second order ode can be made integrable

2.5.18 second order ode can be made integrable

Table 2.1147: second order ode can be made integrable [328]


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

149	\begin{align} 4 y+y^{\prime \prime }&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.126

216	\begin{align} y^{\prime \prime }-9 y&=0 \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 15 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.214

217	\begin{align} 4 y+y^{\prime \prime }&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 8 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.186

218	\begin{align} y^{\prime \prime }+25 y&=0 \\ y \left (0\right ) &= 10 \\ y^{\prime }\left (0\right ) &= -10 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.839

258	\begin{align} y^{\prime \prime }-4 y&=12 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 10 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.279

271	\begin{align} y^{\prime \prime }-4 y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.987

808	\begin{align} y^{\prime \prime }-9 y&=0 \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 15 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.112

809	\begin{align} 4 y+y^{\prime \prime }&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 8 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.139

810	\begin{align} y^{\prime \prime }+25 y&=0 \\ y \left (0\right ) &= 10 \\ y^{\prime }\left (0\right ) &= -10 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.680

839	\begin{align} y^{\prime \prime }-4 y&=12 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 10 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.191

842	\begin{align} y^{\prime \prime }+2 y&=4 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.934

845	\begin{align} y^{\prime \prime }-4 y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.724

1254	\begin{align} 4 y^{\prime \prime }-9 y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.988

1264	\begin{align} 4 y^{\prime \prime }-y&=0 \\ y \left (-2\right ) &= 1 \\ y^{\prime }\left (-2\right ) &= -1 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.177

1265	\begin{align} y^{\prime \prime }-y&=0 \\ y \left (0\right ) &= {\frac {5}{4}} \\ y^{\prime }\left (0\right ) &= -{\frac {3}{4}} \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.099

1268	\begin{align} 4 y^{\prime \prime }-y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= \beta \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✗	0.750

1278	\begin{align} 4 y^{\prime \prime }+9 y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.036

1286	\begin{align} y^{\prime \prime }+y&=0 \\ y \left (\frac {\pi }{3}\right ) &= 2 \\ y^{\prime }\left (\frac {\pi }{3}\right ) &= -4 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.309

1355	\begin{align} u^{\prime \prime }+2 u&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.243

2363	\begin{align} y^{\prime \prime }-y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.357

2544	\begin{align} y^{\prime \prime }-y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.108

2563	\begin{align} y^{\prime \prime }+w^{2} y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.032

2819	\begin{align} z^{\prime \prime }+z^{3}&=0 \\ \end{align}	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	✓	✓	✓	3.783

2820	\begin{align} z^{\prime \prime }+z+z^{5}&=0 \\ \end{align}	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	✓	✓	✗	49.891

2821	\begin{align} z^{\prime \prime }+{\mathrm e}^{z^{2}}&=1 \\ \end{align}	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	✓	✓	✗	1.353

2822	\begin{align} z^{\prime \prime }+\frac {z}{1+z^{2}}&=0 \\ \end{align}	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	✓	✓	✓	2.559

2823	\begin{align} z^{\prime \prime }+z-2 z^{3}&=0 \\ \end{align}	[[_2nd_order, _missing_x], _Duﬃng, [_2nd_order, _reducible, _mu_x_y1]]	✓	✓	✓	✗	1.788

2834	\begin{align} y^{\prime \prime }+\lambda y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (L \right ) &= 0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.546

2837	\begin{align} y^{\prime \prime }+\lambda y&=0 \\ y^{\prime }\left (0\right ) &= 0 \\ y \left (L \right ) &= 0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.945

2839	\begin{align} y^{\prime \prime }+\lambda y&=0 \\ y \left (0\right ) &= 0 \\ y \left (1\right ) &= 0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.967

3058	\begin{align} y^{\prime \prime }-4 y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	2.068

3244	\begin{align} y^{\prime \prime }&=k^{2} y \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	2.597

3245	\begin{align} x^{\prime \prime }+k^{2} x&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.885

3265	\begin{align} y^{\prime \prime }&=y \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.273

3272	\begin{align} 2 y^{\prime \prime }&={\mathrm e}^{y} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align}	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	✓	✓	✗	1.671

3557	\begin{align} y^{\prime \prime }-25 y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.157

3558	\begin{align} 4 y+y^{\prime \prime }&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.827

3563	\begin{align} y^{\prime \prime }-9 y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.699

3697	\begin{align} y^{\prime \prime }-36 y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.026

4124	\begin{align} y^{\prime \prime }+25 y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.805

