Problems 17101 to 17200

2.2.172 Problems 17101 to 17200

Table 2.357: 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]	✓	✓	✓	✓	0.437

17102	\begin{align} y^{\prime }&=y^{3}-1 \\ \end{align}	[_quadrature]	✓	✓	✓	✓	23.464

17103	\begin{align} y^{\prime }&=y^{3}+y \\ \end{align}	[_quadrature]	✓	✓	✓	✓	1.319

17104	\begin{align} y^{\prime }&=y^{3}-y^{2} \\ \end{align}	[_quadrature]	✓	✓	✓	✓	11.197

17105	\begin{align} y^{\prime }&=y^{3}-y \\ \end{align}	[_quadrature]	✓	✓	✓	✓	0.914

17106	\begin{align} y^{\prime }&=y^{3}+y \\ \end{align}	[_quadrature]	✓	✓	✓	✓	0.707

17107	\begin{align} y^{\prime }&=x^{3} \\ y \left (0\right ) &= 0 \\ \end{align}	[_quadrature]	✓	✓	✓	✓	2.887

17108	\begin{align} y^{\prime }&=\cos \left (t \right ) \\ y \left (\frac {\pi }{2}\right ) &= -1 \\ \end{align}	[_quadrature]	✓	✓	✓	✓	0.362

17109	\begin{align} 1&=y^{\prime } \cos \left (y\right ) \\ y \left (0\right ) &= 2 \\ \end{align}	[_quadrature]	✓	✓	✗	✓	3.028

17110	\begin{align} \sin \left (y \right )^{2}&=x^{\prime } \\ x \left (0\right ) &= 0 \\ \end{align}	[_quadrature]	✓	✓	✓	✓	0.400

17111	\begin{align} y^{\prime }&=\frac {\sqrt {t}}{y} \\ y \left (0\right ) &= 2 \\ \end{align}	[_separable]	✓	✓	✓	✓	7.215

17112	\begin{align} y^{\prime }&=\sqrt {\frac {y}{t}} \\ y \left (1\right ) &= 2 \\ \end{align}	[[_homogeneous, ‘class A‘], _dAlembert]	✓	✓	✓	✗	12.843

17113	\begin{align} y^{\prime }&=\frac {{\mathrm e}^{t}}{1+y} \\ y \left (0\right ) &= -2 \\ \end{align}	[_separable]	✓	✓	✓	✓	2.310

17114	\begin{align} y^{\prime }&={\mathrm e}^{t -y} \\ y \left (0\right ) &= 0 \\ \end{align}	[_separable]	✓	✓	✓	✓	5.777

17115	\begin{align} y^{\prime }&=\frac {y}{\ln \left (y\right )} \\ y \left (0\right ) &= {\mathrm e} \\ \end{align}	[_quadrature]	✓	✓	✓	✓	0.845

17116	\begin{align} y^{\prime }&=t \sin \left (t^{2}\right ) \\ y \left (\sqrt {\pi }\right ) &= 0 \\ \end{align}	[_quadrature]	✓	✓	✓	✓	0.423

17117	\begin{align} y^{\prime }&=\frac {1}{x^{2}+1} \\ y \left (0\right ) &= 1 \\ \end{align}	[_quadrature]	✓	✓	✓	✓	0.326

17118	\begin{align} y^{\prime }&=\frac {\sin \left (x \right )}{\cos \left (y\right )+1} \\ y \left (0\right ) &= 0 \\ \end{align}	[_separable]	✓	✓	✗	✓	3.258

17119	\begin{align} y^{\prime }&=\frac {3+y}{1+3 x} \\ y \left (0\right ) &= 1 \\ \end{align}	[_separable]	✓	✓	✓	✓	2.731

17120	\begin{align} y^{\prime }&={\mathrm e}^{x -y} \\ y \left (0\right ) &= 1 \\ \end{align}	[_separable]	✓	✓	✓	✓	2.434

17121	\begin{align} y^{\prime }&={\mathrm e}^{2 x -y} \\ y \left (0\right ) &= 1 \\ \end{align}	[_separable]	✓	✓	✓	✓	2.753

17122	\begin{align} y^{\prime }&=\frac {3 y+1}{x +3} \\ y \left (0\right ) &= 1 \\ \end{align}	[_separable]	✓	✓	✓	✓	2.862

17123	\begin{align} y^{\prime }&=y \cos \left (t \right ) \\ y \left (0\right ) &= 1 \\ \end{align}	[_separable]	✓	✓	✓	✓	2.661

17124	\begin{align} y^{\prime }&=y^{2} \cos \left (t \right ) \\ y \left (0\right ) &= 1 \\ \end{align}	[_separable]	✓	✓	✓	✓	3.060

