second order ode can be made integrable

2.5.18 second order ode can be made integrable

Table 2.1231: second order ode can be made integrable [377]


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

149	\begin{align} 4 y+y^{\prime \prime }&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.336

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]]	✓	✓	✓	✓	88.500

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]]	✓	✓	✓	✓	1.309

271	\begin{align} y^{\prime \prime }-4 y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.436

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]]	✓	✓	✓	✓	3.356

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]]	✓	✓	✓	✓	15.687

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]]	✓	✓	✓	✓	1.404

842	\begin{align} y^{\prime \prime }+2 y&=4 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.437

845	\begin{align} y^{\prime \prime }-4 y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.944

1254	\begin{align} 4 y^{\prime \prime }-9 y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	2.467

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]]	✓	✓	✓	✓	1.808

1278	\begin{align} 4 y^{\prime \prime }+9 y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.658

1355	\begin{align} u^{\prime \prime }+2 u&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	2.366

2363	\begin{align} y^{\prime \prime }-y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.594

2544	\begin{align} y^{\prime \prime }-y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.420

2563	\begin{align} y^{\prime \prime }+w^{2} y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.445

2819	\begin{align} z^{\prime \prime }+z^{3}&=0 \\ \end{align}	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	✓	✓	✓	4.896

2820	\begin{align} z^{\prime \prime }+z+z^{5}&=0 \\ \end{align}	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	✓	✓	✗	44.590

2822	\begin{align} z^{\prime \prime }+\frac {z}{1+z^{2}}&=0 \\ \end{align}	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	✓	✓	✗	3.111

2823	\begin{align} z^{\prime \prime }+z-2 z^{3}&=0 \\ \end{align}	[[_2nd_order, _missing_x], _Duﬃng, [_2nd_order, _reducible, _mu_x_y1]]	✓	✓	✓	✗	1.284

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]]	✓	✓	✓	✓	4.502

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]]	✓	✓	✓	✓	4.475

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]]	✓	✓	✓	✓	2.764

3058	\begin{align} y^{\prime \prime }-4 y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	2.962

3244	\begin{align} y^{\prime \prime }&=k^{2} y \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	3.636

3245	\begin{align} x^{\prime \prime }+k^{2} x&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	2.518

3265	\begin{align} y^{\prime \prime }&=y \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	2.079

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]]	✓	✓	✓	✗	0.980

3281	\begin{align} x^{\prime \prime }-k^{2} x&=0 \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= v_{0} \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	5.328

3557	\begin{align} y^{\prime \prime }-25 y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	3.442

3558	\begin{align} 4 y+y^{\prime \prime }&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	2.174

3563	\begin{align} y^{\prime \prime }-9 y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	2.257

3697	\begin{align} y^{\prime \prime }-36 y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	3.700

4124	\begin{align} y^{\prime \prime }+25 y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.422

5715	\begin{align} y^{\prime \prime }+y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	3.459

5716	\begin{align} y^{\prime \prime }-y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	4.858

5730	\begin{align} -2 y+y^{\prime \prime }&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	3.634

5732	\begin{align} 4 y+y^{\prime \prime }&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	2.308

6298	\begin{align} y^{\prime \prime }&=a y \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	8.533

6299	\begin{align} y^{\prime \prime }&=6 y^{2} \\ \end{align}	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	✓	✓	✓	14.182

6302	\begin{align} y^{\prime \prime }&=2 y^{3} \\ \end{align}	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	✓	✓	✓	17.957

6303	\begin{align} y^{\prime \prime }&=a +b y+2 y^{3} \\ \end{align}	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	✓	✓	✗	99.386

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]]	✓	✓	✓	✗	56.459

6311	\begin{align} a \,{\mathrm e}^{y}+y^{\prime \prime }&=0 \\ \end{align}	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	✓	✓	✓	34.208

6369	\begin{align} 2 y^{\prime \prime }&=1+12 y^{2} \\ \end{align}	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	✓	✓	✗	6.106

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]]	✓	✓	✓	✗	34.083

7042	\begin{align} y^{\prime \prime }-y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	5.190

7126	\begin{align} y^{\prime \prime }&=\frac {3 k y^{2}}{2} \\ \end{align}	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	✓	✓	✓	15.463