5715	\begin{align} y^{\prime \prime }+y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.102

5716	\begin{align} y^{\prime \prime }-y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.223

5730	\begin{align} -2 y+y^{\prime \prime }&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.283

5732	\begin{align} 4 y+y^{\prime \prime }&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.989

6298	\begin{align} y^{\prime \prime }&=a y \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	2.932

6299	\begin{align} y^{\prime \prime }&=6 y^{2} \\ \end{align}	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	✓	✓	✓	4.359

6302	\begin{align} y^{\prime \prime }&=2 y^{3} \\ \end{align}	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	✓	✓	✓	4.543

6303	\begin{align} y^{\prime \prime }&=a +b y+2 y^{3} \\ \end{align}	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	✓	✓	✗	2.761

6308	\begin{align} y^{\prime \prime }&=\operatorname {a0} +\operatorname {a1} y+\operatorname {a2} y^{2}+\operatorname {a3} y^{3} \\ \end{align}	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	✓	✓	✗	4.241

6311	\begin{align} a \,{\mathrm e}^{y}+y^{\prime \prime }&=0 \\ \end{align}	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	✓	✓	✓	6.769

6369	\begin{align} 2 y^{\prime \prime }&=1+12 y^{2} \\ \end{align}	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	✓	✓	✗	60.472

6370	\begin{align} 2 y^{\prime \prime }&=y \left (a -y^{2}\right ) \\ \end{align}	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	✓	✓	✗	10.632

7042	\begin{align} y^{\prime \prime }-y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.534

7126	\begin{align} y^{\prime \prime }&=\frac {3 k y^{2}}{2} \\ \end{align}	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	✓	✓	✓	2.789

7127	\begin{align} y^{\prime \prime }&=2 k y^{3} \\ \end{align}	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	✓	✓	✓	2.558

7137	\begin{align} 2 y^{\prime \prime }&={\mathrm e}^{y} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align}	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	✓	✓	✗	1.135

7264	\begin{align} y^{\prime \prime }+16 y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.501

7367	\begin{align} y^{\prime \prime }&=-4 y \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.178

7369	\begin{align} y^{\prime \prime }&=y \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.026

7570	\begin{align} m y^{\prime \prime }+k y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	2.179

7573	\begin{align} 2 y^{\prime \prime }+18 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	2.905

7619	\begin{align} y^{\prime \prime }-y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	2.073

7665	\begin{align} x^{\prime \prime }-\omega ^{2} x&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	2.651

7780	\begin{align} \frac {x^{\prime \prime }}{2}&=-48 x \\ x \left (0\right ) &= {\frac {1}{6}} \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	2.414

7851	\begin{align} y^{\prime \prime }-y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.282

7982	\begin{align} y^{\prime \prime }+25 y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.103

8214	\begin{align} x^{\prime \prime }+x&=0 \\ x \left (0\right ) &= -1 \\ x^{\prime }\left (0\right ) &= 8 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.351

8216	\begin{align} x^{\prime \prime }+x&=0 \\ x \left (\frac {\pi }{6}\right ) &= {\frac {1}{2}} \\ x^{\prime }\left (\frac {\pi }{6}\right ) &= 0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.861

8217	\begin{align} x^{\prime \prime }+x&=0 \\ x \left (\frac {\pi }{4}\right ) &= \sqrt {2} \\ x^{\prime }\left (\frac {\pi }{4}\right ) &= 2 \sqrt {2} \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.980

8218	\begin{align} y^{\prime \prime }-y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.062

8221	\begin{align} y^{\prime \prime }-y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.538

8247	\begin{align} 4 y+y^{\prime \prime }&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (\pi \right ) &= 0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.677

8249	\begin{align} 4 y+y^{\prime \prime }&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (\pi \right ) &= 5 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.947

8254	\begin{align} 2 y^{\prime \prime }-3 y^{2}&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align}	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	✓	✗	✗	4.409

8261	\begin{align} y^{\prime \prime }+9 y&=18 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.999

8283	\begin{align} y^{\prime \prime }+9 y&=5 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.973

8860	\begin{align} y^{\prime \prime }-y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.207

8861	\begin{align} 4 y+y^{\prime \prime }&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.007

8862	\begin{align} y^{\prime \prime }+k^{2} y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.275

8887	\begin{align} y^{\prime \prime }-4 y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.637

8888	\begin{align} 3 y^{\prime \prime }+2 y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.881

8889	\begin{align} y^{\prime \prime }+16 y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.093

