Problems 19001 to 19100

2.2.191 Problems 19001 to 19100

Table 2.395: Main lookup table. Sorted sequentially by problem number.


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

19001	\begin{align} x_{1}^{\prime }&=x_{1}+8 x_{2}+5 x_{3}+3 x_{4} \\ x_{2}^{\prime }&=2 x_{1}+16 x_{2}+10 x_{3}+6 x_{4} \\ x_{3}^{\prime }&=5 x_{1}-14 x_{2}-11 x_{3}-3 x_{4} \\ x_{4}^{\prime }&=-x_{1}-8 x_{2}-5 x_{3}-3 x_{4} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.983

19002	\begin{align} x_{1}^{\prime }&=-2 x_{1}+2 x_{2}-2 x_{4} \\ x_{2}^{\prime }&=-x_{1}+3 x_{2}-x_{3}+x_{4} \\ x_{3}^{\prime }&=-2 x_{1}-2 x_{2}-4 x_{3}+2 x_{4} \\ x_{4}^{\prime }&=-7 x_{1}+x_{2}-7 x_{3}+3 x_{4} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	1.702

19003	\begin{align} x_{1}^{\prime }&=-5 x_{1}-2 x_{2}-x_{3}+2 x_{4}+3 x_{5} \\ x_{2}^{\prime }&=-3 x_{2} \\ x_{3}^{\prime }&=x_{1}-x_{3}-x_{5} \\ x_{4}^{\prime }&=2 x_{1}+x_{2}-4 x_{4}-2 x_{5} \\ x_{5}^{\prime }&=-3 x_{1}-2 x_{2}-x_{3}+2 x_{4}+x_{5} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	1.455

19004	\begin{align} x_{1}^{\prime }&=-3 x_{2}-2 x_{3}+3 x_{4}+2 x_{5} \\ x_{2}^{\prime }&=8 x_{1}+6 x_{2}+4 x_{3}-8 x_{4}-16 x_{5} \\ x_{3}^{\prime }&=-8 x_{1}-8 x_{2}-6 x_{3}+8 x_{4}-16 x_{5} \\ x_{4}^{\prime }&=8 x_{1}+7 x_{2}+4 x_{3}-9 x_{4}-16 x_{5} \\ x_{5}^{\prime }&=-3 x_{1}-5 x_{2}-3 x_{3}+5 x_{4}+7 x_{5} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	4.635

19005	\begin{align} x_{1}^{\prime }&=-2 x_{1}+2 x_{2}+x_{3} \\ x_{2}^{\prime }&=-2 x_{1}+2 x_{2}+2 x_{3} \\ x_{3}^{\prime }&=2 x_{1}-3 x_{2}-3 x_{3} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	1.001

19006	\begin{align} x_{1}^{\prime }&=2 x_{1}-4 x_{2}-x_{3} \\ x_{2}^{\prime }&=x_{1}+x_{2}+3 x_{3} \\ x_{3}^{\prime }&=3 x_{1}-4 x_{2}-2 x_{3} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.821

19007	\begin{align} x_{1}^{\prime }&=-2 x_{2}-x_{3} \\ x_{2}^{\prime }&=x_{1}-x_{2}+x_{3} \\ x_{3}^{\prime }&=x_{1}-2 x_{2}-2 x_{3} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.887

19008	\begin{align} x_{1}^{\prime }&=-4 x_{1}+2 x_{2}-x_{3} \\ x_{2}^{\prime }&=-6 x_{1}-3 x_{3} \\ x_{3}^{\prime }&=\frac {8 x_{2}}{3}-2 x_{3} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	1.008

19009	\begin{align} x_{1}^{\prime }&=-7 x_{1}+6 x_{2}-6 x_{3} \\ x_{2}^{\prime }&=-9 x_{1}+5 x_{2}-9 x_{3} \\ x_{3}^{\prime }&=-x_{2}-x_{3} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.946

