Problems 15601 to 15700

Table 2.315: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	time (sec)

15601	$y^{'} + \cos (y) = 0$	[_quadrature]	✓	0.453

15602	$y^{'} - y e^{x} = 0$	[_separable]	✓	0.535

15603	$y^{'} - \tan (x) y = 0$	[_separable]	✓	0.675

15604	$\sin (x) y^{''} + x^{2} y^{'} - y e^{x} = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	11.536

15605	$\sinh (x) y^{''} + x^{2} y^{'} - y e^{x} = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	4.706

15606	$\sinh (x) y^{''} + x^{2} y^{'} - y \sin (x) = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	52.899

15607	$e^{3 x} y^{''} + \sin (x) y^{'} + \frac{2 y}{x^{2} + 4} = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	5.342

15608	$y^{''} + \frac{(e^{x} + 1) y}{1 - e^{x}} = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	1.393

15609	$(x^{2} - 4) y^{''} + (x^{2} + x - 6) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.461

15610	$x y^{''} + (1 - e^{x}) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.679

15611	$\sin (π x^{2}) y^{''} + x^{2} y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	2.066

15612	$y^{'} - y e^{x} = 0$	[_separable]	✓	0.564

15613	$y^{'} + e^{2 x} y = 0$	[_separable]	✓	0.543

15614	$y^{'} + y \cos (x) = 0$	[_separable]	✓	0.571

15615	$y^{'} + y \ln (x) = 0$	[_separable]	✓	0.569

15616	$y^{''} - y e^{x} = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.620

15617	$y^{''} + 3 x y^{'} - y e^{x} = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.674

15618	$x y^{''} - 3 x y^{'} + y \sin (x) = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.630

15619	$y^{''} + y \ln (x) = 0$	[_Titchmarsh]	✓	0.572

15620	$\sqrt{x} y^{''} + y = 0$	[[_Emden, _Fowler]]	✓	0.702

15621	$y^{''} + (6 x^{2} + 2 x + 1) y^{'} + (2 + 12 x) y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.476

15622	$y^{'} - y e^{x} = 0$	[_separable]	✓	0.805

15623	$y^{'} + \sqrt{x^{2} + 1} y = 0$	[_separable]	✓	0.907

15624	$\cos (x) y^{'} + y = 0$	[_separable]	✓	1.162

15625	$y^{'} + \sqrt{2 x^{2} + 1} y = 0$	[_separable]	✓	0.860

15626	$y^{''} - y e^{x} = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.636

15627	$y^{''} + y \cos (x) = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.852

15628	$y^{''} + \sin (x) y^{'} + y \cos (x) = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.858

15629	$\sqrt{x} y^{''} + y^{'} + x y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.750

15630	${(x - 3)}^{2} y^{''} - 2 (x - 3) y^{'} + 2 y = 0$	[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	0.358

15631	$2 x^{2} y^{''} + 5 x y^{'} + y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.537

15632	${(- 1 + x)}^{2} y^{''} - 5 (- 1 + x) y^{'} + 9 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.448

15633	${(x + 2)}^{2} y^{''} + (x + 2) y^{'} = 0$	[[_2nd_order, _missing_y]]	✓	0.381

15634	$3 {(- 2 + x)}^{2} y^{''} - 4 (x - 5) y^{'} + 2 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.510

15635	${(x - 5)}^{2} y^{''} + (x - 5) y^{'} + 4 y = 0$	[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	0.455

15636	$x^{2} y^{''} + \frac{x y^{'}}{- 2 + x} + \frac{2 y}{x + 2} = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	1.026

15637	$x^{3} y^{''} + x^{2} y^{'} + y = 0$	[[_Emden, _Fowler]]	✓	0.586

15638	$(- x^{4} + x^{3}) y^{''} + (3 x - 1) y^{'} + 827 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	2.259

15639	$y^{''} + \frac{y^{'}}{x - 3} + \frac{y}{x - 4} = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.805

15640	$y^{''} + \frac{y^{'}}{{(x - 3)}^{2}} + \frac{y}{{(x - 4)}^{2}} = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	1.036

15641	$y^{''} + (\frac{1}{x} - \frac{1}{3}) y^{'} + (\frac{1}{x} - \frac{1}{4}) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.703

