Problems 17101 to 17200

2.2.172 Problems 17101 to 17200

Table 2.361: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	Maple	Mma	Sympy	time(sec)

17101	\begin{align} y^{\prime }&=y^{3}+1 \\ \end{align}	[_quadrature]	✓	✓	✓	✓	1.065

17102	\begin{align} y^{\prime }&=y^{3}-1 \\ \end{align}	[_quadrature]	✓	✓	✓	✓	59.776

17103	\begin{align} y^{\prime }&=y^{3}+y \\ \end{align}	[_quadrature]	✓	✓	✓	✓	6.138

17104	\begin{align} y^{\prime }&=y^{3}-y^{2} \\ \end{align}	[_quadrature]	✓	✓	✓	✓	12.286

17105	\begin{align} y^{\prime }&=y^{3}-y \\ \end{align}	[_quadrature]	✓	✓	✓	✓	2.431

17106	\begin{align} y^{\prime }&=y^{3}+y \\ \end{align}	[_quadrature]	✓	✓	✓	✓	5.052

17107	\begin{align} y^{\prime }&=x^{3} \\ y \left (0\right ) &= 0 \\ \end{align}	[_quadrature]	✓	✓	✓	✓	9.527

17108	\begin{align} y^{\prime }&=\cos \left (t \right ) \\ y \left (\frac {\pi }{2}\right ) &= -1 \\ \end{align}	[_quadrature]	✓	✓	✓	✓	0.513

17109	\begin{align} 1&=\cos \left (y\right ) y^{\prime } \\ y \left (0\right ) &= 2 \\ \end{align}	[_quadrature]	✓	✓	✗	✓	7.683

17110	\begin{align} \sin \left (y \right )^{2}&=x^{\prime } \\ x \left (0\right ) &= 0 \\ \end{align}	[_quadrature]	✓	✓	✓	✓	0.523

17111	\begin{align} y^{\prime }&=\frac {\sqrt {t}}{y} \\ y \left (0\right ) &= 2 \\ \end{align}	[_separable]	✓	✓	✓	✓	31.276

17112	\begin{align} y^{\prime }&=\sqrt {\frac {y}{t}} \\ y \left (1\right ) &= 2 \\ \end{align}	[[_homogeneous, ‘class A‘], _dAlembert]	✓	✓	✓	✗	23.931

17113	\begin{align} y^{\prime }&=\frac {{\mathrm e}^{t}}{1+y} \\ y \left (0\right ) &= -2 \\ \end{align}	[_separable]	✓	✓	✓	✓	6.411

17114	\begin{align} y^{\prime }&={\mathrm e}^{t -y} \\ y \left (0\right ) &= 0 \\ \end{align}	[_separable]	✓	✓	✓	✓	16.835

17115	\begin{align} y^{\prime }&=\frac {y}{\ln \left (y\right )} \\ y \left (0\right ) &= {\mathrm e} \\ \end{align}	[_quadrature]	✓	✓	✓	✓	2.171

17116	\begin{align} y^{\prime }&=t \sin \left (t^{2}\right ) \\ y \left (\sqrt {\pi }\right ) &= 0 \\ \end{align}	[_quadrature]	✓	✓	✓	✓	0.980

17117	\begin{align} y^{\prime }&=\frac {1}{x^{2}+1} \\ y \left (0\right ) &= 1 \\ \end{align}	[_quadrature]	✓	✓	✓	✓	0.463

17118	\begin{align} y^{\prime }&=\frac {\sin \left (x \right )}{\cos \left (y\right )+1} \\ y \left (0\right ) &= 0 \\ \end{align}	[_separable]	✓	✓	✗	✓	4.257

17119	\begin{align} y^{\prime }&=\frac {y+3}{1+3 x} \\ y \left (0\right ) &= 1 \\ \end{align}	[_separable]	✓	✓	✓	✓	4.800