8896	\begin{align} y^{\prime \prime }+y&=0 \\ y \left (0\right ) &= 1 \\ y \left (\frac {\pi }{2}\right ) &= 2 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.961

8897	\begin{align} y^{\prime \prime }+y&=0 \\ y \left (0\right ) &= 0 \\ y \left (\pi \right ) &= 0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.543

8898	\begin{align} y^{\prime \prime }+y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (\frac {\pi }{2}\right ) &= 0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.588

8899	\begin{align} y^{\prime \prime }+y&=0 \\ y \left (0\right ) &= 0 \\ y \left (\frac {\pi }{2}\right ) &= 0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.545

8903	\begin{align} y^{\prime \prime }+10 y&=0 \\ y \left (0\right ) &= \pi \\ y^{\prime }\left (0\right ) &= \pi ^{2} \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	4.563

8925	\begin{align} y^{\prime \prime }+y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.620

8926	\begin{align} y^{\prime \prime }-y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.763

9037	\begin{align} y^{\prime \prime }+k^{2} y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.856

9052	\begin{align} 4 y+y^{\prime \prime }&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.869

9053	\begin{align} y^{\prime \prime }-4 y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.850

9182	\begin{align} y^{\prime \prime }-k^{2} y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.799

9214	\begin{align} y^{\prime \prime }+8 y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.213

9220	\begin{align} y^{\prime \prime }+y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.756

9224	\begin{align} y^{\prime \prime }&=4 y \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.073

9322	\begin{align} y^{\prime \prime }+9 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.345

9345	\begin{align} y^{\prime \prime }&=-3 y \\ y \left (0\right ) &= -1 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.592

9494	\begin{align} y^{\prime \prime }+y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.787

9496	\begin{align} y^{\prime \prime }-y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.948

9582	\begin{align} y^{\prime \prime }+y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.720

9774	\begin{align} y^{\prime \prime }+\beta ^{2} y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.548

9779	\begin{align} y^{\prime \prime }&=-{\mathrm e}^{-2 y} \\ y \left (3\right ) &= 0 \\ y^{\prime }\left (3\right ) &= 1 \\ \end{align}	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	✓	✓	✗	1.756

9780	\begin{align} y^{\prime \prime }&=-{\mathrm e}^{-2 y} \\ y \left (3\right ) &= 0 \\ y^{\prime }\left (3\right ) &= -1 \\ \end{align}	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	✓	✓	✗	1.232

10257	\begin{align} y^{\prime \prime }+{\mathrm e}^{y}&=0 \\ \end{align}	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	✓	✓	✓	4.974

10397	\begin{align} y^{\prime \prime }+y&=1 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.902

12282	\begin{align} y^{\prime \prime }+y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	4.415

12286	\begin{align} y^{\prime \prime }-y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	5.482

12289	\begin{align} y^{\prime \prime }+l y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	5.053

12835	\begin{align} y^{\prime \prime }-y^{2}&=0 \\ \end{align}	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	✓	✓	✓	1.793

12836	\begin{align} y^{\prime \prime }-6 y^{2}&=0 \\ \end{align}	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	✓	✓	✓	1.539

12838	\begin{align} y^{\prime \prime }-6 y^{2}+4 y&=0 \\ \end{align}	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	✓	✓	✗	1.339

12841	\begin{align} y^{\prime \prime }-a y^{3}&=0 \\ \end{align}	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	✓	✓	✓	1.723

12844	\begin{align} y^{\prime \prime }+d +b y^{2}+c y+a y^{3}&=0 \\ \end{align}	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	✓	✓	✗	3.010

12846	\begin{align} y^{\prime \prime }+6 a^{10} y^{11}-y&=0 \\ \end{align}	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	✓	✓	✗	1.279

12848	\begin{align} y^{\prime \prime }-{\mathrm e}^{y}&=0 \\ \end{align}	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	✓	✓	✓	4.173

13662	\begin{align} y^{\prime \prime }+a y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	2.173

14163	\begin{align} 2 y^{\prime \prime }&={\mathrm e}^{y} \\ \end{align}	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	✓	✓	✓	3.915

14290	\begin{align} x^{\prime \prime }-12 x&=0 \\ x \left (0\right ) &= 1 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.530

14584	\begin{align} y^{\prime \prime }+9 y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	2.098

14585	\begin{align} 4 y^{\prime \prime }+y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.139

14845	\begin{align} y^{\prime \prime }+\lambda y&=0 \\ y \left (0\right ) &= 0 \\ y \left (\frac {\pi }{2}\right ) &= 0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.948

