqrt{x}$	[_linear]	✓	4.299

711	$y + 3 x y^{'} = 12 x$	[_linear]	✓	2.407

712	$x y^{'} - y = x$ i.c.	[_linear]	✓	1.959

713	$- 3 y + 2 x y^{'} = 9 x^{3}$	[_linear]	✓	1.630

714	$x y^{'} + y = 3 x y$ i.c.	[_separable]	✓	2.481

715	$x y^{'} + 3 y = 2 x^{5}$ i.c.	[_linear]	✓	1.799

716	$y + y^{'} = e^{x}$ i.c.	[[_linear, ‘class A‘]]	✓	1.551

717	$- 3 y + x y^{'} = x^{3}$ i.c.	[_linear]	✓	1.581

718	$y^{'} + 2 x y = x$ i.c.	[_separable]	✓	1.964

719	$y^{'} = \cos (x) (1 - y)$ i.c.	[_separable]	✓	2.241

720	$(x + 1) y^{'} + y = \cos (x)$ i.c.	[_linear]	✓	1.957

721	$x y^{'} = x^{3} \cos (x) + 2 y$	[_linear]	✓	1.846

722	$\cot (x) y + y^{'} = \cos (x)$	[_linear]	✓	1.938

723	$y^{'} = 1 + x + y + x y$ i.c.	[_separable]	✓	1.962

724	$x y^{'} = 3 y + x^{4} \cos (x)$ i.c.	[_linear]	✓	2.860

725	$y^{'} = 3 x^{2} e^{x^{2}} + 2 x y$ i.c.	[_linear]	✓	3.019

726	$(- 3 + 2 x) y + x y^{'} = 4 x^{4}$	[_linear]	✓	2.520

727	$3 x y + (x^{2} + 4) y^{'} = x$ i.c.	[_separable]	✓	2.373

728	$(x^{2} + 1) y^{'} + 3 x^{3} y = 6 x e^{- \frac{3 x^{2}}{2}}$ i.c.	[_linear]	✓	2.665

729	$(x + y) y^{'} = x - y$	[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	4.268

730	$2 x y y^{'} = x^{2} + y^{2}$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓	7.208

731	$x y^{'} = y + 2 \sqrt{x y}$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	4.945

732	$(x - y) y^{'} = x + y$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	38.127

733	$x (x + y) y^{'} = y (x - y)$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	88.797

734	$(x + 2 y) y^{'} = y$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	4.168

735	$x y^{2} y^{'} = x^{3} + y^{3}$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓	11.345

736	$x^{2} y^{'} = e^{\frac{y}{x}} x^{2} + x y$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	201.691

737	$x^{2} y^{'} = x y + y^{2}$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓	2.401

738	$x y y^{'} = x^{2} + 3 y^{2}$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓	75.796

739	$(x^{2} - y^{2}) y^{'} = 2 x y$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	5.737

740	$x y y^{'} = y^{2} + x \sqrt{4 x^{2} + y^{2}}$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	113.476

741	$x y^{'} = y + \sqrt{x^{2} + y^{2}}$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	8.222

742	$x + y y^{'} = \sqrt{x^{2} + y^{2}}$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	7.916

743	$y (3 x + y) + x (x + y) y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	54.476

744	$y^{'} = \sqrt{1 + x + y}$	[[_homogeneous, ‘class C‘], _dAlembert]	✓	2.700

745	$y^{'} = {(4 x + y)}^{2}$	[[_homogeneous, ‘class C‘], _Riccati]	✓	1.586

746	$(x + y) y^{'} = 0$	[_quadrature]	✓	0.575

747	$2 x y + x^{2} y^{'} = 5 y^{3}$	[[_homogeneous, ‘class G‘], _rational, _Bernoulli]	✓	3.211

748	$2 x y^{3} + y^{2} y^{'} = 6 x$	[_separable]	✓	2.472

749	$y^{'} = y + y^{3}$	[_quadrature]	✓	4.836

750	$2 x y + x^{2} y^{'} = 5 y^{4}$	[[_homogeneous, ‘class G‘], _rational, _Bernoulli]	✓	3.062

751	$6 y + x y^{'} = 3 x y^{4 / 3}$	[[_homogeneous, ‘class G‘], _rational, _Bernoulli]	✓	97.482

752	$y^{3} e^{- 2 x} + 2 x y^{'} = 2 x y$	[_Bernoulli]	✓	2.721

753	$\sqrt{x^{4} + 1} y^{2} (x y^{'} + y) = x$	[_Bernoulli]	✓	6.411

754	$y^{3} + 3 y^{2} y^{'} = e^{- x}$	[[_1st_order, _with_linear_symmetries], _Bernoulli]	✓	2.107

755	$3 x y^{2} y^{'} = 3 x^{4} + y^{3}$	[[_homogeneous, ‘class G‘], _rational, _Bernoulli]	✓	2.684

756	$e^{y} x y^{'} = 2 e^{y} + 2 x^{3} e^{2 x}$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]]	✓	1.737

757	$2 x \cos (y) \sin (y) y^{'} = 4 x^{2} + \sin {(y)}^{2}$	[‘y=_G(x,y’)‘]	✓	3.274

758	$(e^{y} + x) y^{'} = - 1 + x e^{- y}$	[[_1st_order, _with_linear_symmetries]]	✓	1.939

759	$2 x + 3 y + (3 x + 2 y) y^{'} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	4.185

760	$4 x - y + (- x + 6 y) y^{'} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	3.930

761	$3 x^{2} + 2 y^{2} + (4 x y + 6 y^{2}) y^{'} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert]	✓	5.129