17120	\begin{align} y^{\prime }&={\mathrm e}^{x -y} \\ y \left (0\right ) &= 1 \\ \end{align}	[_separable]	✓	✓	✓	✓	4.913

17121	\begin{align} y^{\prime }&={\mathrm e}^{2 x -y} \\ y \left (0\right ) &= 1 \\ \end{align}	[_separable]	✓	✓	✓	✓	5.405

17122	\begin{align} y^{\prime }&=\frac {3 y+1}{x +3} \\ y \left (0\right ) &= 1 \\ \end{align}	[_separable]	✓	✓	✓	✓	5.253

17123	\begin{align} y^{\prime }&=\cos \left (t \right ) y \\ y \left (0\right ) &= 1 \\ \end{align}	[_separable]	✓	✓	✓	✓	4.866

17124	\begin{align} y^{\prime }&=y^{2} \cos \left (t \right ) \\ y \left (0\right ) &= 1 \\ \end{align}	[_separable]	✓	✓	✓	✓	4.796

17125	\begin{align} y^{\prime }&=\sqrt {y}\, \cos \left (t \right ) \\ y \left (0\right ) &= 1 \\ \end{align}	[_separable]	✓	✓	✓	✗	6.536

17126	\begin{align} y^{\prime }+y f \left (t \right )&=0 \\ y \left (0\right ) &= 0 \\ \end{align}	[_separable]	✓	✓	✓	✓	5.640

17127	\begin{align} y^{\prime }&=-\frac {-2+y}{x -2} \\ y \left (0\right ) &= 0 \\ \end{align}	[_separable]	✓	✓	✓	✓	4.931

17128	\begin{align} y^{\prime }&=\frac {x +y+3}{3 x +3 y+1} \\ \end{align}	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	✓	✓	✓	12.388

17129	\begin{align} y^{\prime }&=\frac {x -y+2}{2 x -2 y-1} \\ \end{align}	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	✓	✓	✓	13.173

17130	\begin{align} y^{\prime }&=\left (x +y-4\right )^{2} \\ \end{align}	[[_homogeneous, ‘class C‘], _Riccati]	✓	✓	✓	✓	6.647

17131	\begin{align} y^{\prime }&=\left (3 y+1\right )^{4} \\ \end{align}	[_quadrature]	✓	✓	✓	✓	0.552

17132	\begin{align} y^{\prime }&=3 y \\ \end{align}	[_quadrature]	✓	✓	✓	✓	1.801

17133	\begin{align} y^{\prime }&=-y \\ \end{align}	[_quadrature]	✓	✓	✓	✓	1.490

17134	\begin{align} y^{\prime }&=y^{2}-y \\ \end{align}	[_quadrature]	✓	✓	✓	✓	1.799

17135	\begin{align} y^{\prime }&=16 y-8 y^{2} \\ \end{align}	[_quadrature]	✓	✓	✓	✓	2.520

17136	\begin{align} y^{\prime }&=12+4 y-y^{2} \\ \end{align}	[_quadrature]	✓	✓	✓	✓	1.745

17137	\begin{align} y^{\prime }&=y f \left (t \right ) \\ y \left (1\right ) &= 1 \\ \end{align}	[_separable]	✓	✓	✓	✓	4.602

17138	\begin{align} -y+y^{\prime }&=10 \\ \end{align}	[_quadrature]	✓	✓	✓	✓	0.588

17139	\begin{align} -y+y^{\prime }&=2 \,{\mathrm e}^{-t} \\ \end{align}	[[_linear, ‘class A‘]]	✓	✓	✓	✓	2.454

17140	\begin{align} -y+y^{\prime }&=2 \cos \left (t \right ) \\ \end{align}	[[_linear, ‘class A‘]]	✓	✓	✓	✓	2.467

17141	\begin{align} -y+y^{\prime }&=t^{2}-2 t \\ \end{align}	[[_linear, ‘class A‘]]	✓	✓	✓	✓	2.294