14846	\begin{align} y^{\prime \prime }+\lambda y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (\pi \right ) &= 0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.960

14847	\begin{align} y^{\prime \prime }+\lambda y&=0 \\ y \left (0\right ) &= 0 \\ y \left (L \right ) &= 0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.967

14929	\begin{align} y^{\prime \prime }-4 y&=0 \\ y \left (0\right ) &= 10 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.771

15084	\begin{align} y^{\prime \prime }&=3 \sqrt {y} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align}	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	✓	✓	✗	2.240

15109	\begin{align} y^{\prime \prime }&=2 y^{3} \\ y \left (1\right ) &= 1 \\ y^{\prime }\left (1\right ) &= 1 \\ \end{align}	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	✓	✓	✗	1.438

15316	\begin{align} y^{\prime \prime }+\alpha ^{2} y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.006

15317	\begin{align} y^{\prime \prime }-\alpha ^{2} y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.309

15401	\begin{align} y^{\prime \prime }&=a^{2} y \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.631

15410	\begin{align} y^{\prime \prime }&=9 y \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.386

15411	\begin{align} y^{\prime \prime }+y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.955

15412	\begin{align} y^{\prime \prime }-y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.099

15477	\begin{align} x^{\prime \prime }+x-x^{3}&=0 \\ \end{align}	[[_2nd_order, _missing_x], _Duﬃng, [_2nd_order, _reducible, _mu_x_y1]]	✓	✓	✓	✗	2.234

15478	\begin{align} x^{\prime \prime }+x+x^{3}&=0 \\ \end{align}	[[_2nd_order, _missing_x], _Duﬃng, [_2nd_order, _reducible, _mu_x_y1]]	✓	✓	✓	✗	1.579

15481	\begin{align} x^{\prime \prime }&=\left (2 \cos \left (x\right )-1\right ) \sin \left (x\right ) \\ \end{align}	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	✓	✓	✗	1.970

15510	\begin{align} y^{\prime \prime }-y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.296

15659	\begin{align} y^{\prime \prime }-y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.851

15660	\begin{align} y^{\prime \prime }+y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.954

15666	\begin{align} y^{\prime \prime }-4 y&=31 \\ y \left (0\right ) &= -9 \\ y^{\prime }\left (0\right ) &= 6 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.772

15679	\begin{align} y^{\prime \prime }+\alpha y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.645

16069	\begin{align} y^{\prime \prime }+2 y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= -\sqrt {2} \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	2.035

16469	\begin{align} 4 y+y^{\prime \prime }&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 6 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.334

16482	\begin{align} y^{\prime \prime }-4 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.859

16490	\begin{align} y^{\prime \prime }-25 y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.094

16492	\begin{align} 4 y^{\prime \prime }-y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.019

16497	\begin{align} y^{\prime \prime }-9 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.359

16499	\begin{align} y^{\prime \prime }-9 y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= -3 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.804

16512	\begin{align} y^{\prime \prime }+25 y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.775

16517	\begin{align} 4 y^{\prime \prime }+y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.765

16520	\begin{align} y^{\prime \prime }+16 y&=0 \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= 12 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.112

16588	\begin{align} y^{\prime \prime }-9 y&=36 \\ y \left (0\right ) &= 8 \\ y^{\prime }\left (0\right ) &= 6 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.188

16708	\begin{align} y^{\prime \prime }+36 y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.732

16711	\begin{align} y^{\prime \prime }-36 y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.888

16717	\begin{align} y^{\prime \prime }+3 y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.906

17350	\begin{align} y^{\prime \prime }-y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.731

17353	\begin{align} y^{\prime \prime }+9 y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.709

17355	\begin{align} y^{\prime \prime }+9 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -3 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.239

17360	\begin{align} y^{\prime \prime }+16 y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.427

17386	\begin{align} 4 y^{\prime \prime }+9 y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.108

17387	\begin{align} y^{\prime \prime }+16 y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.132

17388	\begin{align} y^{\prime \prime }+8 y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.263

17389	\begin{align} y^{\prime \prime }+7 y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.293

17400	\begin{align} y^{\prime \prime }+36 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= -6 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	2.599

17401	\begin{align} y^{\prime \prime }+100 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 10 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.503

17419	\begin{align} y^{\prime \prime }-16 y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.287

17458	\begin{align} y^{\prime \prime }-y&=4 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.509

17481	\begin{align} y^{\prime \prime }+4 y&=1 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.602

