First order ODE’s solved using series method. Ordinary point

Column notations: A is ODE degree. B is Program Number of solutions generated. C is CAS Number of solutions generated.

Table 2.574: ﬁrst order ode series method. Ordinary point


#	ODE	A	B	C	CAS classiﬁcation	Solved?	Veriﬁed?	time (sec)

392	\[ {}y^{\prime } = y \]	1	2	1	[_quadrature]	✓	✓	0.459

393	\[ {}y^{\prime } = 4 y \]	1	2	1	[_quadrature]	✓	✓	0.543

394	\[ {}2 y^{\prime }+3 y = 0 \]	1	2	1	[_quadrature]	✓	✓	0.548

395	\[ {}2 x y+y^{\prime } = 0 \]	1	2	1	[_separable]	✓	✓	0.53

396	\[ {}y^{\prime } = x^{2} y \]	1	2	1	[_separable]	✓	✓	0.488

397	\[ {}\left (-2+x \right ) y^{\prime }+y = 0 \]	1	2	1	[_separable]	✓	✓	0.584

398	\[ {}\left (2 x -1\right ) y^{\prime }+2 y = 0 \]	1	2	1	[_separable]	✓	✓	0.601

399	\[ {}2 \left (1+x \right ) y^{\prime } = y \]	1	2	1	[_separable]	✓	✓	0.608

400	\[ {}\left (-1+x \right ) y^{\prime }+2 y = 0 \]	1	2	1	[_separable]	✓	✓	0.592

401	\[ {}2 \left (-1+x \right ) y^{\prime } = 3 y \]	1	2	1	[_separable]	✓	✓	0.584

746	\[ {}y^{\prime }-y = 0 \]	1	2	1	[_quadrature]	✓	✓	0.5

747	\[ {}y^{\prime }-x y = 0 \]	1	2	1	[_separable]	✓	✓	0.516

748	\[ {}\left (1-x \right ) y^{\prime } = y \]	1	2	1	[_separable]	✓	✓	0.556

2365	\[ {}y^{\prime } = x y-x^{2} \] i.c.	1	2	1	[_linear]	✓	✓	2.225

2367	\[ {}y^{\prime } = 3 x +\frac {y}{x} \] i.c.	1	1	1	[_linear]	✓	✓	1.091

4894	\[ {}y^{\prime } = 3 x^{2} y \]	1	2	1	[_separable]	✓	✓	0.328

5011	\[ {}y^{\prime }+\left (2+x \right ) y = 0 \]	1	2	1	[_separable]	✓	✓	0.401

5012	\[ {}y^{\prime }-y = 0 \]	1	2	1	[_quadrature]	✓	✓	0.368

5013	\[ {}z^{\prime }-x^{2} z = 0 \]	1	2	1	[_separable]	✓	✓	0.358

5025	\[ {}y^{\prime }+2 \left (-1+x \right ) y = 0 \]	1	1	1	[_separable]	✓	✓	0.348

5026	\[ {}y^{\prime }-2 x y = 0 \]	1	1	1	[_separable]	✓	✓	0.415

5031	\[ {}x^{\prime }+\sin \left (t \right ) x = 0 \] i.c.	1	2	1	[_separable]	✓	✓	2.027

5032	\[ {}y^{\prime }-{\mathrm e}^{x} y = 0 \] i.c.	1	2	1	[_separable]	✓	✓	1.951

5036	\[ {}y^{\prime }-x y = \sin \left (x \right ) \]	1	2	1	[_linear]	✓	✓	0.528

5037	\[ {}w^{\prime }+x w = {\mathrm e}^{x} \]	1	2	1	[_linear]	✓	✓	0.481

5449	\[ {}\left (1-x \right ) y^{\prime } = x^{2}-y \]	1	2	1	[_linear]	✓	✓	0.369

5450	\[ {}x y^{\prime } = 1-x +2 y \]	1	1	1	[_linear]	✓	✓	0.432

5452	\[ {}y^{\prime } = 2 x^{2}+3 y \]	1	2	1	[[_linear, ‘class A‘]]	✓	✓	0.52

5453	\[ {}\left (1+x \right ) y^{\prime } = x^{2}-2 x +y \]	1	2	1	[_linear]	✓	✓	0.385

5498	\[ {}y^{\prime }+x y = \cos \left (x \right ) \]	1	2	1	[_linear]	✓	✓	0.548

5507	\[ {}y^{\prime }-x y = 0 \]	1	2	1	[_separable]	✓	✓	0.402

5623	\[ {}\left (1+x \right ) y^{\prime } = y \]	1	2	1	[_separable]	✓	✓	0.339

5624	\[ {}y^{\prime } = -2 x y \]	1	2	1	[_separable]	✓	✓	0.392

5632	\[ {}y^{\prime }+4 y = 1 \] i.c.	1	2	1	[_quadrature]	✓	✓	1.404

5635	\[ {}\left (-2+x \right ) y^{\prime } = x y \] i.c.	1	2	1	[_separable]	✓	✓	1.513