7127	\begin{align} y^{\prime \prime }&=2 k y^{3} \\ \end{align}	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	✓	✓	✓	16.480

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]]	✓	✓	✓	✗	2.403

7264	\begin{align} y^{\prime \prime }+16 y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	4.912

7367	\begin{align} y^{\prime \prime }&=-4 y \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	2.998

7369	\begin{align} y^{\prime \prime }&=y \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	4.617

7570	\begin{align} m y^{\prime \prime }+k y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	9.618

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]]	✓	✓	✓	✓	9.898

7606	\begin{align} y^{\prime \prime }+y&=0 \\ y \left (0\right ) &= 2 \\ y \left (\frac {\pi }{2}\right ) &= 0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	9.849

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]]	✓	✓	✓	✓	10.792

7665	\begin{align} x^{\prime \prime }-\omega ^{2} x&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	11.974

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]]	✓	✓	✓	✓	11.841

7851	\begin{align} y^{\prime \prime }-y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	5.604

7982	\begin{align} y^{\prime \prime }+25 y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	3.898

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]]	✓	✓	✓	✓	11.687

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]]	✓	✓	✓	✓	4.803

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]]	✓	✓	✓	✓	6.504

8220	\begin{align} y^{\prime \prime }-y&=0 \\ y \left (-1\right ) &= 5 \\ y^{\prime }\left (-1\right ) &= -5 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	2.267

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]]	✓	✓	✓	✓	2.566

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]]	✓	✓	✓	✓	4.877

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]]	✓	✓	✓	✓	8.245

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]]	✓	✓	✗	✗	14.751

8261	\begin{align} y^{\prime \prime }+9 y&=18 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	5.048

8283	\begin{align} y^{\prime \prime }+9 y&=5 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	4.940

8860	\begin{align} y^{\prime \prime }-y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	6.792

8861	\begin{align} 4 y+y^{\prime \prime }&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	3.935

8862	\begin{align} y^{\prime \prime }+k^{2} y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	11.553

8887	\begin{align} y^{\prime \prime }-4 y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	6.588

8888	\begin{align} 3 y^{\prime \prime }+2 y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	5.644

8889	\begin{align} y^{\prime \prime }+16 y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	3.835

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]]	✓	✓	✓	✓	11.769

8897	\begin{align} y^{\prime \prime }+y&=0 \\ y \left (0\right ) &= 0 \\ y \left (\pi \right ) &= 0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	4.932

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]]	✓	✓	✓	✓	5.001

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]]	✓	✓	✓	✓	4.879

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]]	✓	✓	✓	✓	17.816

8925	\begin{align} y^{\prime \prime }+y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	3.645

8926	\begin{align} y^{\prime \prime }-y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	3.165

9037	\begin{align} y^{\prime \prime }+k^{2} y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	9.263

9052	\begin{align} 4 y+y^{\prime \prime }&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	5.318

9053	\begin{align} y^{\prime \prime }-4 y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	6.319

9182	\begin{align} y^{\prime \prime }-k^{2} y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	14.440

9214	\begin{align} y^{\prime \prime }+8 y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	10.444

9220	\begin{align} y^{\prime \prime }+y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	3.565

9224	\begin{align} y^{\prime \prime }&=4 y \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	6.090

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]]	✓	✓	✓	✓	10.168

9345	\begin{align} y^{\prime \prime }&=-3 y \\ y \left (0\right ) &= -1 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	15.022

9494	\begin{align} y^{\prime \prime }+y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	4.143

9496	\begin{align} y^{\prime \prime }-y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	6.128

9582	\begin{align} y^{\prime \prime }+y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	3.864

9774	\begin{align} y^{\prime \prime }+\beta ^{2} y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	12.234

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]]	✓	✓	✓	✗	3.378

9781	\begin{align} 2 y^{\prime \prime }&=\sin \left (2 y\right ) \\ y \left (0\right ) &= \frac {\pi }{2} \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align}	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	✗	✗	✗	207.089

9782	\begin{align} 2 y^{\prime \prime }&=\sin \left (2 y\right ) \\ y \left (0\right ) &= -\frac {\pi }{2} \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align}	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	✗	✗	✗	202.917