19010	\begin{align} x_{1}^{\prime }&=\frac {4 x_{1}}{3}+\frac {4 x_{2}}{3}-\frac {11 x_{3}}{3} \\ x_{2}^{\prime }&=-\frac {16 x_{1}}{3}-\frac {x_{2}}{3}+\frac {14 x_{3}}{3} \\ x_{3}^{\prime }&=3 x_{1}-2 x_{2}-2 x_{3} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.870

19011	\begin{align} x_{1}^{\prime }&=x_{1}+x_{2}+x_{3} \\ x_{2}^{\prime }&=2 x_{1}+x_{2}-x_{3} \\ x_{3}^{\prime }&=-8 x_{1}-5 x_{2}-3 x_{3} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.668

19012	\begin{align} x_{1}^{\prime }&=x_{1}-x_{2}+4 x_{3} \\ x_{2}^{\prime }&=3 x_{1}+2 x_{2}-x_{3} \\ x_{3}^{\prime }&=2 x_{1}+x_{2}-x_{3} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.573

19013	\begin{align} x_{1}^{\prime }&=\frac {3 x_{1}}{4}+\frac {29 x_{2}}{4}-\frac {11 x_{3}}{2} \\ x_{2}^{\prime }&=-\frac {3 x_{1}}{4}+\frac {3 x_{2}}{4}-\frac {5 x_{3}}{2} \\ x_{3}^{\prime }&=\frac {5 x_{1}}{4}+\frac {11 x_{2}}{4}-\frac {5 x_{3}}{2} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.846

19014	\begin{align} x_{1}^{\prime }&=-2 x_{1}-x_{2}+4 x_{3}+2 x_{4} \\ x_{2}^{\prime }&=-19 x_{1}-6 x_{2}+6 x_{3}+16 x_{4} \\ x_{3}^{\prime }&=-9 x_{1}-x_{2}+x_{3}+6 x_{4} \\ x_{4}^{\prime }&=-5 x_{1}-3 x_{2}+6 x_{3}+5 x_{4} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	2.562

19015	\begin{align} x_{1}^{\prime }&=-3 x_{1}+6 x_{2}+2 x_{3}-2 x_{4} \\ x_{2}^{\prime }&=2 x_{1}-3 x_{2}-6 x_{3}+2 x_{4} \\ x_{3}^{\prime }&=-4 x_{1}+8 x_{2}+3 x_{3}-4 x_{4} \\ x_{4}^{\prime }&=2 x_{1}-2 x_{2}-6 x_{3}+x_{4} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	2.229

19016	\begin{align} x_{1}^{\prime }&=-3 x_{1}-4 x_{2}+5 x_{3}+9 x_{4} \\ x_{2}^{\prime }&=-2 x_{1}-5 x_{2}+4 x_{3}+12 x_{4} \\ x_{3}^{\prime }&=-2 x_{1}-x_{3}+2 x_{4} \\ x_{4}^{\prime }&=-2 x_{2}+2 x_{3}+3 x_{4} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	2.290

19017	\begin{align} x_{1}^{\prime }&=-3 x_{1}-5 x_{2}+8 x_{3}+14 x_{4} \\ x_{2}^{\prime }&=-6 x_{1}-8 x_{2}+11 x_{3}+27 x_{4} \\ x_{3}^{\prime }&=-6 x_{1}-4 x_{2}+7 x_{3}+17 x_{4} \\ x_{4}^{\prime }&=-2 x_{2}+2 x_{3}+4 x_{4} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	2.941

19018	\begin{align} x_{1}^{\prime }&=3 x_{2}-2 x_{4} \\ x_{2}^{\prime }&=-\frac {x_{1}}{2}+x_{2}-3 x_{3}-\frac {5 x_{4}}{2} \\ x_{3}^{\prime }&=3 x_{2}-5 x_{3}-3 x_{4} \\ x_{4}^{\prime }&=x_{1}+3 x_{2}-3 x_{4} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	1.748

19019	\begin{align} x_{1}^{\prime }&=3 x_{1}-2 x_{2} \\ x_{2}^{\prime }&=2 x_{1}-2 x_{2} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.351

19020	\begin{align} x_{1}^{\prime }&=-3 x_{1}+2 x_{2} \\ x_{2}^{\prime }&=\frac {x_{1}}{2}-3 x_{2} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.332