6404	\[ {}y^{\prime } = 2 x y \]	1	2	1	[_separable]	✓	✓	1.259

6406	\[ {}y^{\prime }+y = 1 \]	1	2	1	[_quadrature]	✓	✓	1.225

6408	\[ {}y^{\prime }-y = 2 \]	1	2	1	[_quadrature]	✓	✓	1.184

6410	\[ {}y^{\prime }+y = 0 \]	1	2	1	[_quadrature]	✓	✓	1.085

6412	\[ {}y^{\prime }-y = 0 \]	1	2	1	[_quadrature]	✓	✓	0.718

6414	\[ {}y^{\prime }-y = x^{2} \]	1	2	1	[[_linear, ‘class A‘]]	✓	✓	0.91

6423	\[ {}y^{\prime } = \frac {1}{\sqrt {-x^{2}+1}} \]	1	2	1	[_quadrature]	✓	✓	1.063

6424	\[ {}y^{\prime } = y+1 \]	1	2	1	[_quadrature]	✓	✓	0.765

6425	\[ {}y^{\prime } = x -y \] i.c.	1	2	1	[[_linear, ‘class A‘]]	✓	✓	7.867

6546	\[ {}y^{\prime }-2 y = x^{2} \] i.c.	1	1	1	[[_linear, ‘class A‘]]	✓	✓	3.437

13910	\[ {}y^{\prime }-2 y = 0 \]	1	2	1	[_quadrature]	✓	✓	0.687

13911	\[ {}y^{\prime }-2 x y = 0 \]	1	2	1	[_separable]	✓	✓	0.564

13912	\[ {}y^{\prime }+\frac {2 y}{2 x -1} = 0 \]	1	2	1	[_separable]	✓	✓	0.599

13913	\[ {}\left (x -3\right ) y^{\prime }-2 y = 0 \]	1	2	1	[_separable]	✓	✓	0.537

13914	\[ {}\left (x^{2}+1\right ) y^{\prime }-2 x y = 0 \]	1	2	1	[_separable]	✓	✓	0.451

13915	\[ {}y^{\prime }+\frac {y}{-1+x} = 0 \]	1	2	1	[_separable]	✓	✓	0.584

13916	\[ {}y^{\prime }+\frac {y}{-1+x} = 0 \]	1	1	1	[_separable]	✓	✓	0.532

13917	\[ {}\left (1-x \right ) y^{\prime }-2 y = 0 \]	1	1	1	[_separable]	✓	✓	0.664

13918	\[ {}\left (-x^{3}+2\right ) y^{\prime }-3 x^{2} y = 0 \]	1	2	1	[_separable]	✓	✓	0.634

13919	\[ {}\left (-x^{3}+2\right ) y^{\prime }+3 x^{2} y = 0 \]	1	2	1	[_separable]	✓	✓	0.55

13920	\[ {}\left (1+x \right ) y^{\prime }-x y = 0 \]	1	2	1	[_separable]	✓	✓	0.624

13921	\[ {}\left (1+x \right ) y^{\prime }+\left (1-x \right ) y = 0 \]	1	2	1	[_separable]	✓	✓	0.684

13944	\[ {}y^{\prime }-{\mathrm e}^{x} y = 0 \]	1	2	1	[_separable]	✓	✓	0.733

13945	\[ {}y^{\prime }-\tan \left (x \right ) y = 0 \]	1	2	1	[_separable]	✓	✓	0.992

13954	\[ {}y^{\prime }-{\mathrm e}^{x} y = 0 \]	1	2	1	[_separable]	✓	✓	0.621

13955	\[ {}y^{\prime }+{\mathrm e}^{2 x} y = 0 \]	1	2	1	[_separable]	✓	✓	0.686

13956	\[ {}y^{\prime }+y \cos \left (x \right ) = 0 \]	1	2	1	[_separable]	✓	✓	0.691

13957	\[ {}y^{\prime }+\ln \left (x \right ) y = 0 \]	1	1	1	[_separable]	✓	✓	1.01

13964	\[ {}y^{\prime }-{\mathrm e}^{x} y = 0 \]	1	2	1	[_separable]	✓	✓	0.969

13965	\[ {}y^{\prime }+y \sqrt {x^{2}+1} = 0 \]	1	2	1	[_separable]	✓	✓	1.208

13966	\[ {}\cos \left (x \right ) y^{\prime }+y = 0 \]	1	2	1	[_separable]	✓	✓	1.845

13967	\[ {}y^{\prime }+\sqrt {2 x^{2}+1}\, y = 0 \]	1	2	1	[_separable]	✓	✓	1.302

15467	\[ {}y^{\prime } = 1-x y \] i.c.	1	2	1	[_linear]	✓	✓	1.467

15469	\[ {}y^{\prime } = \sin \left (x \right ) y \] i.c.	1	2	1	[_separable]	✓	✓	1.372

15475	\[ {}y^{\prime }-2 x y = 0 \] i.c.	1	2	1	[_separable]	✓	✓	1.181

15483	\[ {}\left (1+x \right ) y^{\prime }-n y = 0 \]	1	2	1	[_separable]	✓	✓	0.543

2.21.1.30 First order ODE’s solved using series method. Ordinary point