17796	\begin{align} 4 x^{\prime \prime }+9 x&=0 \\ x \left (0\right ) &= -1 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.671

17797	\begin{align} 9 x^{\prime \prime }+4 x&=0 \\ x \left (0\right ) &= -{\frac {1}{2}} \\ x^{\prime }\left (0\right ) &= 1 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.722

17798	\begin{align} x^{\prime \prime }+64 x&=0 \\ x \left (0\right ) &= {\frac {3}{4}} \\ x^{\prime }\left (0\right ) &= -2 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	2.749

17799	\begin{align} x^{\prime \prime }+100 x&=0 \\ x \left (0\right ) &= -{\frac {1}{4}} \\ x^{\prime }\left (0\right ) &= 1 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.825

17800	\begin{align} x^{\prime \prime }+x&=0 \\ x \left (0\right ) &= 3 \\ x^{\prime }\left (0\right ) &= -4 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.560

17801	\begin{align} x^{\prime \prime }+4 x&=0 \\ x \left (0\right ) &= 1 \\ x^{\prime }\left (0\right ) &= 1 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.797

17802	\begin{align} x^{\prime \prime }+16 x&=0 \\ x \left (0\right ) &= -2 \\ x^{\prime }\left (0\right ) &= 1 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.681

17803	\begin{align} x^{\prime \prime }+256 x&=0 \\ x \left (0\right ) &= 2 \\ x^{\prime }\left (0\right ) &= 4 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	2.040

17804	\begin{align} x^{\prime \prime }+9 x&=0 \\ x \left (0\right ) &= {\frac {1}{3}} \\ x^{\prime }\left (0\right ) &= -1 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.249

17805	\begin{align} 10 x^{\prime \prime }+\frac {x}{10}&=0 \\ x \left (0\right ) &= -5 \\ x^{\prime }\left (0\right ) &= 1 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	2.694

18084	\begin{align} y^{\prime \prime }+y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.980

18115	\begin{align} 2 y^{\prime \prime }&=3 y^{2} \\ y \left (-2\right ) &= 1 \\ y^{\prime }\left (-2\right ) &= -1 \\ \end{align}	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	✓	✓	✗	1.872

18122	\begin{align} y^{\prime \prime }&={\mathrm e}^{2 y} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align}	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	✓	✓	✗	1.141

18125	\begin{align} y^{\prime \prime }-y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.011

18162	\begin{align} y^{\prime \prime }+k^{2} y&=k \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.147

18185	\begin{align} y^{\prime \prime }+9 y&=9 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.941

18282	\begin{align} y^{\prime \prime }-y&=1 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.464

18354	\begin{align} y^{\prime \prime }+\lambda y&=0 \\ y \left (0\right ) &= 0 \\ y \left (1\right ) &= 0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.815

18365	\begin{align} y^{\prime \prime }+\lambda ^{2} y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (\pi \right ) &= 0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.856

18740	\begin{align} y^{\prime \prime }+4 y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.044

18769	\begin{align} 4 y^{\prime \prime }-9 y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.022

18778	\begin{align} 4 y^{\prime \prime }+9 y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.955

18791	\begin{align} y^{\prime \prime }+y&=0 \\ y \left (\frac {\pi }{3}\right ) &= 2 \\ y^{\prime }\left (\frac {\pi }{3}\right ) &= -4 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.427

18798	\begin{align} 4 y^{\prime \prime }-y&=0 \\ y \left (-2\right ) &= 1 \\ y^{\prime }\left (-2\right ) &= -1 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.815

19176	\begin{align} y^{\prime \prime }+y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	2.024

19231	\begin{align} 4 y+y^{\prime \prime }&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	2.099

19232	\begin{align} y^{\prime \prime }-4 y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	2.373

19360	\begin{align} y^{\prime \prime }-k y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	6.181

19433	\begin{align} y^{\prime \prime }-y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	4.101

19461	\begin{align} y^{\prime \prime }+8 y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	2.653

19471	\begin{align} y^{\prime \prime }&=4 y \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	2.785


19736	\begin{align} \theta ^{\prime \prime }&=-p^{2} \theta \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	4.881

19739	\begin{align} \phi ^{\prime \prime }&=\frac {4 \pi n c}{\sqrt {v_{0}^{2}+\frac {2 e \left (\phi -V_{0} \right )}{m}}} \\ \end{align}	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	✓	✓	✗	234.255

19750	\begin{align} \theta ^{\prime \prime }-p^{2} \theta &=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	7.025

19751	\begin{align} y^{\prime \prime }+y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	2.621