15642	$(4 x^{2} - 1) y^{''} + (4 - \frac{2}{x}) y^{'} + \frac{(- x^{2} + 1) y}{x^{2} + 1} = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	1.702

15643	${(x^{2} + 4)}^{2} y^{''} + y = 0$	[[_Emden, _Fowler]]	✓	0.402

15644	$x^{2} y^{''} - 2 x y^{'} + (x^{2} + 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.677

15645	$4 x^{2} y^{''} + (1 - 4 x) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.635

15646	$x^{2} y^{''} + x y^{'} + (4 x - 4) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	1.343

15647	$(- 9 x^{4} + x^{2}) y^{''} - 6 x y^{'} + 10 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.773

15648	$x^{2} y^{''} - x y^{'} + \frac{y}{1 - x} = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.733

15649	$y^{''} + \frac{y^{'}}{x} + y = 0$	[_Lienard]	✓	0.453

15650	$y^{''} + \frac{y^{'}}{x} + (1 - \frac{1}{x^{2}}) y = 0$	[_Bessel]	✓	1.253

15651	$2 x^{2} y^{''} + (- 2 x^{3} + 5 x) y^{'} + (- x^{2} + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.717

15652	$x^{2} y^{''} - (2 x^{2} + 5 x) y^{'} + (9 + 4 x) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.727

15653	$(- 3 x^{3} + 3 x^{2}) y^{''} - (5 x^{2} + 4 x) y^{'} + 2 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.780

15654	$x^{2} y^{''} - (x^{2} + x) y^{'} + 4 x y = 0$	[_Laguerre]	✓	1.419

15655	$4 x^{2} y^{''} + 8 x^{2} y^{'} + y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.725

15656	$x^{2} y^{''} + (- x^{4} + x) y^{'} + 3 x^{3} y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.471

15657	$(9 x^{3} + 9 x^{2}) y^{''} + (27 x^{2} + 9 x) y^{'} + (8 x - 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.687

15658	$(x - 3) y^{''} + (x - 3) y^{'} + y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	1.303

15659	$y^{''} + \frac{2 y^{'}}{x + 2} + y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.645

15660	$4 y^{''} + \frac{(4 x - 3) y}{{(- 1 + x)}^{2}} = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.722

15661	${(x - 3)}^{2} y^{''} + (x^{2} - 3 x) y^{'} - 3 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.766

15662	$x^{2} y^{''} - 2 x y^{'} + (- x^{2} + 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.679

15663	$x^{2} y^{''} - 2 x^{2} y^{'} + (x^{2} - 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.782

15664	$y^{''} + \frac{y^{'}}{x} + y = 0$	[_Lienard]	✓	0.446

15665	$x^{2} (- x^{2} + 2) y^{''} + (4 x^{2} + 5 x) y^{'} + (x^{2} + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.870

15666	$x^{2} y^{''} - (2 x^{2} + 5 x) y^{'} + 9 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.706

15667	$x^{2} (2 x + 1) y^{''} + x y^{'} + (4 x^{3} - 4) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	1.528

15668	$4 x^{2} y^{''} + 8 x y^{'} + (1 - 4 x) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.737

15669	$x^{2} y^{''} + x y^{'} - (2 x + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	1.358

15670	$x y^{''} + 4 y^{'} + \frac{12 y}{{(x + 2)}^{2}} = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.858

15671	$x y^{''} + 4 y^{'} + \frac{12 y}{{(x + 2)}^{2}} = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.828

15672	$(x - 3) y^{''} + (x - 3) y^{'} + y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	1.351

15673	$(- x^{2} + 1) y^{''} - x y^{'} + 3 y = 0$	[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	0.829

15674	$4 x^{2} y^{''} + (1 - 4 x) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.694

15675	$y^{''} + \frac{y^{'}}{x} + y = 0$	[_Lienard]	✓	0.446

15676	$x^{2} y^{''} - (x^{2} + x) y^{'} + 4 x y = 0$	[_Laguerre]	✓	1.444

15677	$x^{2} y^{''} + x y^{'} + (4 x - 4) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	1.452

15678	$[\begin{matrix} x^{'} = 2 y \\ y^{'} = 1 - 2 x \end{matrix}]$	system_of_ODEs	✓	0.684

