Problems 24901 to 25000

2.2.250 Problems 24901 to 25000

Table 2.513: Main lookup table. Sorted sequentially by problem number.


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

24901	\begin{align} x^{4} y^{\prime \prime }&=y^{\prime } \left (y^{\prime }+x^{3}\right ) \\ y \left (1\right ) &= 2 \\ y^{\prime }\left (1\right ) &= 1 \\ \end{align}	[[_2nd_order, _missing_y]]	✓	✓	✓	✓	4.924

24902	\begin{align} y^{\prime \prime }&=2 x +\left (x^{2}-y^{\prime }\right )^{2} \\ \end{align}	[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_xy]]	✓	✓	✓	✓	824.461

24903	\begin{align} {y^{\prime \prime }}^{2}-2 y^{\prime \prime }+{y^{\prime }}^{2}-2 y^{\prime } x +x^{2}&=0 \\ y \left (0\right ) &= {\frac {1}{2}} \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align}	[[_2nd_order, _missing_y]]	✓	✓	✗	✗	878.937

24904	\begin{align} y^{\prime }-y^{\prime \prime } x +{y^{\prime \prime }}^{2}&=0 \\ \end{align}	[[_2nd_order, _missing_y]]	✓	✓	✓	✓	431.708

24905	\begin{align} {y^{\prime \prime }}^{3}&=12 y^{\prime } \left (-2 y^{\prime }+y^{\prime \prime } x \right ) \\ \end{align}	[[_2nd_order, _missing_y]]	✓	✓	✗	✗	447.350

24906	\begin{align} 3 y y^{\prime } y^{\prime \prime }&=-1+{y^{\prime }}^{3} \\ \end{align}	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	✓	✓	✗	3.479

24907	\begin{align} 4 y {y^{\prime }}^{2} y^{\prime \prime }&=3+{y^{\prime }}^{4} \\ \end{align}	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	✓	✓	✗	2.468

24908	\begin{align} y^{\prime }&=2 y \\ \end{align}	[_quadrature]	✓	✓	✓	✓	0.486

24909	\begin{align} y^{\prime } t&=y \\ \end{align}	[_separable]	✓	✓	✓	✓	1.343

24910	\begin{align} y^{\prime \prime }+4 y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	2.963

24911	\begin{align} y^{\prime }&=2 y \left (y-1\right ) \\ \end{align}	[_quadrature]	✓	✓	✓	✓	0.669

24912	\begin{align} 2 y y^{\prime }&=1 \\ \end{align}	[_quadrature]	✓	✓	✓	✓	0.485

24913	\begin{align} 2 y y^{\prime }&=y^{2}+t -1 \\ \end{align}	[_rational, _Bernoulli]	✓	✓	✓	✓	1.425

24914	\begin{align} y^{\prime }&=\frac {y^{2}-4 t y+6 t^{2}}{t^{2}} \\ \end{align}	[[_homogeneous, ‘class A‘], _rational, _Riccati]	✓	✓	✓	✓	2.075

24915	\begin{align} y^{\prime }&=3 y+12 \\ \end{align}	[_quadrature]	✓	✓	✓	✓	0.351

24916	\begin{align} y^{\prime }&=-y+3 t \\ \end{align}	[[_linear, ‘class A‘]]	✓	✓	✓	✓	0.623

24917	\begin{align} y^{\prime }&=y^{2}-y \\ \end{align}	[_quadrature]	✓	✓	✓	✓	0.503

24918	\begin{align} y^{\prime }&=2 t y \\ \end{align}	[_separable]	✓	✓	✓	✓	1.351

24919	\begin{align} y^{\prime }&=-{\mathrm e}^{y}-1 \\ \end{align}	[_quadrature]	✓	✓	✓	✓	0.864

24920	\begin{align} \left (1+t \right ) y^{\prime }+y&=0 \\ \end{align}	[_separable]	✓	✓	✓	✓	1.264

24921	\begin{align} y^{\prime }&=y^{2} \\ \end{align}	[_quadrature]	✓	✓	✓	✓	0.881

24922	\begin{align} y^{\prime }&=t +3 \\ \end{align}	[_quadrature]	✓	✓	✓	✓	0.173

24923	\begin{align} y^{\prime }&={\mathrm e}^{2 t}-1 \\ \end{align}	[_quadrature]	✓	✓	✓	✓	0.186

24924	\begin{align} y^{\prime }&=t \,{\mathrm e}^{-t} \\ \end{align}	[_quadrature]	✓	✓	✓	✓	0.199