10257	\begin{align} y^{\prime \prime }+{\mathrm e}^{y}&=0 \\ \end{align}	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	✓	✓	✓	73.260

10397	\begin{align} y^{\prime \prime }+y&=1 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	4.970

12282	\begin{align} y^{\prime \prime }+y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	3.597

12286	\begin{align} y^{\prime \prime }-y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	4.401

12289	\begin{align} y^{\prime \prime }+l y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	3.983

12835	\begin{align} y^{\prime \prime }-y^{2}&=0 \\ \end{align}	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	✓	✓	✓	12.549

12836	\begin{align} y^{\prime \prime }-6 y^{2}&=0 \\ \end{align}	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	✓	✓	✓	10.628

12838	\begin{align} y^{\prime \prime }-6 y^{2}+4 y&=0 \\ \end{align}	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	✓	✓	✗	4.680

12841	\begin{align} y^{\prime \prime }-a y^{3}&=0 \\ \end{align}	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	✓	✓	✓	8.284

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]]	✓	✓	✓	✗	61.843

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]]	✓	✓	✓	✗	7.115

12848	\begin{align} y^{\prime \prime }-{\mathrm e}^{y}&=0 \\ \end{align}	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	✓	✓	✓	21.684

13662	\begin{align} y^{\prime \prime }+a y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	6.611

14163	\begin{align} 2 y^{\prime \prime }&={\mathrm e}^{y} \\ \end{align}	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	✓	✓	✓	40.502

14289	\begin{align} x^{\prime \prime }+9 x&=0 \\ x \left (0\right ) &= 1 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	7.595

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]]	✓	✓	✓	✓	8.736

14584	\begin{align} y^{\prime \prime }+9 y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	6.138

14585	\begin{align} 4 y^{\prime \prime }+y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	3.237

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]]	✓	✓	✓	✓	14.325

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]]	✓	✓	✓	✓	7.585

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]]	✓	✓	✓	✓	7.168

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]]	✓	✓	✓	✓	7.621

14931	\begin{align} y^{\prime \prime }+\omega ^{2} y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	15.579

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]]	✓	✓	✓	✗	50.875

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]]	✓	✓	✓	✗	1.904

15316	\begin{align} y^{\prime \prime }+\alpha ^{2} y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	8.932

15317	\begin{align} y^{\prime \prime }-\alpha ^{2} y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	9.825

15401	\begin{align} y^{\prime \prime }&=a^{2} y \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	11.948

15410	\begin{align} y^{\prime \prime }&=9 y \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	10.202

15411	\begin{align} y^{\prime \prime }+y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	3.227

15412	\begin{align} y^{\prime \prime }-y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	5.779

15477	\begin{align} x^{\prime \prime }+x-x^{3}&=0 \\ \end{align}	[[_2nd_order, _missing_x], _Duﬃng, [_2nd_order, _reducible, _mu_x_y1]]	✓	✓	✓	✗	8.175

15478	\begin{align} x^{\prime \prime }+x+x^{3}&=0 \\ \end{align}	[[_2nd_order, _missing_x], _Duﬃng, [_2nd_order, _reducible, _mu_x_y1]]	✓	✓	✓	✗	7.134

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]]	✓	✓	✓	✗	8.365

15510	\begin{align} y^{\prime \prime }-y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	4.625

15659	\begin{align} y^{\prime \prime }-y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	11.538

15660	\begin{align} y^{\prime \prime }+y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	3.521

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]]	✓	✓	✓	✓	9.996

15679	\begin{align} y^{\prime \prime }+\alpha y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	10.295

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]]	✓	✓	✓	✓	15.615

16095	\begin{align} y^{\prime \prime }+2 y&=-3 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	7.740

16097	\begin{align} y^{\prime \prime }+9 y&=6 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	59.044

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]]	✓	✓	✓	✓	9.928

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]]	✓	✓	✓	✓	8.537

16490	\begin{align} y^{\prime \prime }-25 y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	9.249

16492	\begin{align} 4 y^{\prime \prime }-y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	7.115

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]]	✓	✓	✓	✓	10.852

16512	\begin{align} y^{\prime \prime }+25 y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	4.722