15679	$[\begin{matrix} x^{'} = 4 x - 3 y \\ y^{'} = 6 x - 7 y \end{matrix}]$	system_of_ODEs	✓	0.495

15680	$[\begin{matrix} t x^{'} + 2 x = 15 y \\ t y^{'} = x \end{matrix}]$	system_of_ODEs	✗	0.032

15681	$[\begin{matrix} x^{'} = x + 2 y \\ y^{'} = 5 x - 2 y \end{matrix}]$ i.c.	system_of_ODEs	✓	0.634

15682	$[\begin{matrix} x^{'} = 5 x + 4 y \\ y^{'} = 8 x + y \end{matrix}]$ i.c.	system_of_ODEs	✓	0.607

15683	$[\begin{matrix} x^{'} = 4 x + 2 y \\ y^{'} = 3 x - y \end{matrix}]$ i.c.	system_of_ODEs	✓	0.637

15684	$[\begin{matrix} x^{'} = x + 2 y \\ y^{'} = 5 x - 2 y \end{matrix}]$ i.c.	system_of_ODEs	✓	0.635

15685	$[\begin{matrix} x^{'} = 2 y \\ y^{'} = 2 x \end{matrix}]$	system_of_ODEs	✓	0.464

15686	$[\begin{matrix} x^{'} = 2 y \\ y^{'} = - 2 x \end{matrix}]$	system_of_ODEs	✓	0.556

15687	$[\begin{matrix} x^{'} = - 2 y \\ y^{'} = 8 x \end{matrix}]$	system_of_ODEs	✓	0.542

15688	$[\begin{matrix} x^{'} = 4 x - 13 y \\ y^{'} = x \end{matrix}]$ i.c.	system_of_ODEs	✓	0.638

15689	$[\begin{matrix} x^{'} = 3 x + 2 y \\ y^{'} = - 2 x + 3 y \end{matrix}]$ i.c.	system_of_ODEs	✓	0.564

15690	$[\begin{matrix} x^{'} = 8 x + 2 y - 17 \\ y^{'} = 4 x + y - 13 \end{matrix}]$ i.c.	system_of_ODEs	✓	0.784

15691	$[\begin{matrix} x^{'} = 8 x + 2 y + 7 e^{2 t} \\ y^{'} = 4 x + y - 7 e^{2 t} \end{matrix}]$ i.c.	system_of_ODEs	✓	0.600

15692	$[\begin{matrix} x^{'} = 4 x + 3 y - 6 e^{3 t} \\ y^{'} = x + 6 y + 2 e^{3 t} \end{matrix}]$ i.c.	system_of_ODEs	✓	0.625

15693	$[\begin{matrix} x^{'} = - y \\ y^{'} = 4 x + 24 t \end{matrix}]$ i.c.	system_of_ODEs	✓	0.683

15694	$[\begin{matrix} x^{'} = 4 x - 13 y \\ y^{'} = x + 19 \cos (4 t) - 13 \sin (4 t) \end{matrix}]$ i.c.	system_of_ODEs	✓	1.774

15695	$[\begin{matrix} x^{'} = 4 x + 3 y + 5 Heaviside (t - 2) \\ y^{'} = x + 6 y + 17 Heaviside (t - 2) \end{matrix}]$ i.c.	system_of_ODEs	✓	0.766

15696	$[\begin{matrix} x^{'} = 5 x + 4 y \\ y^{'} = 8 x + y \end{matrix}]$	system_of_ODEs	✓	0.486

15697	$[\begin{matrix} x^{'} = 2 x - 5 y \\ y^{'} = 3 x - 7 y \end{matrix}]$	system_of_ODEs	✓	0.622

15698	$[\begin{matrix} x^{'} = 2 x - 5 y + 4 \\ y^{'} = 3 x - 7 y + 5 \end{matrix}]$	system_of_ODEs	✓	1.037

15699	$[\begin{matrix} x^{'} = 3 x + y \\ y^{'} = 6 x + 2 y \end{matrix}]$	system_of_ODEs	✓	0.481

15700	$[\begin{matrix} x^{'} = x y - 6 y \\ y^{'} = x - y - 5 \end{matrix}]$	system_of_ODEs	✗	0.033

2.2.157 Problems 15601 to 15700