24925	\begin{align} y^{\prime }&=\frac {1+t}{t} \\ \end{align}	[_quadrature]	✓	✓	✓	✓	0.172

24926	\begin{align} y^{\prime \prime }&=2 t +1 \\ \end{align}	[[_2nd_order, _quadrature]]	✓	✓	✓	✓	1.153

24927	\begin{align} y^{\prime \prime }&=6 \sin \left (3 t \right ) \\ \end{align}	[[_2nd_order, _quadrature]]	✓	✓	✓	✓	1.102

24928	\begin{align} y^{\prime }&=3 y+12 \\ y \left (0\right ) &= -2 \\ \end{align}	[_quadrature]	✓	✓	✓	✓	0.544

24929	\begin{align} y^{\prime }&=-y+3 t \\ y \left (0\right ) &= 0 \\ \end{align}	[[_linear, ‘class A‘]]	✓	✓	✓	✓	0.764

24930	\begin{align} y^{\prime }&=y^{2}-y \\ y \left (0\right ) &= {\frac {1}{2}} \\ \end{align}	[_quadrature]	✓	✓	✓	✓	0.811

24931	\begin{align} \left (1+t \right ) y^{\prime }+y&=0 \\ y \left (1\right ) &= -9 \\ \end{align}	[_separable]	✓	✓	✓	✓	1.474

24932	\begin{align} y^{\prime }&={\mathrm e}^{2 t}-1 \\ y \left (0\right ) &= 4 \\ \end{align}	[_quadrature]	✓	✓	✓	✓	0.282

24933	\begin{align} y^{\prime }&=t \,{\mathrm e}^{-t} \\ y \left (0\right ) &= -1 \\ \end{align}	[_quadrature]	✓	✓	✓	✓	0.301

24934	\begin{align} y^{\prime \prime }&=6 \sin \left (3 t \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align}	[[_2nd_order, _quadrature]]	✓	✓	✓	✓	3.408

24935	\begin{align} y^{\prime }&=t \\ \end{align}	[_quadrature]	✓	✓	✓	✓	0.251

24936	\begin{align} y^{\prime }&=y^{2} \\ \end{align}	[_quadrature]	✓	✓	✓	✓	0.835

24937	\begin{align} y^{\prime }&=y \left (y+t \right ) \\ \end{align}	[_Bernoulli]	✓	✓	✓	✓	1.120

24938	\begin{align} y^{\prime }&=1-y^{2} \\ \end{align}	[_quadrature]	✓	✓	✓	✓	1.251

24939	\begin{align} y^{\prime }&=-t +y \\ \end{align}	[[_linear, ‘class A‘]]	✓	✓	✓	✓	0.618

24940	\begin{align} y^{\prime }&=-t y \\ \end{align}	[_separable]	✓	✓	✓	✓	1.379

24941	\begin{align} y^{\prime }&=y-t^{2} \\ \end{align}	[[_linear, ‘class A‘]]	✓	✓	✓	✓	1.149

24942	\begin{align} y^{\prime }&=t y^{2} \\ \end{align}	[_separable]	✓	✓	✓	✓	2.486

24943	\begin{align} y^{\prime }&=\frac {t y}{1+y} \\ \end{align}	[_separable]	✓	✓	✓	✓	1.627

24944	\begin{align} y^{\prime }&=y^{2} \\ \end{align}	[_quadrature]	✓	✓	✓	✓	0.638

24945	\begin{align} y^{\prime }&=y \left (y+t \right ) \\ \end{align}	[_Bernoulli]	✓	✓	✓	✓	1.085

24946	\begin{align} y^{\prime }&=-t +y \\ \end{align}	[[_linear, ‘class A‘]]	✓	✓	✓	✓	0.582

24947	\begin{align} y^{\prime }&=1-y^{2} \\ \end{align}	[_quadrature]	✓	✓	✓	✓	0.490

24948	\begin{align} y^{\prime }&=2 y \left (5-y\right ) \\ \end{align}	[_quadrature]	✓	✓	✓	✓	0.713

24949	\begin{align} y y^{\prime }&=1-y \\ \end{align}	[_quadrature]	✓	✓	✓	✓	0.345

24950	\begin{align} t^{2} y^{\prime }&=1-2 t y \\ \end{align}	[_linear]	✓	✓	✓	✓	0.832

24951	\begin{align} \frac {y^{\prime }}{y}&=-t +y \\ \end{align}	[_Bernoulli]	✓	✓	✓	✓	1.112