16517	\begin{align} 4 y^{\prime \prime }+y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	3.455

16518	\begin{align} y^{\prime \prime }+16 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	11.283

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]]	✓	✓	✓	✓	7.828

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]]	✓	✓	✓	✓	14.268

16708	\begin{align} y^{\prime \prime }+36 y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	5.379

16711	\begin{align} y^{\prime \prime }-36 y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	7.961

16717	\begin{align} y^{\prime \prime }+3 y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	6.982

17350	\begin{align} y^{\prime \prime }-y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	2.402

17353	\begin{align} y^{\prime \prime }+9 y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	2.087

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]]	✓	✓	✓	✓	1.856

17360	\begin{align} y^{\prime \prime }+16 y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.658

17386	\begin{align} 4 y^{\prime \prime }+9 y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.327

17387	\begin{align} y^{\prime \prime }+16 y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.244

17388	\begin{align} y^{\prime \prime }+8 y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.512

17389	\begin{align} y^{\prime \prime }+7 y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.546

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]]	✓	✓	✓	✓	2.668

17419	\begin{align} y^{\prime \prime }-16 y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.765

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]]	✓	✓	✓	✓	3.929

17481	\begin{align} y^{\prime \prime }+4 y&=1 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.296

17765	\begin{align} y^{\prime \prime }+25 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	2.576

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]]	✓	✓	✓	✓	2.055

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]]	✓	✓	✓	✓	2.809

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]]	✓	✓	✓	✓	2.920

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]]	✓	✓	✓	✓	3.034

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]]	✓	✓	✓	✓	2.733

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]]	✓	✓	✓	✓	2.580

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]]	✓	✓	✓	✓	2.269

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]]	✓	✓	✓	✓	3.710

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]]	✓	✓	✓	✓	1.724

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]]	✓	✓	✓	✓	2.813

18084	\begin{align} y^{\prime \prime }+y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.988

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]]	✓	✓	✓	✗	12.413

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]]	✓	✓	✓	✗	1.260

18125	\begin{align} y^{\prime \prime }-y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	2.086

18162	\begin{align} y^{\prime \prime }+k^{2} y&=k \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	2.910

18185	\begin{align} y^{\prime \prime }+9 y&=9 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.889

18282	\begin{align} y^{\prime \prime }-y&=1 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	2.679

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]]	✓	✓	✓	✓	4.411

18355	\begin{align} y^{\prime \prime }-y&=0 \\ y \left (0\right ) &= 0 \\ y \left (2 \pi \right ) &= 1 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	3.388

18358	\begin{align} y^{\prime \prime }+y&=0 \\ y \left (0\right ) &= 0 \\ y \left (\frac {\pi }{2}\right ) &= \alpha \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	3.606

18359	\begin{align} y^{\prime \prime }-y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (1\right ) &= 1 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	3.443

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]]	✓	✓	✓	✓	3.964

18725	\begin{align} y^{\prime \prime }+y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	4.163

18726	\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]]	✓	✓	✓	✓	3.675

18740	\begin{align} y^{\prime \prime }+4 y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	2.323

18769	\begin{align} 4 y^{\prime \prime }-9 y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	3.842

18778	\begin{align} 4 y^{\prime \prime }+9 y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	2.059

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]]	✓	✓	✓	✓	2.860

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]]	✓	✓	✓	✓	2.872

18814	\begin{align} m y^{\prime \prime }+k y&=0 \\ y \left (0\right ) &= a \\ y^{\prime }\left (0\right ) &= b \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	12.369

19176	\begin{align} y^{\prime \prime }+y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	2.700


19231	\begin{align} 4 y+y^{\prime \prime }&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	2.704

19232	\begin{align} y^{\prime \prime }-4 y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	3.292

19360	\begin{align} y^{\prime \prime }-k y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	6.825

19433	\begin{align} y^{\prime \prime }-y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	4.790

19461	\begin{align} y^{\prime \prime }+8 y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	3.160

19471	\begin{align} y^{\prime \prime }&=4 y \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	3.457

19736	\begin{align} \theta ^{\prime \prime }&=-p^{2} \theta \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	5.224