19021	\begin{align} x_{1}^{\prime }&=3 x_{1}-4 x_{2} \\ x_{2}^{\prime }&=x_{1}-x_{2} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.286

19022	\begin{align} x_{1}^{\prime }&=\frac {x_{1}}{2}-\frac {x_{2}}{4} \\ x_{2}^{\prime }&=x_{1}-\frac {x_{2}}{2} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.273

19023	\begin{align} x_{1}^{\prime }&=x_{1}-\frac {5 x_{2}}{2} \\ x_{2}^{\prime }&=\frac {x_{1}}{2}-x_{2} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.390

19024	\begin{align} x_{1}^{\prime }&=-x_{1}-4 x_{2} \\ x_{2}^{\prime }&=x_{1}-x_{2} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.349

19025	\begin{align} x_{1}^{\prime }&=5 x_{1}-x_{2} \\ x_{2}^{\prime }&=3 x_{1}+x_{2} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.342

19026	\begin{align} x_{1}^{\prime }&=x_{1}-x_{2} \\ x_{2}^{\prime }&=5 x_{1}-3 x_{2} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.463

19027	\begin{align} x_{1}^{\prime }&=2 x_{1}-x_{2} \\ x_{2}^{\prime }&=3 x_{1}-2 x_{2} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.346

19028	\begin{align} x_{1}^{\prime }&=\frac {x_{1}}{2}+\frac {x_{2}}{2} \\ x_{2}^{\prime }&=2 x_{1}-x_{2} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.342

19029	\begin{align} x_{1}^{\prime }&=-3 x_{1}+4 x_{2} \\ x_{2}^{\prime }&=-x_{1}-2 x_{2} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.692

19030	\begin{align} x_{1}^{\prime }&=-3 x_{1}+\frac {5 x_{2}}{2} \\ x_{2}^{\prime }&=-\frac {5 x_{1}}{2}+2 x_{2} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.290

19031	\begin{align} x_{1}^{\prime }&=x_{1}+x_{2}+x_{3} \\ x_{2}^{\prime }&=2 x_{1}+x_{2}-x_{3} \\ x_{3}^{\prime }&=-8 x_{1}-5 x_{2}-3 x_{3} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.656

19032	\begin{align} x_{1}^{\prime }&=x_{1}-x_{2}+4 x_{3} \\ x_{2}^{\prime }&=3 x_{1}+2 x_{2}-x_{3} \\ x_{3}^{\prime }&=2 x_{1}+x_{2}-x_{3} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.592

19033	\begin{align} x_{1}^{\prime }&=-3 x_{1}-9 x_{2} \\ x_{2}^{\prime }&=x_{1}-3 x_{2} \\ \end{align} With initial conditions \begin{align} x_{1} \left (0\right ) &= 4 \\ x_{2} \left (0\right ) &= 1 \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.408

19034	\begin{align} x_{1}^{\prime }&=2 x_{1}-x_{2} \\ x_{2}^{\prime }&=3 x_{1}-2 x_{2} \\ \end{align} With initial conditions \begin{align} x_{1} \left (0\right ) &= 2 \\ x_{2} \left (0\right ) &= -1 \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.358

19035	\begin{align} x_{1}^{\prime }&=-4 x_{1}-x_{2} \\ x_{2}^{\prime }&=x_{1}-2 x_{2} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.125

19036	\begin{align} x_{1}^{\prime }&=5 x_{1}-x_{2} \\ x_{2}^{\prime }&=x_{1}+3 x_{2} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.120

19037	\begin{align} x_{1}^{\prime }&=-x_{1}-5 x_{2} \\ x_{2}^{\prime }&=x_{1}+3 x_{2} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.120

19038	\begin{align} x_{1}^{\prime }&=x_{2}-x_{3} \\ x_{2}^{\prime }&=x_{1}+x_{3} \\ x_{3}^{\prime }&=x_{1}+x_{2} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.168