17125	\begin{align} y^{\prime }&=\sqrt {y}\, \cos \left (t \right ) \\ y \left (0\right ) &= 1 \\ \end{align}	[_separable]	✓	✓	✓	✗	4.303

17126	\begin{align} y^{\prime }+y f \left (t \right )&=0 \\ y \left (0\right ) &= 0 \\ \end{align}	[_separable]	✓	✓	✓	✓	2.043

17127	\begin{align} y^{\prime }&=-\frac {y-2}{x -2} \\ y \left (0\right ) &= 0 \\ \end{align}	[_separable]	✓	✓	✓	✓	2.592

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‘]]	✓	✓	✓	✓	6.226

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‘]]	✓	✓	✓	✓	6.199

17130	\begin{align} y^{\prime }&=\left (x +y-4\right )^{2} \\ \end{align}	[[_homogeneous, ‘class C‘], _Riccati]	✓	✓	✓	✓	3.576

17131	\begin{align} y^{\prime }&=\left (3 y+1\right )^{4} \\ \end{align}	[_quadrature]	✓	✓	✓	✓	0.303

17132	\begin{align} y^{\prime }&=3 y \\ \end{align}	[_quadrature]	✓	✓	✓	✓	0.719

17133	\begin{align} y^{\prime }&=-y \\ \end{align}	[_quadrature]	✓	✓	✓	✓	0.592

17134	\begin{align} y^{\prime }&=y^{2}-y \\ \end{align}	[_quadrature]	✓	✓	✓	✓	0.779

17135	\begin{align} y^{\prime }&=16 y-8 y^{2} \\ \end{align}	[_quadrature]	✓	✓	✓	✓	1.021

17136	\begin{align} y^{\prime }&=12+4 y-y^{2} \\ \end{align}	[_quadrature]	✓	✓	✓	✓	0.757

17137	\begin{align} y^{\prime }&=y f \left (t \right ) \\ y \left (1\right ) &= 1 \\ \end{align}	[_separable]	✓	✓	✓	✓	2.370

17138	\begin{align} -y+y^{\prime }&=10 \\ \end{align}	[_quadrature]	✓	✓	✓	✓	0.327

17139	\begin{align} -y+y^{\prime }&=2 \,{\mathrm e}^{-t} \\ \end{align}	[[_linear, ‘class A‘]]	✓	✓	✓	✓	1.325

17140	\begin{align} -y+y^{\prime }&=2 \cos \left (t \right ) \\ \end{align}	[[_linear, ‘class A‘]]	✓	✓	✓	✓	1.682

17141	\begin{align} -y+y^{\prime }&=t^{2}-2 t \\ \end{align}	[[_linear, ‘class A‘]]	✓	✓	✓	✓	1.175

17142	\begin{align} -y+y^{\prime }&=4 t \,{\mathrm e}^{-t} \\ \end{align}	[[_linear, ‘class A‘]]	✓	✓	✓	✓	1.632

17143	\begin{align} t y^{\prime }+y&=t^{2} \\ \end{align}	[_linear]	✓	✓	✓	✓	2.266

17144	\begin{align} t y^{\prime }+y&=t \\ \end{align}	[_linear]	✓	✓	✓	✓	3.035

17145	\begin{align} y^{\prime } x +y&=x \,{\mathrm e}^{x} \\ \end{align}	[_linear]	✓	✓	✓	✓	1.579

17146	\begin{align} y^{\prime } x +y&={\mathrm e}^{-x} \\ \end{align}	[_linear]	✓	✓	✓	✓	1.832

17147	\begin{align} y^{\prime }-\frac {2 t y}{t^{2}+1}&=2 \\ \end{align}	[_linear]	✓	✓	✓	✓	2.218

17148	\begin{align} y^{\prime }-\frac {4 t y}{4 t^{2}+1}&=4 t \\ \end{align}	[_linear]	✓	✓	✓	✓	2.685

17149	\begin{align} y^{\prime }&=2 x +\frac {x y}{x^{2}-1} \\ \end{align}	[_linear]	✓	✓	✓	✓	5.862

17150	\begin{align} y^{\prime }+\cot \left (t \right ) y&=\cos \left (t \right ) \\ \end{align}	[_linear]	✓	✓	✓	✓	2.066

17151	\begin{align} y^{\prime }-\frac {3 t y}{t^{2}-4}&=t \\ \end{align}	[_linear]	✓	✓	✓	✓	2.872

17152	\begin{align} y^{\prime }-\frac {4 t y}{4 t^{2}-9}&=t \\ \end{align}	[_linear]	✓	✓	✓	✓	7.391

17153	\begin{align} y^{\prime }-\frac {9 x y}{9 x^{2}+49}&=x \\ \end{align}	[_linear]	✓	✓	✓	✓	7.060