19753	\begin{align} r^{\prime \prime }-a^{2} r&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	6.171

19769	\begin{align} y^{\prime \prime }&=-m^{2} y \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	5.289

19852	\begin{align} e y^{\prime \prime }&=P \left (-y+a \right ) \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	13.066

19869	\begin{align} y^{\prime \prime }&=-a^{2} y \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	5.720

19895	\begin{align} y^{\prime \prime }-k^{2} y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	7.502

20037	\begin{align} y^{\prime \prime }-m^{2} y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.098

20126	\begin{align} y^{\prime \prime }+a^{2} y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.836

20328	\begin{align} y^{\prime \prime }-n^{2} y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.855

20543	\begin{align} y^{\prime \prime }&=y \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	2.059

20545	\begin{align} y^{\prime \prime }-a^{2} y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	2.516

20547	\begin{align} y^{\prime \prime }&=y^{3}-y \\ \end{align}	[[_2nd_order, _missing_x], _Duﬃng, [_2nd_order, _reducible, _mu_x_y1]]	✓	✓	✓	✗	3.559

20548	\begin{align} y^{\prime \prime }&={\mathrm e}^{2 y} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align}	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	✓	✓	✗	5.609

20589	\begin{align} y^{\prime \prime }&={\mathrm e}^{y} \\ \end{align}	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	✓	✓	✓	7.499

20590	\begin{align} y^{\prime \prime }+a^{2} y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.428

20845	\begin{align} y^{\prime \prime }-y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	2.702

21123	\begin{align} x^{\prime \prime }+\lambda ^{2} x&=0 \\ x \left (0\right ) &= 0 \\ x \left (\pi \right ) &= 0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	3.337

21124	\begin{align} x^{\prime \prime }+x&=0 \\ x \left (a \right ) &= 0 \\ x \left (b \right ) &= 0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.115

21125	\begin{align} x^{\prime \prime }-x&=0 \\ x \left (0\right ) &= 0 \\ x \left (1\right ) &= 0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	2.962

21254	\begin{align} x^{\prime \prime }&=x-x^{3} \\ \end{align}	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	✓	✓	✗	4.690

21255	\begin{align} x^{\prime \prime }&=x^{3}-x \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= {\frac {1}{2}} \\ \end{align}	[[_2nd_order, _missing_x], _Duﬃng, [_2nd_order, _reducible, _mu_x_y1]]	✓	✓	✗	✗	7.876

21257	\begin{align} x^{\prime \prime }&=x^{3}-x \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 1 \\ \end{align}	[[_2nd_order, _missing_x], _Duﬃng, [_2nd_order, _reducible, _mu_x_y1]]	✓	✓	✗	✗	3.771

21258	\begin{align} x^{\prime \prime }&=x-x^{3} \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 1 \\ \end{align}	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	✓	✓	✗	2.670

21261	\begin{align} x^{\prime \prime }+x+8 x^{7}&=0 \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= a \\ \end{align}	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	✓	✗	✗	9.929

21265	\begin{align} x^{\prime \prime }-x+3 x^{2}&=0 \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 1 \\ \end{align}	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	✓	✗	✗	4.403

21318	\begin{align} x^{\prime \prime }-x^{3}&=0 \\ x \left (0\right ) &= 0 \\ x \left (b \right ) &= 0 \\ \end{align}	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	✓	✓	✗	2.931

21319	\begin{align} x^{\prime \prime }+4 x^{3}&=0 \\ x \left (a \right ) &= 0 \\ x \left (b \right ) &= 0 \\ \end{align}	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	✓	✓	✗	2.655

21320	\begin{align} x^{\prime \prime }+6 x^{5}&=0 \\ x \left (0\right ) &= 0 \\ x \left (b \right ) &= 0 \\ \end{align}	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	✓	✗	✗	4.634

21321	\begin{align} x^{\prime \prime }+\lambda x-x^{3}&=0 \\ x \left (0\right ) &= 0 \\ x \left (1\right ) &= 0 \\ \end{align}	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	✓	✗	✗	13.216

21323	\begin{align} x^{\prime \prime }+4 x^{3}&=0 \\ x \left (0\right ) &= 0 \\ x \left (b \right ) &= 0 \\ \end{align}	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	✓	✓	✗	2.507

21477	\begin{align} y^{\prime \prime }-y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	4.929

21481	\begin{align} y^{\prime \prime }-5 y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	3.631

21488	\begin{align} y^{\prime \prime }+y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.629

21489	\begin{align} 4 y+y^{\prime \prime }&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.789