17142	\begin{align} -y+y^{\prime }&=4 t \,{\mathrm e}^{-t} \\ \end{align}	[[_linear, ‘class A‘]]	✓	✓	✓	✓	2.352

17143	\begin{align} t y^{\prime }+y&=t^{2} \\ \end{align}	[_linear]	✓	✓	✓	✓	4.981

17144	\begin{align} t y^{\prime }+y&=t \\ \end{align}	[_linear]	✓	✓	✓	✓	8.460

17145	\begin{align} x y^{\prime }+y&=x \,{\mathrm e}^{x} \\ \end{align}	[_linear]	✓	✓	✓	✓	2.217

17146	\begin{align} x y^{\prime }+y&={\mathrm e}^{-x} \\ \end{align}	[_linear]	✓	✓	✓	✓	2.476

17147	\begin{align} y^{\prime }-\frac {2 t y}{t^{2}+1}&=2 \\ \end{align}	[_linear]	✓	✓	✓	✓	3.206

17148	\begin{align} y^{\prime }-\frac {4 t y}{4 t^{2}+1}&=4 t \\ \end{align}	[_linear]	✓	✓	✓	✓	3.884

17149	\begin{align} y^{\prime }&=2 x +\frac {x y}{x^{2}-1} \\ \end{align}	[_linear]	✓	✓	✓	✓	14.337

17150	\begin{align} y^{\prime }+\cot \left (t \right ) y&=\cos \left (t \right ) \\ \end{align}	[_linear]	✓	✓	✓	✓	2.973

17151	\begin{align} y^{\prime }-\frac {3 t y}{t^{2}-4}&=t \\ \end{align}	[_linear]	✓	✓	✓	✓	4.444

17152	\begin{align} y^{\prime }-\frac {4 t y}{4 t^{2}-9}&=t \\ \end{align}	[_linear]	✓	✓	✓	✓	15.191

17153	\begin{align} y^{\prime }-\frac {9 x y}{9 x^{2}+49}&=x \\ \end{align}	[_linear]	✓	✓	✓	✓	14.408

17154	\begin{align} y^{\prime }+2 y \cot \left (x \right )&=\cos \left (x \right ) \\ \end{align}	[_linear]	✓	✓	✓	✓	3.044

17155	\begin{align} y^{\prime }+y x&=x^{3} \\ \end{align}	[_linear]	✓	✓	✓	✓	3.590

17156	\begin{align} y^{\prime }-y x&=x \\ \end{align}	[_separable]	✓	✓	✓	✓	3.799

17157	\begin{align} y^{\prime }&=\frac {1}{x +y^{2}} \\ \end{align}	[[_1st_order, _with_exponential_symmetries]]	✓	✓	✓	✓	3.261

17158	\begin{align} y^{\prime }-x&=y \\ \end{align}	[[_linear, ‘class A‘]]	✓	✓	✓	✓	1.919

17159	\begin{align} y-\left (x +3 y^{2}\right ) y^{\prime }&=0 \\ \end{align}	[[_homogeneous, ‘class G‘], _rational]	✓	✓	✓	✓	5.802

17160	\begin{align} x^{\prime }&=\frac {3 x t^{2}}{-t^{3}+1} \\ \end{align}	[_separable]	✓	✓	✓	✓	3.263

17161	\begin{align} p^{\prime }&=t^{3}+\frac {p}{t} \\ \end{align}	[_linear]	✓	✓	✓	✓	4.092

17162	\begin{align} v^{\prime }+v&={\mathrm e}^{-s} \\ \end{align}	[[_linear, ‘class A‘]]	✓	✓	✓	✓	2.043

17163	\begin{align} -y+y^{\prime }&=4 \,{\mathrm e}^{t} \\ y \left (0\right ) &= 4 \\ \end{align}	[[_linear, ‘class A‘]]	✓	✓	✓	✓	2.262

17164	\begin{align} y+y^{\prime }&={\mathrm e}^{-t} \\ y \left (0\right ) &= -1 \\ \end{align}	[[_linear, ‘class A‘]]	✓	✓	✓	✓	2.164