17154	\begin{align} y^{\prime }+2 \cot \left (x \right ) y&=\cos \left (x \right ) \\ \end{align}	[_linear]	✓	✓	✓	✓	2.180

17155	\begin{align} y^{\prime }+y x&=x^{3} \\ \end{align}	[_linear]	✓	✓	✓	✓	2.122

17156	\begin{align} y^{\prime }-y x&=x \\ \end{align}	[_separable]	✓	✓	✓	✓	1.964

17157	\begin{align} y^{\prime }&=\frac {1}{x +y^{2}} \\ \end{align}	[[_1st_order, _with_exponential_symmetries]]	✓	✓	✓	✓	1.730

17158	\begin{align} y^{\prime }-x&=y \\ \end{align}	[[_linear, ‘class A‘]]	✓	✓	✓	✓	0.898

17159	\begin{align} y-\left (x +3 y^{2}\right ) y^{\prime }&=0 \\ \end{align}	[[_homogeneous, ‘class G‘], _rational]	✓	✓	✓	✓	2.622

17160	\begin{align} x^{\prime }&=\frac {3 x t^{2}}{-t^{3}+1} \\ \end{align}	[_separable]	✓	✓	✓	✓	1.705

17161	\begin{align} p^{\prime }&=t^{3}+\frac {p}{t} \\ \end{align}	[_linear]	✓	✓	✓	✓	2.228

17162	\begin{align} v^{\prime }+v&={\mathrm e}^{-s} \\ \end{align}	[[_linear, ‘class A‘]]	✓	✓	✓	✓	1.125

17163	\begin{align} -y+y^{\prime }&=4 \,{\mathrm e}^{t} \\ y \left (0\right ) &= 4 \\ \end{align}	[[_linear, ‘class A‘]]	✓	✓	✓	✓	1.329

17164	\begin{align} y+y^{\prime }&={\mathrm e}^{-t} \\ y \left (0\right ) &= -1 \\ \end{align}	[[_linear, ‘class A‘]]	✓	✓	✓	✓	1.192

17165	\begin{align} y^{\prime }+3 t^{2} y&={\mathrm e}^{-t^{3}} \\ y \left (0\right ) &= 2 \\ \end{align}	[_linear]	✓	✓	✓	✓	3.263

17166	\begin{align} 2 t y+y^{\prime }&=2 t \\ y \left (0\right ) &= -1 \\ \end{align}	[_separable]	✓	✓	✓	✓	2.131

17167	\begin{align} t y^{\prime }+y&=\cos \left (t \right ) \\ y \left (\frac {\pi }{2}\right ) &= \frac {4}{\pi } \\ \end{align}	[_linear]	✓	✓	✓	✓	2.083

17168	\begin{align} t y^{\prime }+y&=2 \,{\mathrm e}^{t} t \\ y \left (1\right ) &= -1 \\ \end{align}	[_linear]	✓	✓	✓	✓	1.766

17169	\begin{align} \left (1+{\mathrm e}^{t}\right ) y^{\prime }+y \,{\mathrm e}^{t}&=t \\ y \left (0\right ) &= -1 \\ \end{align}	[_linear]	✓	✓	✓	✓	2.193

17170	\begin{align} \left (t^{2}+4\right ) y^{\prime }+2 t y&=2 t \\ y \left (0\right ) &= -4 \\ \end{align}	[_separable]	✓	✓	✓	✓	2.445

17171	\begin{align} x^{\prime }&=x+t +1 \\ x \left (0\right ) &= 2 \\ \end{align}	[[_linear, ‘class A‘]]	✓	✓	✓	✓	1.078

17172	\begin{align} y^{\prime }&=2 y+{\mathrm e}^{2 t} \\ y \left (0\right ) &= 0 \\ \end{align}	[[_linear, ‘class A‘]]	✓	✓	✓	✓	2.262

17173	\begin{align} y^{\prime }-\frac {y}{t}&=\ln \left (t \right ) \\ \end{align}	[_linear]	✓	✓	✓	✓	1.885

17174	\begin{align} y^{\prime \prime }-\frac {y^{\prime }}{t}+\frac {y}{t^{2}}&=\frac {1}{t} \\ \end{align}	[[_2nd_order, _exact, _linear, _nonhomogeneous]]	✓	✓	✓	✓	1.850

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‘]]	✓	✓	✓	✗	0.928

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‘]]	✓	✓	✓	✗	0.968

17177	\begin{align} -y+y^{\prime }&=\sin \left (2 t \right ) \\ \end{align}	[[_linear, ‘class A‘]]	✓	✓	✓	✓	1.723