21563	\begin{align} y^{\prime \prime }-y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.915

21566	\begin{align} y^{\prime \prime }+y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.273

21568	\begin{align} y^{\prime \prime }+k^{2} y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	4.260

21624	\begin{align} y^{\prime \prime }+4 y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	2.889

21729	\begin{align} 4 y+y^{\prime \prime }&=0 \\ y \left (0\right ) &= 4 \\ y \left (\pi \right ) &= 4 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✗	2.327

21730	\begin{align} 4 y+y^{\prime \prime }&=0 \\ y \left (0\right ) &= 0 \\ y \left (L \right ) &= 7 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	2.780

21787	\begin{align} x^{\prime \prime }&=4 x^{3}-4 x \\ \end{align}	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	✓	✓	✗	5.672

21789	\begin{align} x^{\prime \prime }&=x^{2}-4 x+\lambda \\ \end{align}	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	✓	✓	✗	102.660

21792	\begin{align} y^{\prime \prime }+y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.678

21968	\begin{align} 4 y+y^{\prime \prime }&=0 \\ y \left (\frac {\pi }{8}\right ) &= 0 \\ y \left (\frac {\pi }{6}\right ) &= 1 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.237

21970	\begin{align} y^{\prime \prime }-y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.695

22079	\begin{align} y^{\prime \prime }-y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.847

22095	\begin{align} y^{\prime \prime }-5 y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.188

22097	\begin{align} 4 y+y^{\prime \prime }&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.906

22101	\begin{align} y^{\prime \prime }-y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.533

22104	\begin{align} y^{\prime \prime }+y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.694

22106	\begin{align} y^{\prime \prime }-7 y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.104

22168	\begin{align} y^{\prime \prime }+y&=0 \\ y \left (2\right ) &= 0 \\ y^{\prime }\left (2\right ) &= 0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.608

22282	\begin{align} y^{\prime \prime }+y&=0 \\ y \left (0\right ) &= 0 \\ y \left (\frac {\pi }{2}\right ) &= 0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.586

22286	\begin{align} y^{\prime \prime }+y&=0 \\ y \left (\frac {\pi }{2}\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.602

22299	\begin{align} s^{\prime \prime }&=-9 s \\ s \left (0\right ) &= 9 \\ s^{\prime }\left (0\right ) &= 18 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.164

22317	\begin{align} y^{\prime \prime }+y^{2}&=0 \\ \end{align}	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	✓	✓	✓	2.037

22334	\begin{align} y^{\prime \prime }+\lambda y&=0 \\ y \left (0\right ) &= 0 \\ y \left (1\right ) &= 0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.078

22485	\begin{align} 4 y+y^{\prime \prime }&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.261

22487	\begin{align} y^{\prime \prime }-y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.067

22629	\begin{align} 4 y^{\prime \prime }-25 y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.926

22630	\begin{align} y^{\prime \prime }-4 y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.754

22634	\begin{align} y^{\prime \prime }-y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= -3 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.993

22654	\begin{align} 4 y+y^{\prime \prime }&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.968

22656	\begin{align} 4 y^{\prime \prime }+9 y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.767

22739	\begin{align} y^{\prime \prime }-y&=1 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.219

22803	\begin{align} y^{\prime \prime }+\lambda y&=0 \\ y \left (0\right ) &= 0 \\ y \left (\pi \right ) &= 0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.015

23001	\begin{align} y^{\prime \prime }-4 y&=0 \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.864

23013	\begin{align} y^{\prime \prime }-3 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.272

23014	\begin{align} y^{\prime \prime }-8 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.490

23015	\begin{align} 4 y^{\prime \prime }-7 y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.010

23018	\begin{align} x^{\prime \prime }+36 x&=0 \\ x \left (0\right ) &= 5 \\ x \left (\frac {\pi }{12}\right ) &= 7 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.852

23019	\begin{align} y^{\prime \prime }+3 y&=0 \\ y \left (0\right ) &= 0 \\ y \left (\frac {\pi \sqrt {3}}{6}\right ) &= 4 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.989

23021	\begin{align} 9 y^{\prime \prime }+49 y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.477

23032	\begin{align} y^{\prime \prime }-9 y&=5 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.215

23087	\begin{align} y^{\prime \prime }-4 y&=12 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.171

23097	\begin{align} y^{\prime \prime }-y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.666

23098	\begin{align} y^{\prime \prime }+y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.643

23099	\begin{align} y^{\prime \prime }-4 y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.610