17165	\begin{align} y^{\prime }+3 t^{2} y&={\mathrm e}^{-t^{3}} \\ y \left (0\right ) &= 2 \\ \end{align}	[_linear]	✓	✓	✓	✓	4.431

17166	\begin{align} 2 y t +y^{\prime }&=2 t \\ y \left (0\right ) &= -1 \\ \end{align}	[_separable]	✓	✓	✓	✓	3.877

17167	\begin{align} t y^{\prime }+y&=\cos \left (t \right ) \\ y \left (\frac {\pi }{2}\right ) &= \frac {4}{\pi } \\ \end{align}	[_linear]	✓	✓	✓	✓	2.870

17168	\begin{align} t y^{\prime }+y&=2 \,{\mathrm e}^{t} t \\ y \left (1\right ) &= -1 \\ \end{align}	[_linear]	✓	✓	✓	✓	2.460

17169	\begin{align} \left (1+{\mathrm e}^{t}\right ) y^{\prime }+{\mathrm e}^{t} y&=t \\ y \left (0\right ) &= -1 \\ \end{align}	[_linear]	✓	✓	✓	✓	3.057

17170	\begin{align} \left (t^{2}+4\right ) y^{\prime }+2 y t&=2 t \\ y \left (0\right ) &= -4 \\ \end{align}	[_separable]	✓	✓	✓	✓	4.168

17171	\begin{align} x^{\prime }&=x+t +1 \\ x \left (0\right ) &= 2 \\ \end{align}	[[_linear, ‘class A‘]]	✓	✓	✓	✓	2.113

17172	\begin{align} y^{\prime }&=2 y+{\mathrm e}^{2 t} \\ y \left (0\right ) &= 0 \\ \end{align}	[[_linear, ‘class A‘]]	✓	✓	✓	✓	2.224

17173	\begin{align} y^{\prime }-\frac {y}{t}&=\ln \left (t \right ) \\ \end{align}	[_linear]	✓	✓	✓	✓	3.135

17174	\begin{align} y^{\prime \prime }-\frac {y^{\prime }}{t}+\frac {y}{t^{2}}&=\frac {1}{t} \\ \end{align}	[[_2nd_order, _exact, _linear, _nonhomogeneous]]	✓	✓	✓	✓	11.326

17175	\begin{align} y+y^{\prime }&=\left \{\begin {array}{cc} 4 & 0\le t <2 \\ 0 & 2\le t \end {array}\right . \\ y \left (0\right ) &= 0 \\ \end{align}	[[_linear, ‘class A‘]]	✓	✓	✓	✗	1.975

17176	\begin{align} y+y^{\prime }&=\left \{\begin {array}{cc} t & 0\le t <1 \\ 0 & 1\le t \end {array}\right . \\ y \left (0\right ) &= 1 \\ \end{align}	[[_linear, ‘class A‘]]	✓	✓	✓	✗	2.050

17177	\begin{align} -y+y^{\prime }&=\sin \left (2 t \right ) \\ \end{align}	[[_linear, ‘class A‘]]	✓	✓	✓	✓	2.608

17178	\begin{align} y+y^{\prime }&=5 \,{\mathrm e}^{2 t} \\ \end{align}	[[_linear, ‘class A‘]]	✓	✓	✓	✓	2.470

17179	\begin{align} y+y^{\prime }&={\mathrm e}^{-t} \\ \end{align}	[[_linear, ‘class A‘]]	✓	✓	✓	✓	1.829

17180	\begin{align} y+y^{\prime }&=2-{\mathrm e}^{2 t} \\ \end{align}	[[_linear, ‘class A‘]]	✓	✓	✓	✓	3.013

17181	\begin{align} y^{\prime }-5 y&=t \\ \end{align}	[[_linear, ‘class A‘]]	✓	✓	✓	✓	2.085