19039	\begin{align} x_{1}^{\prime }&=-k_{1} x_{1} \\ x_{2}^{\prime }&=k_{1} x_{1}-k_{2} x_{2} \\ x_{3}^{\prime }&=k_{2} x_{2} \\ \end{align} With initial conditions \begin{align} x_{1} \left (0\right ) &= m_{0} \\ x_{2} \left (0\right ) &= 0 \\ x_{3} \left (0\right ) &= 0 \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.638

19040	\begin{align} x_{1}^{\prime }&=2 x_{1}-x_{2}+{\mathrm e}^{t} \\ x_{2}^{\prime }&=3 x_{1}-2 x_{2}+t \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.759

19041	\begin{align} x_{1}^{\prime }&=x_{1}+\sqrt {3}\, x_{2}+{\mathrm e}^{t} \\ x_{2}^{\prime }&=\sqrt {3}\, x_{1}-x_{2}+\sqrt {3}\, {\mathrm e}^{-t} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	1.551

19042	\begin{align} x_{1}^{\prime }&=2 x_{1}-5 x_{2}-\cos \left (t \right ) \\ x_{2}^{\prime }&=x_{1}-2 x_{2}+\sin \left (t \right ) \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.770

19043	\begin{align} x_{1}^{\prime }&=x_{1}+x_{2}+{\mathrm e}^{-2 t} \\ x_{2}^{\prime }&=4 x_{1}-2 x_{2}-2 \,{\mathrm e}^{t} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.585

19044	\begin{align} x_{1}^{\prime }&=1-x_{2}+x_{3} \\ x_{2}^{\prime }&=2 x_{2}+t \\ x_{3}^{\prime }&=-2 x_{1}-x_{2}+3 x_{3}+{\mathrm e}^{-t} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.814

19045	\begin{align} x_{1}^{\prime }&=-\frac {x_{1}}{2}+\frac {x_{2}}{2}-\frac {x_{3}}{2}+1 \\ x_{2}^{\prime }&=-x_{1}-2 x_{2}+x_{3}+t \\ x_{3}^{\prime }&=\frac {x_{1}}{2}+\frac {x_{2}}{2}-\frac {3 x_{3}}{2}+11 \,{\mathrm e}^{-3 t} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.926

19046	\begin{align} x_{1}^{\prime }&=-4 x_{1}+x_{2}+3 x_{3}+3 t \\ x_{2}^{\prime }&=-2 x_{2} \\ x_{3}^{\prime }&=-2 x_{1}+x_{2}+x_{3}+3 \cos \left (t \right ) \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.964

19047	\begin{align} x_{1}^{\prime }&=-\frac {x_{1}}{2}+x_{2}+\frac {x_{3}}{2} \\ x_{2}^{\prime }&=x_{1}-x_{2}+x_{3}-\sin \left (t \right ) \\ x_{3}^{\prime }&=\frac {x_{1}}{2}+x_{2}-\frac {x_{3}}{2} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.996

19048	\begin{align} x_{1}^{\prime }&=2 x_{1}+x_{2}+1 \\ x_{2}^{\prime }&=x_{1}-2 x_{2}+x_{3} \\ x_{3}^{\prime }&=x_{2}-x_{3} \\ \end{align} With initial conditions \begin{align} x_{1} \left (0\right ) &= 0 \\ x_{2} \left (0\right ) &= 0 \\ x_{3} \left (0\right ) &= 0 \\ \end{align}	system_of_ODEs	✓	✓	✓	✗	64.401

19049	\begin{align} x_{1}^{\prime }&=4 x_{1}-9 x_{2} \\ x_{2}^{\prime }&=x_{1}-2 x_{2} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.294

19050	\begin{align} x_{1}^{\prime }&=3 x_{1}-9 x_{2} \\ x_{2}^{\prime }&=x_{1}-3 x_{2} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.254

19051	\begin{align} x_{1}^{\prime }&=x_{1}+x_{2}+x_{3} \\ x_{2}^{\prime }&=2 x_{1}+x_{2}-x_{3} \\ x_{3}^{\prime }&=-3 x_{1}+2 x_{2}+4 x_{3} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.500