24952	\begin{align} y^{\prime } t&=y-2 t y \\ \end{align}	[_separable]	✓	✓	✓	✓	0.844

24953	\begin{align} y^{\prime }&=t y^{2}-y^{2}+t -1 \\ \end{align}	[_separable]	✓	✓	✓	✓	2.208

24954	\begin{align} \left (t^{2}+3 y^{2}\right ) y^{\prime }&=-2 t y \\ \end{align}	[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert]	✓	✓	✓	✗	3.477

24955	\begin{align} y^{\prime }&=t^{2}+y^{2} \\ \end{align}	[[_Riccati, _special]]	✓	✓	✓	✗	39.619

24956	\begin{align} {\mathrm e}^{t} y^{\prime }&=y^{3}-y \\ \end{align}	[_separable]	✓	✓	✓	✓	3.775

24957	\begin{align} y y^{\prime }&=t \\ y \left (2\right ) &= -1 \\ \end{align}	[_separable]	✓	✓	✓	✓	4.724

24958	\begin{align} 1-y^{2}-t y y^{\prime }&=0 \\ \end{align}	[_separable]	✓	✓	✓	✓	4.242

24959	\begin{align} y^{3} y^{\prime }&=t \\ \end{align}	[_separable]	✓	✓	✓	✓	1.953

24960	\begin{align} y^{4} y^{\prime }&=t +2 \\ \end{align}	[_separable]	✓	✓	✓	✓	1.566

24961	\begin{align} y^{\prime }&=t y^{2} \\ \end{align}	[_separable]	✓	✓	✓	✓	2.179

24962	\begin{align} \tan \left (t \right ) y+y^{\prime }&=\tan \left (t \right ) \\ \end{align}	[_separable]	✓	✓	✓	✓	1.744

24963	\begin{align} y^{\prime }&=t^{m} y^{n} \\ \end{align}	[_separable]	✓	✓	✓	✓	3.130

24964	\begin{align} y^{\prime }&=4 y-y^{2} \\ \end{align}	[_quadrature]	✓	✓	✓	✓	0.735

24965	\begin{align} y y^{\prime }&=1+y^{2} \\ \end{align}	[_quadrature]	✓	✓	✓	✓	0.573

24966	\begin{align} y^{\prime }&=1+y^{2} \\ \end{align}	[_quadrature]	✓	✓	✓	✓	1.421

24967	\begin{align} t y y^{\prime }+t^{2}+1&=0 \\ \end{align}	[_separable]	✓	✓	✓	✓	1.364

24968	\begin{align} y+1+\left (y-1\right ) \left (t^{2}+1\right ) y^{\prime }&=0 \\ \end{align}	[_separable]	✓	✓	✓	✓	2.698

24969	\begin{align} 2 y y^{\prime }&={\mathrm e}^{t} \\ \end{align}	[_separable]	✓	✓	✓	✓	1.334

24970	\begin{align} \left (1-t \right ) y^{\prime }&=y^{2} \\ \end{align}	[_separable]	✓	✓	✓	✓	1.512

24971	\begin{align} -y+y^{\prime }&=y^{2} \\ y \left (0\right ) &= 0 \\ \end{align}	[_quadrature]	✓	✓	✓	✗	1.219

24972	\begin{align} y^{\prime }&=4 t y^{2} \\ y \left (1\right ) &= 0 \\ \end{align}	[_separable]	✓	✓	✓	✗	3.330

24973	\begin{align} y^{\prime }&=\frac {y x +2 y}{x} \\ y \left (1\right ) &= {\mathrm e} \\ \end{align}	[_separable]	✓	✓	✓	✓	1.355

24974	\begin{align} 2 t y+y^{\prime }&=0 \\ y \left (0\right ) &= 4 \\ \end{align}	[_separable]	✓	✓	✓	✓	1.726

24975	\begin{align} y^{\prime }&=\frac {\cot \left (y\right )}{t} \\ y \left (1\right ) &= \frac {\pi }{4} \\ \end{align}	[_separable]	✓	✓	✓	✓	4.118

24976	\begin{align} \frac {\left (u^{2}+1\right ) y^{\prime }}{y}&=u \\ y \left (0\right ) &= 2 \\ \end{align}	[_separable]	✓	✓	✓	✗	2.876

24977	\begin{align} t y-\left (t +2\right ) y^{\prime }&=0 \\ \end{align}	[_separable]	✓	✓	✓	✓	1.855