17182	\begin{align} 3 y+y^{\prime }&=27 t^{2}+9 \\ \end{align}	[[_linear, ‘class A‘]]	✓	✓	✓	✓	2.755

17183	\begin{align} -\frac {y}{2}+y^{\prime }&=5 \cos \left (t \right )+2 \,{\mathrm e}^{t} \\ \end{align}	[[_linear, ‘class A‘]]	✓	✓	✓	✓	3.150

17184	\begin{align} y^{\prime }+4 y&=8 \cos \left (4 t \right ) \\ \end{align}	[[_linear, ‘class A‘]]	✓	✓	✓	✓	2.650

17185	\begin{align} y^{\prime }+10 y&=2 \,{\mathrm e}^{t} \\ \end{align}	[[_linear, ‘class A‘]]	✓	✓	✓	✓	2.461

17186	\begin{align} y^{\prime }-3 y&=27 t^{2} \\ \end{align}	[[_linear, ‘class A‘]]	✓	✓	✓	✓	3.116

17187	\begin{align} -y+y^{\prime }&=2 \,{\mathrm e}^{t} \\ \end{align}	[[_linear, ‘class A‘]]	✓	✓	✓	✓	1.923

17188	\begin{align} y+y^{\prime }&=4+3 \,{\mathrm e}^{t} \\ \end{align}	[[_linear, ‘class A‘]]	✓	✓	✓	✓	3.320

17189	\begin{align} y+y^{\prime }&=2 \cos \left (t \right )+t \\ \end{align}	[[_linear, ‘class A‘]]	✓	✓	✓	✓	2.765

17190	\begin{align} \frac {y}{2}+y^{\prime }&=\sin \left (t \right ) \\ y \left (0\right ) &= a \\ \end{align}	[[_linear, ‘class A‘]]	✓	✓	✓	✓	2.565

17191	\begin{align} -\frac {y}{2}+y^{\prime }&=\sin \left (t \right ) \\ y \left (0\right ) &= a \\ \end{align}	[[_linear, ‘class A‘]]	✓	✓	✓	✓	2.524

17192	\begin{align} t y^{\prime }+y&=\cos \left (t \right ) t \\ \end{align}	[_linear]	✓	✓	✓	✓	2.339

17193	\begin{align} y+y^{\prime }&=t \\ y \left (0\right ) &= 0 \\ \end{align}	[[_linear, ‘class A‘]]	✓	✓	✓	✓	2.145

17194	\begin{align} y+y^{\prime }&=\sin \left (t \right ) \\ y \left (0\right ) &= 0 \\ \end{align}	[[_linear, ‘class A‘]]	✓	✓	✓	✓	2.610

17195	\begin{align} y+y^{\prime }&=\cos \left (t \right ) \\ y \left (0\right ) &= 0 \\ \end{align}	[[_linear, ‘class A‘]]	✓	✓	✓	✓	2.625

17196	\begin{align} y+y^{\prime }&={\mathrm e}^{t} \\ y \left (0\right ) &= 0 \\ \end{align}	[[_linear, ‘class A‘]]	✓	✓	✓	✓	2.406

17197	\begin{align} y^{2}-\frac {y}{2 \sqrt {t}}+\left (2 y t -\sqrt {t}+1\right ) y^{\prime }&=0 \\ \end{align}	[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	✓	✓	✗	1.267

17198	\begin{align} \frac {t}{\sqrt {t^{2}+y^{2}}}+\frac {y y^{\prime }}{\sqrt {t^{2}+y^{2}}}&=0 \\ \end{align}	[_separable]	✓	✓	✓	✓	13.264

17199	\begin{align} y \cos \left (y t \right )+t \cos \left (y t \right ) y^{\prime }&=0 \\ \end{align}	[_separable]	✓	✓	✓	✓	0.238

17200	\begin{align} \sec \left (t \right )^{2} y+2 t +\tan \left (t \right ) y^{\prime }&=0 \\ \end{align}	[_linear]	✓	✓	✓	✗	13.272

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