762	$3 x^{2} + 2 x y^{2} + (2 x^{2} y + 4 y^{3}) y^{'} = 0$	[_exact, _rational]	✓	2.072

763	$x^{3} + \frac{y}{x} + (y^{2} + \ln (x)) y^{'} = 0$	[_exact]	✓	1.701

764	$1 + y e^{x y} + (2 y + x e^{x y}) y^{'} = 0$	[_exact]	✓	2.142

765	$\cos (x) + \ln (y) + (e^{y} + \frac{x}{y}) y^{'} = 0$	[_exact]	✓	3.711

766	$x + \arctan (y) + \frac{(x + y) y^{'}}{1 + y^{2}} = 0$	[_exact]	✓	1.965

767	$3 x^{2} y^{3} + y^{4} + (3 x^{3} y^{2} + y^{4} + 4 x y^{3}) y^{'} = 0$	[_exact, _rational]	✓	1.664

768	$e^{x} \sin (y) + \tan (y) + (e^{x} \cos (y) + x \sec {(y)}^{2}) y^{'} = 0$	[_exact]	✓	17.374

769	$\frac{2 x}{y} - \frac{3 y^{2}}{x^{4}} + (- \frac{x^{2}}{y^{2}} + \frac{1}{\sqrt{y}} + \frac{2 y}{x^{3}}) y^{'} = 0$	[_exact, _rational]	✓	17.326

770	$\frac{2 x^{5 / 2} - 3 y^{5 / 3}}{2 x^{5 / 2} y^{2 / 3}} + \frac{(- 2 x^{5 / 2} + 3 y^{5 / 3}) y^{'}}{3 x^{3 / 2} y^{5 / 3}} = 0$	[[_1st_order, _with_linear_symmetries], _exact, _rational]	✓	2.405

771	$x^{3} + 3 y - x y^{'} = 0$	[_linear]	✓	1.294

772	$3 y^{2} + x y^{2} - x^{2} y^{'} = 0$	[_separable]	✓	1.838

773	$x y + y^{2} - x^{2} y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓	2.397

774	$2 x y^{3} + e^{x} + (3 y^{2} x^{2} + \sin (y)) y^{'} = 0$	[_exact]	✓	2.442

775	$3 y + x^{4} y^{'} = 2 x y$	[_separable]	✓	1.989

776	$2 x y^{2} + x^{2} y^{'} = y^{2}$	[_separable]	✓	1.869

777	$2 x^{2} y + x^{3} y^{'} = 1$	[_linear]	✓	1.280

778	$2 x y + x^{2} y^{'} = y^{2}$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓	3.280

779	$2 y + x y^{'} = 6 x^{2} \sqrt{y}$	[[_homogeneous, ‘class G‘], _rational, _Bernoulli]	✓	5.329

780	$y^{'} = 1 + x^{2} + y^{2} + y^{2} x^{2}$	[_separable]	✓	2.387

781	$x^{2} y^{'} = x y + 3 y^{2}$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓	2.403

782	$6 x y^{3} + 2 y^{4} + (9 y^{2} x^{2} + 8 x y^{3}) y^{'} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	454.237

783	$y^{'} = 1 + x^{2} + y^{2} + x^{2} y^{4}$	[‘y=_G(x,y’)‘]	✗	1.104

784	$x^{3} y^{'} = x^{2} y - y^{3}$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓	73.185

785	$y^{'} + 3 y = 3 x^{2} e^{- 3 x}$	[[_linear, ‘class A‘]]	✓	1.814

786	$y^{'} = x^{2} - 2 x y + y^{2}$	[[_homogeneous, ‘class C‘], _Riccati]	✓	1.773

787	$e^{x} + y e^{x y} + (e^{y} + x e^{x y}) y^{'} = 0$	[_exact]	✓	2.326

788	$2 x^{2} y - x^{3} y^{'} = y^{3}$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓	76.950

789	$3 x^{5} y^{2} + x^{3} y^{'} = 2 y^{2}$	[_separable]	✓	1.928

790	$x y^{'} + 3 y = \frac{3}{x^{3 / 2}}$	[_linear]	✓	1.988

791	$(- 1 + x) y + (x^{2} - 1) y^{'} = 1$	[_linear]	✓	1.385

792	$x y^{'} = 12 x^{4} y^{2 / 3} + 6 y$	[[_homogeneous, ‘class G‘], _rational, _Bernoulli]	✓	5.748

793	$e^{y} + y \cos (x) + (x e^{y} + \sin (x)) y^{'} = 0$	[_exact]	✓	38.583

794	$9 y^{2} x^{2} + x^{3 / 2} y^{'} = y^{2}$	[_separable]	✓	1.941

795	$2 y + (x + 1) y^{'} = 3 + 3 x$	[_linear]	✓	1.933

796	$9 \sqrt{x} y^{4 / 3} - 12 x^{1 / 5} y^{3 / 2} + (8 x^{3 / 2} y^{1 / 3} - 15 x^{6 / 5} \sqrt{y}) y^{'} = 0$	[[_homogeneous, ‘class G‘], _exact, _rational]	✓	0.281

797	$3 y + x^{3} y^{4} + 3 x y^{'} = 0$	[[_homogeneous, ‘class G‘], _rational, _Bernoulli]	✓	2.747

798	$x y^{'} + y = 2 e^{2 x}$	[_linear]	✓	1.215

799	$y + (2 x + 1) y^{'} = {(2 x + 1)}^{3 / 2}$	[_linear]	✓	3.808

800	$y^{'} = 3 x^{2} (7 + y)$	[_separable]	✓	1.508

2.2.8 Problems 701 to 800