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]]	✓	✓	✓	✗	328.539

19750	\begin{align} \theta ^{\prime \prime }-p^{2} \theta &=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	7.344

19751	\begin{align} y^{\prime \prime }+y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	2.957

19753	\begin{align} r^{\prime \prime }-a^{2} r&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	6.967

19769	\begin{align} y^{\prime \prime }&=-m^{2} y \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	5.336

19852	\begin{align} e y^{\prime \prime }&=P \left (-y+a \right ) \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	11.418

19869	\begin{align} y^{\prime \prime }&=-a^{2} y \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	5.530

19895	\begin{align} y^{\prime \prime }-k^{2} y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	7.382

20037	\begin{align} y^{\prime \prime }-m^{2} y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	7.914

20126	\begin{align} y^{\prime \prime }+a^{2} y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	4.945

20328	\begin{align} y^{\prime \prime }-n^{2} y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	8.733

20543	\begin{align} y^{\prime \prime }&=y \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	5.227

20545	\begin{align} y^{\prime \prime }-a^{2} y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	8.612

20547	\begin{align} y^{\prime \prime }&=y^{3}-y \\ \end{align}	[[_2nd_order, _missing_x], _Duﬃng, [_2nd_order, _reducible, _mu_x_y1]]	✓	✓	✓	✗	6.476

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]]	✓	✓	✓	✗	12.724

20589	\begin{align} y^{\prime \prime }&={\mathrm e}^{y} \\ \end{align}	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	✓	✓	✓	32.443

20590	\begin{align} y^{\prime \prime }+a^{2} y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	5.475

20845	\begin{align} y^{\prime \prime }-y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	5.057

21105	\begin{align} x^{\prime \prime }+4 x&=0 \\ x \left (0\right ) &= 1 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	6.198

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]]	✓	✓	✓	✓	12.079

21124	\begin{align} x^{\prime \prime }+x&=0 \\ x \left (a \right ) &= 0 \\ x \left (b \right ) &= 0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	5.303

21125	\begin{align} x^{\prime \prime }-x&=0 \\ x \left (0\right ) &= 0 \\ x \left (1\right ) &= 0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	6.698

21254	\begin{align} x^{\prime \prime }&=x-x^{3} \\ \end{align}	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	✓	✓	✗	7.809

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]]	✓	✓	✗	✗	53.060

21256	\begin{align} x^{\prime \prime }&=x^{3}-x \\ x \left (0\right ) &= 2 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align}	[[_2nd_order, _missing_x], _Duﬃng, [_2nd_order, _reducible, _mu_x_y1]]	✓	✓	✗	✗	4.461

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]]	✓	✓	✗	✗	5.619

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]]	✓	✓	✓	✗	5.582

21259	\begin{align} x^{\prime \prime }&=x-x^{3} \\ x \left (0\right ) &= 2 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align}	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	✓	✓	✗	4.177

21260	\begin{align} x^{\prime \prime }&=x-x^{3} \\ x \left (0\right ) &= \frac {\sqrt {2}}{2} \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align}	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	✓	✗	✗	18.534

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]]	✓	✓	✗	✗	16.510

21262	\begin{align} x^{\prime \prime }+x+\frac {x^{2}}{3}&=0 \\ x \left (0\right ) &= 1 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align}	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	✓	✗	✗	5.119

21264	\begin{align} x^{\prime \prime }-x+3 x^{2}&=0 \\ x \left (0\right ) &= {\frac {1}{4}} \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align}	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	✓	✗	✗	88.192

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]]	✓	✓	✗	✗	23.399

21266	\begin{align} x^{\prime \prime }-x+3 x^{2}&=0 \\ x \left (0\right ) &= -{\frac {1}{4}} \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align}	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	✓	✗	✗	3.870

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]]	✓	✓	✓	✗	11.936

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]]	✓	✓	✓	✗	9.540

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]]	✓	✓	✗	✗	22.098

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]]	✓	✓	✗	✗	17.175

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]]	✓	✓	✓	✗	11.086

21477	\begin{align} y^{\prime \prime }-y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	7.837

21481	\begin{align} y^{\prime \prime }-5 y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	5.559

21488	\begin{align} y^{\prime \prime }+y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	3.172