19052	\begin{align} x_{1}^{\prime }&=5 x_{1}-3 x_{2}-2 x_{3} \\ x_{2}^{\prime }&=8 x_{1}-5 x_{2}-4 x_{3} \\ x_{3}^{\prime }&=-4 x_{1}+3 x_{2}+3 x_{3} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.586

19053	\begin{align} x_{1}^{\prime }&=-7 x_{1}+9 x_{2}-6 x_{3} \\ x_{2}^{\prime }&=-8 x_{1}+11 x_{2}-7 x_{3} \\ x_{3}^{\prime }&=-2 x_{1}+3 x_{2}-x_{3} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.678

19054	\begin{align} x_{1}^{\prime }&=5 x_{1}+6 x_{2}+2 x_{3} \\ x_{2}^{\prime }&=-2 x_{1}-2 x_{2}-x_{3} \\ x_{3}^{\prime }&=-2 x_{1}-3 x_{2} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.521

19055	\begin{align} x_{1}^{\prime }&=-8 x_{1}-16 x_{2}-16 x_{3}-17 x_{4} \\ x_{2}^{\prime }&=-2 x_{1}-10 x_{2}-8 x_{3}-7 x_{4} \\ x_{3}^{\prime }&=-2 x_{1}-2 x_{3}-3 x_{4} \\ x_{4}^{\prime }&=6 x_{1}+14 x_{2}+14 x_{3}+14 x_{4} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	1.635

19056	\begin{align} x_{1}^{\prime }&=x_{1}-x_{2}-2 x_{3}+3 x_{4} \\ x_{2}^{\prime }&=2 x_{1}-\frac {3 x_{2}}{2}-x_{3}+\frac {7 x_{4}}{2} \\ x_{3}^{\prime }&=-x_{1}+\frac {x_{2}}{2}-\frac {3 x_{4}}{2} \\ x_{4}^{\prime }&=-2 x_{1}+\frac {3 x_{2}}{2}+3 x_{3}-\frac {7 x_{4}}{2} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.772

19057	\begin{align} x_{1}^{\prime }&=x_{1}-4 x_{2} \\ x_{2}^{\prime }&=4 x_{1}-7 x_{2} \\ \end{align} With initial conditions \begin{align} x_{1} \left (0\right ) &= 7 \\ x_{2} \left (0\right ) &= 1 \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.332

19058	\begin{align} x_{1}^{\prime }&=3 x_{1}-4 x_{2} \\ x_{2}^{\prime }&=x_{1}-x_{2} \\ \end{align} With initial conditions \begin{align} x_{1} \left (0\right ) &= -5 \\ x_{2} \left (0\right ) &= 7 \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.326

19059	\begin{align} x_{1}^{\prime }&=4 x_{1}+x_{2}+3 x_{3} \\ x_{2}^{\prime }&=6 x_{1}+4 x_{2}+6 x_{3} \\ x_{3}^{\prime }&=-5 x_{1}-2 x_{2}-4 x_{3} \\ \end{align} With initial conditions \begin{align} x_{1} \left (0\right ) &= 1 \\ x_{2} \left (0\right ) &= -2 \\ x_{3} \left (0\right ) &= 5 \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.581

19060	\begin{align} x_{1}^{\prime }&=x_{1}+x_{2} \\ x_{2}^{\prime }&=-14 x_{1}-5 x_{2}+x_{3} \\ x_{3}^{\prime }&=15 x_{1}+5 x_{2}-2 x_{3} \\ \end{align} With initial conditions \begin{align} x_{1} \left (0\right ) &= 5 \\ x_{2} \left (0\right ) &= 5 \\ x_{3} \left (0\right ) &= -4 \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.608

19061	\begin{align} x^{\prime }&=-2 y+x y \\ y^{\prime }&=x+4 x y \\ \end{align}	system_of_ODEs	✗	✓	✓	✗	0.029

19062	\begin{align} x^{\prime }&=1+5 y \\ y^{\prime }&=1-6 x^{2} \\ \end{align}	system_of_ODEs	✗	✓	✓	✗	0.025

19063	\begin{align} y^{\prime }&=2 \\ \end{align}	[_quadrature]	✓	✓	✓	✓	0.370

19064	\begin{align} y^{\prime }&=-x^{3} \\ \end{align}	[_quadrature]	✓	✓	✓	✓	0.270