24978	\begin{align} y^{\prime }&=\frac {1+y^{2}}{t} \\ y \left (1\right ) &= \sqrt {3} \\ \end{align}	[_separable]	✓	✓	✓	✓	2.646

24979	\begin{align} 3 y+y^{\prime }&={\mathrm e}^{t} \\ y \left (0\right ) &= -2 \\ \end{align}	[[_linear, ‘class A‘]]	✓	✓	✓	✓	1.080

24980	\begin{align} \cos \left (t \right ) y^{\prime }+\sin \left (t \right ) y&=1 \\ y \left (0\right ) &= 5 \\ \end{align}	[_linear]	✓	✓	✓	✓	3.076

24981	\begin{align} -2 y+y^{\prime }&={\mathrm e}^{2 t} \\ y \left (0\right ) &= 4 \\ \end{align}	[[_linear, ‘class A‘]]	✓	✓	✓	✓	1.985

24982	\begin{align} y^{\prime } t +y&={\mathrm e}^{t} \\ y \left (1\right ) &= 0 \\ \end{align}	[_linear]	✓	✓	✓	✓	1.451

24983	\begin{align} y^{\prime } t +m y&=t \ln \left (t \right ) \\ \end{align}	[_linear]	✓	✓	✓	✓	2.088

24984	\begin{align} y^{\prime }&=-\frac {y}{t}+\cos \left (t^{2}\right ) \\ \end{align}	[_linear]	✓	✓	✓	✓	1.494

24985	\begin{align} y^{\prime }+2 y&=\sin \left (t \right ) \\ \end{align}	[[_linear, ‘class A‘]]	✓	✓	✓	✓	1.398

24986	\begin{align} y^{\prime }-3 y&=25 \cos \left (4 t \right ) \\ \end{align}	[[_linear, ‘class A‘]]	✓	✓	✓	✓	1.485

24987	\begin{align} t \left (1+t \right ) y^{\prime }&=2+y \\ \end{align}	[_separable]	✓	✓	✓	✓	1.554

24988	\begin{align} z^{\prime }&=2 t \left (z-t^{2}\right ) \\ \end{align}	[_linear]	✓	✓	✓	✓	1.676

24989	\begin{align} y^{\prime }+a y&=b \\ \end{align}	[_quadrature]	✓	✓	✓	✓	0.498

24990	\begin{align} y \cos \left (t \right )+y^{\prime }&=\cos \left (t \right ) \\ y \left (0\right ) &= 0 \\ \end{align}	[_separable]	✓	✓	✓	✓	2.116

24991	\begin{align} y^{\prime }-\frac {2 y}{1+t}&=\left (1+t \right )^{2} \\ \end{align}	[_linear]	✓	✓	✓	✓	1.938

24992	\begin{align} y^{\prime }-\frac {2 y}{t}&=\frac {1+t}{t} \\ y \left (1\right ) &= -3 \\ \end{align}	[_linear]	✓	✓	✓	✓	1.955

24993	\begin{align} y^{\prime }+a y&={\mathrm e}^{-a t} \\ \end{align}	[[_linear, ‘class A‘]]	✓	✓	✓	✓	0.806

24994	\begin{align} y^{\prime }+a y&={\mathrm e}^{b t} \\ \end{align}	[[_linear, ‘class A‘]]	✓	✓	✓	✓	1.166

24995	\begin{align} y^{\prime }+a y&=t^{n} {\mathrm e}^{-a t} \\ \end{align}	[[_linear, ‘class A‘]]	✓	✓	✓	✓	2.717

24996	\begin{align} y^{\prime }&=\tan \left (t \right ) y+\sec \left (t \right ) \\ \end{align}	[_linear]	✓	✓	✓	✓	1.455

24997	\begin{align} y^{\prime } t +2 y \ln \left (t \right )&=4 \ln \left (t \right ) \\ \end{align}	[_separable]	✓	✓	✓	✓	2.324

24998	\begin{align} y^{\prime }-\frac {n y}{t}&={\mathrm e}^{t} t^{n} \\ \end{align}	[_linear]	✓	✓	✓	✓	1.790

24999	\begin{align} -y+y^{\prime }&={\mathrm e}^{2 t} t \\ y \left (0\right ) &= a \\ \end{align}	[[_linear, ‘class A‘]]	✓	✓	✓	✓	1.431

25000	\begin{align} y^{\prime } t +3 y&=t^{2} \\ y \left (-1\right ) &= 2 \\ \end{align}	[_linear]	✓	✓	✓	✓	2.278

[next] [prev] [prev-tail] [front] [up]