21489	\begin{align} 4 y+y^{\prime \prime }&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	3.401

21563	\begin{align} y^{\prime \prime }-y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	2.927

21566	\begin{align} y^{\prime \prime }+y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	2.950

21568	\begin{align} y^{\prime \prime }+k^{2} y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	8.616

21620	\begin{align} y^{\prime \prime }+\omega ^{2} y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= v \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	22.040

21624	\begin{align} y^{\prime \prime }+4 y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	5.301

21728	\begin{align} 4 y+y^{\prime \prime }&=0 \\ y \left (0\right ) &= 0 \\ y \left (\frac {\pi }{4}\right ) &= 7 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	10.405

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]]	✓	✓	✓	✗	6.966

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]]	✓	✓	✓	✓	7.573

21787	\begin{align} x^{\prime \prime }&=4 x^{3}-4 x \\ \end{align}	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	✓	✓	✗	8.727

21789	\begin{align} x^{\prime \prime }&=x^{2}-4 x+\lambda \\ \end{align}	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	✓	✓	✗	58.688

21792	\begin{align} y^{\prime \prime }+y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	3.394

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]]	✓	✓	✓	✓	10.747

21970	\begin{align} y^{\prime \prime }-y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	6.629

22079	\begin{align} y^{\prime \prime }-y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	9.010

22095	\begin{align} y^{\prime \prime }-5 y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	6.293

22097	\begin{align} 4 y+y^{\prime \prime }&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	3.730

22101	\begin{align} y^{\prime \prime }-y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	2.697

22104	\begin{align} y^{\prime \prime }+y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	3.356

22106	\begin{align} y^{\prime \prime }-7 y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	6.218

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]]	✓	✓	✓	✓	4.799

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]]	✓	✓	✓	✓	6.075

22284	\begin{align} y^{\prime \prime }+y&=0 \\ y \left (0\right ) &= 0 \\ y \left (\frac {\pi }{2}\right ) &= 1 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	7.480

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]]	✓	✓	✓	✓	5.364

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]]	✓	✓	✓	✓	9.253

22317	\begin{align} y^{\prime \prime }+y^{2}&=0 \\ \end{align}	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	✓	✓	✓	29.493

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]]	✓	✓	✓	✓	11.819

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]]	✓	✓	✓	✓	10.908

22487	\begin{align} y^{\prime \prime }-y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	9.190

22629	\begin{align} 4 y^{\prime \prime }-25 y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	13.225

22630	\begin{align} y^{\prime \prime }-4 y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	7.312

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]]	✓	✓	✓	✓	10.006

22654	\begin{align} 4 y+y^{\prime \prime }&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	4.914

22656	\begin{align} 4 y^{\prime \prime }+9 y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	4.097

22660	\begin{align} y^{\prime \prime }+y&=0 \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	15.267

22739	\begin{align} y^{\prime \prime }-y&=1 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	7.856

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]]	✓	✓	✓	✓	17.674

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]]	✓	✓	✓	✓	32.056

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]]	✓	✓	✓	✓	19.300

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]]	✓	✓	✓	✓	18.966

23015	\begin{align} 4 y^{\prime \prime }-7 y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	13.766

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]]	✓	✓	✓	✓	23.208

23032	\begin{align} y^{\prime \prime }-9 y&=5 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	10.132

23054	\begin{align} s^{\prime \prime }&=-9 s \\ s \left (0\right ) &= 9 \\ s^{\prime }\left (0\right ) &= 0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	11.289

23087	\begin{align} y^{\prime \prime }-4 y&=12 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	10.125

23097	\begin{align} y^{\prime \prime }-y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	8.231

23098	\begin{align} y^{\prime \prime }+y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	4.651

23099	\begin{align} y^{\prime \prime }-4 y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	6.003

23100	\begin{align} 4 y+y^{\prime \prime }&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	4.720

23233	\begin{align} y^{\prime \prime }-y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	13.649

23266	\begin{align} y^{\prime \prime }+9 y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	7.039

23267	\begin{align} y^{\prime \prime }-4 y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	8.514

23268	\begin{align} y^{\prime \prime }+a^{2} y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	12.975

23273	\begin{align} y^{\prime \prime }+y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	4.601