17178	\begin{align} y+y^{\prime }&=5 \,{\mathrm e}^{2 t} \\ \end{align}	[[_linear, ‘class A‘]]	✓	✓	✓	✓	1.310

17179	\begin{align} y+y^{\prime }&={\mathrm e}^{-t} \\ \end{align}	[[_linear, ‘class A‘]]	✓	✓	✓	✓	0.994

17180	\begin{align} y+y^{\prime }&=2-{\mathrm e}^{2 t} \\ \end{align}	[[_linear, ‘class A‘]]	✓	✓	✓	✓	1.872

17181	\begin{align} y^{\prime }-5 y&=t \\ \end{align}	[[_linear, ‘class A‘]]	✓	✓	✓	✓	0.958

17182	\begin{align} 3 y+y^{\prime }&=27 t^{2}+9 \\ \end{align}	[[_linear, ‘class A‘]]	✓	✓	✓	✓	1.704

17183	\begin{align} -\frac {y}{2}+y^{\prime }&=5 \cos \left (t \right )+2 \,{\mathrm e}^{t} \\ \end{align}	[[_linear, ‘class A‘]]	✓	✓	✓	✓	2.349

17184	\begin{align} y^{\prime }+4 y&=8 \cos \left (4 t \right ) \\ \end{align}	[[_linear, ‘class A‘]]	✓	✓	✓	✓	1.799

17185	\begin{align} y^{\prime }+10 y&=2 \,{\mathrm e}^{t} \\ \end{align}	[[_linear, ‘class A‘]]	✓	✓	✓	✓	1.336

17186	\begin{align} y^{\prime }-3 y&=27 t^{2} \\ \end{align}	[[_linear, ‘class A‘]]	✓	✓	✓	✓	1.727

17187	\begin{align} -y+y^{\prime }&=2 \,{\mathrm e}^{t} \\ \end{align}	[[_linear, ‘class A‘]]	✓	✓	✓	✓	1.088

17188	\begin{align} y+y^{\prime }&=4+3 \,{\mathrm e}^{t} \\ \end{align}	[[_linear, ‘class A‘]]	✓	✓	✓	✓	2.056

17189	\begin{align} y+y^{\prime }&=2 \cos \left (t \right )+t \\ \end{align}	[[_linear, ‘class A‘]]	✓	✓	✓	✓	1.920

17190	\begin{align} \frac {y}{2}+y^{\prime }&=\sin \left (t \right ) \\ y \left (0\right ) &= a \\ \end{align}	[[_linear, ‘class A‘]]	✓	✓	✓	✓	1.839

17191	\begin{align} -\frac {y}{2}+y^{\prime }&=\sin \left (t \right ) \\ y \left (0\right ) &= a \\ \end{align}	[[_linear, ‘class A‘]]	✓	✓	✓	✓	1.848

17192	\begin{align} t y^{\prime }+y&=t \cos \left (t \right ) \\ \end{align}	[_linear]	✓	✓	✓	✓	1.680

17193	\begin{align} y+y^{\prime }&=t \\ y \left (0\right ) &= 0 \\ \end{align}	[[_linear, ‘class A‘]]	✓	✓	✓	✓	2.090

17194	\begin{align} y+y^{\prime }&=\sin \left (t \right ) \\ y \left (0\right ) &= 0 \\ \end{align}	[[_linear, ‘class A‘]]	✓	✓	✓	✓	1.743

17195	\begin{align} y+y^{\prime }&=\cos \left (t \right ) \\ y \left (0\right ) &= 0 \\ \end{align}	[[_linear, ‘class A‘]]	✓	✓	✓	✓	1.786

17196	\begin{align} y+y^{\prime }&={\mathrm e}^{t} \\ y \left (0\right ) &= 0 \\ \end{align}	[[_linear, ‘class A‘]]	✓	✓	✓	✓	1.403

17197	\begin{align} y^{2}-\frac {y}{2 \sqrt {t}}+\left (2 t y-\sqrt {t}+1\right ) y^{\prime }&=0 \\ \end{align}	[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	✓	✓	✗	0.520

17198	\begin{align} \frac {t}{\sqrt {t^{2}+y^{2}}}+\frac {y y^{\prime }}{\sqrt {t^{2}+y^{2}}}&=0 \\ \end{align}	[_separable]	✓	✓	✓	✓	4.652

17199	\begin{align} y \cos \left (t y\right )+t \cos \left (t y\right ) y^{\prime }&=0 \\ \end{align}	[_separable]	✓	✓	✓	✓	0.090

17200	\begin{align} \sec \left (t \right )^{2} y+2 t +\tan \left (t \right ) y^{\prime }&=0 \\ \end{align}	[_linear]	✓	✓	✓	✗	13.542

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