23100	\begin{align} 4 y+y^{\prime \prime }&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.843

23233	\begin{align} y^{\prime \prime }-y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.018

23266	\begin{align} y^{\prime \prime }+9 y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.511

23267	\begin{align} y^{\prime \prime }-4 y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.927

23268	\begin{align} y^{\prime \prime }+a^{2} y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.293

23273	\begin{align} y^{\prime \prime }+y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.702

23280	\begin{align} 4 y+y^{\prime \prime }&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.946

23301	\begin{align} 4 y+y^{\prime \prime }&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (1\right ) &= 0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.665

23302	\begin{align} y^{\prime \prime }+a^{2} y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.933

23316	\begin{align} y^{\prime \prime }+9 y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.295

23322	\begin{align} 2 y^{\prime \prime }+y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.983

23323	\begin{align} y^{\prime \prime }+16 y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.089

23326	\begin{align} y^{\prime \prime }+9 y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.963

23329	\begin{align} 4 y+y^{\prime \prime }&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.856

23331	\begin{align} y^{\prime \prime }+25 y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.765

23337	\begin{align} y^{\prime \prime }+6 y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.940

23338	\begin{align} y^{\prime \prime }-9 y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.997

23346	\begin{align} y^{\prime \prime }+3 y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= -6 \sqrt {3} \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	2.201

23930	\begin{align} y^{\prime \prime }-k^{2} y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	2.044

23931	\begin{align} y^{\prime \prime }+k^{2} y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.764

23977	\begin{align} y^{\prime \prime }+y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.752

24471	\begin{align} y^{\prime \prime }+9 y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.976

24472	\begin{align} y^{\prime \prime }-9 y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	2.102

24519	\begin{align} y^{\prime \prime }+y&=1 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.767

24520	\begin{align} 4 y+y^{\prime \prime }&=8 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.613

24879	\begin{align} y^{\prime \prime }+\beta ^{2} y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.889

24884	\begin{align} y^{\prime \prime }+{\mathrm e}^{-2 y}&=0 \\ y \left (3\right ) &= 0 \\ y^{\prime }\left (3\right ) &= 1 \\ \end{align}	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	✓	✓	✗	0.911

24885	\begin{align} y^{\prime \prime }+{\mathrm e}^{-2 y}&=0 \\ y \left (3\right ) &= 0 \\ y^{\prime }\left (3\right ) &= -1 \\ \end{align}	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	✓	✓	✗	0.677

24910	\begin{align} y^{\prime \prime }+4 y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.079

25470	\begin{align} m y^{\prime \prime }+k y&=F \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	2.354

25515	\begin{align} m y^{\prime \prime }+k y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.921

25517	\begin{align} y^{\prime \prime }&=-9 y \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.943

25523	\begin{align} y^{\prime \prime }+100 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 10 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.481

25528	\begin{align} m y^{\prime \prime }+k y&=1 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	12.042

25533	\begin{align} y^{\prime \prime }+\omega ^{2} y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.660

25544	\begin{align} y^{\prime \prime }&=\operatorname {Direct}_{t} \\ \end{align}	[[_2nd_order, _quadrature]]	✓	✓	✓	✓	0.838

25556	\begin{align} y^{\prime \prime }+k y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.690

25561	\begin{align} y^{\prime \prime }+\omega ^{2} y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.504

25583	\begin{align} y^{\prime \prime }+y&=4 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.612

25624	\begin{align} y^{\prime \prime }+y&=1 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.541

25697	\begin{align} x^{\prime \prime }+x&=0 \\ x \left (0\right ) &= -1 \\ x^{\prime }\left (0\right ) &= 8 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.403

25699	\begin{align} x^{\prime \prime }+x&=0 \\ x \left (\frac {\pi }{6}\right ) &= {\frac {1}{2}} \\ x^{\prime }\left (\frac {\pi }{6}\right ) &= 0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.704

25700	\begin{align} x^{\prime \prime }+x&=0 \\ x \left (\frac {\pi }{4}\right ) &= \sqrt {2} \\ x^{\prime }\left (\frac {\pi }{4}\right ) &= 2 \sqrt {2} \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.792

25701	\begin{align} y^{\prime \prime }-y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.242

25704	\begin{align} y^{\prime \prime }-y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.444

25725	\begin{align} y^{\prime \prime }+9 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (\pi \right ) &= 0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.165

25727	\begin{align} y^{\prime \prime }+9 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (\pi \right ) &= 5 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.452

25739	\begin{align} y^{\prime \prime }+9 y&=18 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.339

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