23280	\begin{align} 4 y+y^{\prime \prime }&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	4.770

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]]	✓	✓	✓	✓	9.805

23302	\begin{align} y^{\prime \prime }+a^{2} y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	10.477

23316	\begin{align} y^{\prime \prime }+9 y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	5.227

23322	\begin{align} 2 y^{\prime \prime }+y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	9.175

23323	\begin{align} y^{\prime \prime }+16 y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	6.747

23326	\begin{align} y^{\prime \prime }+9 y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	4.839

23329	\begin{align} 4 y+y^{\prime \prime }&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	4.892

23331	\begin{align} y^{\prime \prime }+25 y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	5.879

23337	\begin{align} y^{\prime \prime }+6 y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	8.379

23338	\begin{align} y^{\prime \prime }-9 y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	8.917

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]]	✓	✓	✓	✓	23.582

23351	\begin{align} 4 y+y^{\prime \prime }&=0 \\ y \left (\frac {\pi }{4}\right ) &= 1 \\ y^{\prime }\left (\frac {\pi }{4}\right ) &= 0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	6.773

23930	\begin{align} y^{\prime \prime }-k^{2} y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	23.147

23931	\begin{align} y^{\prime \prime }+k^{2} y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	10.291

23976	\begin{align} y^{\prime \prime }-y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	4.750

23977	\begin{align} y^{\prime \prime }+y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	8.442

24471	\begin{align} y^{\prime \prime }+9 y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	11.273

24472	\begin{align} y^{\prime \prime }-9 y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	15.063

24476	\begin{align} y^{\prime \prime }-y&=0 \\ y \left (0\right ) &= y_{0} \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	24.849

24477	\begin{align} y^{\prime \prime }+y&=0 \\ y \left (0\right ) &= y_{0} \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	28.645

24519	\begin{align} y^{\prime \prime }+y&=1 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	9.642

24520	\begin{align} 4 y+y^{\prime \prime }&=8 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	7.335

24569	\begin{align} 4 y^{\prime \prime }+y&=2 \\ y \left (\pi \right ) &= 0 \\ y^{\prime }\left (\pi \right ) &= 1 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	37.799

24721	\begin{align} y^{\prime \prime }+y&=3 \\ y \left (\frac {\pi }{2}\right ) &= 1 \\ y^{\prime }\left (\frac {\pi }{2}\right ) &= 0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	12.061

24879	\begin{align} y^{\prime \prime }+\beta ^{2} y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	25.881

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]]	✓	✓	✓	✗	6.359

24886	\begin{align} 2 y^{\prime \prime }&=\sin \left (2 y\right ) \\ y \left (0\right ) &= \frac {\pi }{2} \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align}	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	✗	✓	✗	273.195

24887	\begin{align} 2 y^{\prime \prime }&=\sin \left (2 y\right ) \\ y \left (0\right ) &= -\frac {\pi }{2} \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align}	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	✗	✓	✗	263.700

24910	\begin{align} y^{\prime \prime }+4 y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	11.773

25470	\begin{align} m y^{\prime \prime }+k y&=F \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	58.118

25515	\begin{align} m y^{\prime \prime }+k y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	29.690

25517	\begin{align} y^{\prime \prime }&=-9 y \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	12.839

25528	\begin{align} m y^{\prime \prime }+k y&=1 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	119.973

25533	\begin{align} y^{\prime \prime }+\omega ^{2} y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	26.205

25544	\begin{align} y^{\prime \prime }&=\operatorname {Direct}_{t} \\ \end{align}	[[_2nd_order, _quadrature]]	✓	✓	✓	✓	9.026

25545	\begin{align} y^{\prime \prime }+y&=1 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	15.326

25556	\begin{align} y^{\prime \prime }+k y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	22.164

25561	\begin{align} y^{\prime \prime }+\omega ^{2} y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	15.358

25581	\begin{align} r^{\prime \prime }+r&=1 \\ r \left (0\right ) &= 0 \\ r^{\prime }\left (0\right ) &= 0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	16.678

25583	\begin{align} y^{\prime \prime }+y&=4 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	12.476

25624	\begin{align} y^{\prime \prime }+y&=1 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	11.043