19065	\begin{align} y^{\prime \prime }&=\sin \left (x \right ) \\ \end{align}	[[_2nd_order, _quadrature]]	✓	✓	✓	✓	0.660

19066	\begin{align} y y^{\prime } \sqrt {x^{2}+1}+x \sqrt {1+y^{2}}&=0 \\ y \left (0\right ) &= 1 \\ \end{align}	[_separable]	✓	✓	✓	✗	3.550

19067	\begin{align} \sec \left (x \right )^{2} \tan \left (y\right )+\sec \left (y\right )^{2} \tan \left (x \right ) y^{\prime }&=0 \\ \end{align}	[_separable]	✓	✓	✓	✓	27.748

19068	\begin{align} y^{\prime } \sqrt {-x^{2}+1}+\sqrt {1-y^{2}}&=0 \\ \end{align}	[_separable]	✓	✓	✓	✓	5.407

19069	\begin{align} y^{\prime }&=\frac {2 x y}{y^{2}+x^{2}} \\ \end{align}	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	✓	✓	✓	11.903

19070	\begin{align} y^{\prime }&=\frac {y \left (1+\ln \left (y\right )-\ln \left (x \right )\right )}{x} \\ \end{align}	[[_homogeneous, ‘class A‘], _dAlembert]	✓	✓	✓	✓	4.763

19071	\begin{align} x^{2} y^{\prime }+y^{2}&=x y^{\prime } y \\ \end{align}	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	✓	✓	✓	7.682

19072	\begin{align} \left (x +y\right ) y^{\prime }&=y-x \\ \end{align}	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	✓	✓	✓	3.427

19073	\begin{align} x -y \cos \left (\frac {y}{x}\right )+x \cos \left (\frac {y}{x}\right ) y^{\prime }&=0 \\ \end{align}	[[_homogeneous, ‘class A‘], _dAlembert]	✓	✓	✓	✓	3.379

19074	\begin{align} 3 y-7 x +7&=\left (3 x -7 y-3\right ) y^{\prime } \\ \end{align}	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	✓	✓	✓	59.456

19075	\begin{align} \left (x +2 y+1\right ) y^{\prime }&=3+2 x +4 y \\ \end{align}	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	✓	✓	✓	5.704

19076	\begin{align} y^{\prime }&=\frac {2 \left (y+2\right )^{2}}{\left (x +y-1\right )^{2}} \\ \end{align}	[[_homogeneous, ‘class C‘], _rational]	✓	✓	✓	✗	2.528

19077	\begin{align} \left (x +y\right )^{2} y^{\prime }&=a^{2} \\ \end{align}	[[_homogeneous, ‘class C‘], _dAlembert]	✓	✓	✓	✓	4.238

19078	\begin{align} y^{\prime } x -4 y&=\sqrt {y}\, x^{2} \\ \end{align}	[[_homogeneous, ‘class G‘], _rational, _Bernoulli]	✓	✓	✓	✓	2.692

19079	\begin{align} \cos \left (x \right ) y^{\prime }&=y \sin \left (x \right )+\cos \left (x \right )^{2} \\ \end{align}	[_linear]	✓	✓	✓	✓	2.353

19080	\begin{align} y^{\prime }&=2 y x -x^{3}+x \\ \end{align}	[_linear]	✓	✓	✓	✓	1.762

19081	\begin{align} y^{\prime }+\frac {x y}{x^{2}+1}&=\frac {1}{x \left (x^{2}+1\right )} \\ \end{align}	[_linear]	✓	✓	✓	✓	1.267

19082	\begin{align} \left (x -2 y x -y^{2}\right ) y^{\prime }+y^{2}&=0 \\ \end{align}	[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]	✓	✓	✓	✓	2.335

19083	\begin{align} y^{\prime } x +y&=x y^{2} \ln \left (x \right ) \\ \end{align}	[_Bernoulli]	✓	✓	✓	✓	2.833

19084	\begin{align} y^{\prime }-\frac {x y}{2 x^{2}-2}-\frac {x}{2 y}&=0 \\ \end{align}	[_rational, _Bernoulli]	✓	✓	✓	✓	2.022