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]]	✓	✓	✓	✓	31.057

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]]	✓	✓	✓	✓	12.576

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]]	✓	✓	✓	✓	18.546

25703	\begin{align} y^{\prime \prime }-y&=0 \\ y \left (-1\right ) &= 5 \\ y^{\prime }\left (-1\right ) &= -5 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	5.303

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]]	✓	✓	✓	✓	6.050

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]]	✓	✓	✓	✓	13.815

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]]	✓	✓	✓	✓	23.029

25739	\begin{align} y^{\prime \prime }+9 y&=18 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	13.313

25924	\begin{align} 4 y+y^{\prime \prime }&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	14.150

26096	\begin{align} y^{\prime \prime }+18 \sin \left (y\right ) \cos \left (y\right )^{3}&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align}	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	✓	✓	✗	7.204

26097	\begin{align} y^{\prime \prime }&=18 y^{3} \\ y \left (1\right ) &= 1 \\ y^{\prime }\left (1\right ) &= 3 \\ \end{align}	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	✓	✓	✗	4.266

26108	\begin{align} y^{\prime \prime }+y&=1 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	10.929

26142	\begin{align} y^{\prime \prime }-y&=0 \\ y \left (0\right ) &= 0 \\ y \left (2 \pi \right ) &= 1 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	33.855

26144	\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]]	✓	✓	✓	✓	43.920

26428	\begin{align} y^{\prime \prime }+y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	13.095

26474	\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]]	✓	✓	✓	✗	9.418

26480	\begin{align} y^{\prime \prime }-y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	18.464

26517	\begin{align} y^{\prime \prime }+k^{2} y&=k \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	27.168

26542	\begin{align} y^{\prime \prime }+9 y-9&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	13.558

26685	\begin{align} y^{\prime \prime }+\lambda y&=0 \\ y \left (0\right ) &= 0 \\ y \left (1\right ) &= 0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	42.763

26686	\begin{align} y^{\prime \prime }-y&=0 \\ y \left (0\right ) &= 0 \\ y \left (2 \pi \right ) &= 1 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	20.958

26688	\begin{align} y^{\prime \prime }-k^{2} y&=0 \\ y \left (0\right ) &= v_{1} \\ y \left (x_{0} \right ) &= v_{2} \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	99.264

26689	\begin{align} y^{\prime \prime }-k^{2} y&=0 \\ y \left (0\right ) &= v \\ y \left (x_{0} \right ) &= 0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	57.523

26690	\begin{align} y^{\prime \prime }-\alpha ^{2} s y&=0 \\ y \left (0\right ) &= \frac {1}{s} \\ y \left (x_{0} \right ) &= 0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	88.606

26691	\begin{align} y^{\prime \prime }-\alpha ^{2} s y&=0 \\ y \left (0\right ) &= -\frac {1}{s} \\ y \left (x_{0} \right ) &= 0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	61.786

26693	\begin{align} y^{\prime \prime }-\lambda ^{2} y&=0 \\ y \left (0\right ) &= 0 \\ y \left (1\right ) &= \frac {1}{\lambda } \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	62.369

26694	\begin{align} y^{\prime \prime }-\lambda ^{2} y&=0 \\ y^{\prime }\left (0\right ) &= 0 \\ y \left (1\right ) &= \frac {1}{\lambda } \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	30.456

26695	\begin{align} y^{\prime \prime }-\lambda ^{2} y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (1\right ) &= \frac {1}{\lambda } \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	45.119

26696	\begin{align} y^{\prime \prime }-\lambda ^{2} y&=0 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime }\left (1\right ) &= \frac {1}{\lambda } \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	50.104

26925	\begin{align} y^{\prime \prime }+36 y&=0 \\ y \left (0\right ) &= -5 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	34.828

26926	\begin{align} y^{\prime \prime }-16 y&=0 \\ y \left (0\right ) &= 12 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	99.511

27611	\begin{align} y^{\prime \prime }+\sin \left (y\right )&=0 \\ y \left (\infty \right ) &= \pi \\ \end{align}	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	✓	✗	✗	636.684

27618	\begin{align} 4 y+y^{\prime \prime }&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	19.776

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