19085	\begin{align} \left (x^{2} y^{3}+y x \right ) y^{\prime }&=1 \\ \end{align}	[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]	✓	✓	✓	✓	1.475

19086	\begin{align} x -y^{2}+2 x y^{\prime } y&=0 \\ \end{align}	[[_homogeneous, ‘class G‘], _rational, _Bernoulli]	✓	✓	✓	✓	1.811

19087	\begin{align} y^{\prime }&=\frac {y^{2}}{3}+\frac {2}{3 x^{2}} \\ \end{align}	[[_homogeneous, ‘class G‘], _rational, [_Riccati, _special]]	✓	✓	✓	✓	2.378

19088	\begin{align} y^{\prime }+y^{2}+\frac {y}{x}-\frac {4}{x^{2}}&=0 \\ \end{align}	[[_homogeneous, ‘class G‘], _rational, _Riccati]	✓	✓	✓	✓	2.900

19089	\begin{align} y^{\prime } x -3 y+y^{2}&=4 x^{2}-4 x \\ \end{align}	[_rational, _Riccati]	✓	✓	✓	✓	1.848

19090	\begin{align} y^{\prime }&=y^{2}+\frac {1}{x^{4}} \\ \end{align}	[_rational, [_Riccati, _special]]	✓	✓	✓	✓	3.029

19091	\begin{align} \left (y-x \right ) \sqrt {x^{2}+1}\, y^{\prime }&=\left (1+y^{2}\right )^{{3}/{2}} \\ \end{align}	[‘y=_G(x,y’)‘]	✓	✓	✓	✗	6.054

19092	\begin{align} y^{\prime } \left (x^{2}+y^{2}+3\right )&=2 x \left (2 y-\frac {x^{2}}{y}\right ) \\ \end{align}	[_rational]	✗	✓	✓	✗	3.823

19093	\begin{align} y^{\prime }&=\frac {x -y^{2}}{2 y \left (x +y^{2}\right )} \\ \end{align}	[[_homogeneous, ‘class G‘], _rational]	✓	✓	✓	✓	2.273

19094	\begin{align} \left (x \left (x +y\right )+a^{2}\right ) y^{\prime }&=y \left (x +y\right )+b^{2} \\ \end{align}	[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	✓	✓	✓	7.234

19095	\begin{align} y^{\prime }&=k y+f \left (x \right ) \\ \end{align}	[[_linear, ‘class A‘]]	✓	✓	✓	✓	1.304

19096	\begin{align} y^{\prime }&=y^{2}-x^{2} \\ \end{align}	[_Riccati]	✓	✓	✓	✗	6.468

19097	\begin{align} \frac {y^{\prime } y+x}{\sqrt {1+x^{2}+y^{2}}}+\frac {y-y^{\prime } x}{y^{2}+x^{2}}&=0 \\ \end{align}	[[_1st_order, _with_linear_symmetries], _exact]	✓	✓	✓	✗	4.214

19098	\begin{align} \frac {2 x}{y^{3}}+\frac {\left (y^{2}-3 x^{2}\right ) y^{\prime }}{y^{4}}&=0 \\ \end{align}	[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert]	✓	✓	✓	✗	4.365

19099	\begin{align} \frac {\sin \left (\frac {x}{y}\right )}{y}-\frac {y \cos \left (\frac {y}{x}\right )}{x^{2}}+1+\left (\frac {\cos \left (\frac {y}{x}\right )}{x}-\frac {x \sin \left (\frac {x}{y}\right )}{y^{2}}+\frac {1}{y^{2}}\right ) y^{\prime }&=0 \\ \end{align}	[_exact]	✓	✓	✓	✗	7.042

19100	\begin{align} \frac {1}{x}-\frac {y^{2}}{\left (x -y\right )^{2}}+\left (\frac {x^{2}}{\left (x -y\right )^{2}}-\frac {1}{y}\right ) y^{\prime }&=0 \\ \end{align}	[_exact, _rational]	✓	✓	✓	✗	2.275

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