Problems 1401 to 1500

2.2.15 Problems 1401 to 1500

Table 2.47: Main lookup table. Sorted sequentially by problem number.


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

1401	\begin{align} x_{1}^{\prime }&=3 x_{1}-2 x_{2} \\ x_{2}^{\prime }&=4 x_{1}-x_{2} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.643

1402	\begin{align} x_{1}^{\prime }&=-x_{1}-4 x_{2} \\ x_{2}^{\prime }&=x_{1}-x_{2} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.517

1403	\begin{align} x_{1}^{\prime }&=2 x_{1}-5 x_{2} \\ x_{2}^{\prime }&=x_{1}-2 x_{2} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.518

1404	\begin{align} x_{1}^{\prime }&=2 x_{1}-\frac {5 x_{2}}{2} \\ x_{2}^{\prime }&=\frac {9 x_{1}}{5}-x_{2} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.655

1405	\begin{align} x_{1}^{\prime }&=x_{1}-x_{2} \\ x_{2}^{\prime }&=5 x_{1}-3 x_{2} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.634

1406	\begin{align} x_{1}^{\prime }&=x_{1}+2 x_{2} \\ x_{2}^{\prime }&=-5 x_{1}-x_{2} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.552

1407	\begin{align} x_{1}^{\prime }&=x_{1} \\ x_{2}^{\prime }&=2 x_{1}+x_{2}-2 x_{3} \\ x_{3}^{\prime }&=3 x_{1}+2 x_{2}+x_{3} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.954

1408	\begin{align} x_{1}^{\prime }&=-3 x_{1}+2 x_{3} \\ x_{2}^{\prime }&=x_{1}-x_{2} \\ x_{3}^{\prime }&=-2 x_{1}-x_{2} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	2.633

1409	\begin{align} x_{1}^{\prime }&=x_{1}-5 x_{2} \\ x_{2}^{\prime }&=x_{1}-3 x_{2} \\ \end{align} With initial conditions \begin{align} x_{1} \left (0\right ) &= 1 \\ x_{2} \left (0\right ) &= 1 \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.604

1410	\begin{align} x_{1}^{\prime }&=-3 x_{1}+2 x_{2} \\ x_{2}^{\prime }&=-x_{1}-x_{2} \\ \end{align} With initial conditions \begin{align} x_{1} \left (0\right ) &= 1 \\ x_{2} \left (0\right ) &= -2 \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.648

1411	\begin{align} x_{1}^{\prime }&=\frac {3 x_{1}}{4}-2 x_{2} \\ x_{2}^{\prime }&=x_{1}-\frac {5 x_{2}}{4} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.603

1412	\begin{align} x_{1}^{\prime }&=-\frac {4 x_{1}}{5}+2 x_{2} \\ x_{2}^{\prime }&=-x_{1}+\frac {6 x_{2}}{5} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.603

1413	\begin{align} x_{1}^{\prime }&=-\frac {x_{1}}{4}+x_{2} \\ x_{2}^{\prime }&=-x_{1}-\frac {x_{2}}{4} \\ x_{3}^{\prime }&=-\frac {x_{3}}{4} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.744

1414	\begin{align} x_{1}^{\prime }&=-\frac {x_{1}}{4}+x_{2} \\ x_{2}^{\prime }&=-x_{1}-\frac {x_{2}}{4} \\ x_{3}^{\prime }&=\frac {x_{3}}{10} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.801

1415	\begin{align} x_{1}^{\prime }&=-\frac {x_{1}}{2}-\frac {x_{2}}{8} \\ x_{2}^{\prime }&=2 x_{1}-\frac {x_{2}}{2} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.534

1416	\begin{align} x_{1}^{\prime }&=3 x_{1}-4 x_{2} \\ x_{2}^{\prime }&=x_{1}-x_{2} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.423

1417	\begin{align} x_{1}^{\prime }&=4 x_{1}-2 x_{2} \\ x_{2}^{\prime }&=8 x_{1}-4 x_{2} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.401

1418	\begin{align} x_{1}^{\prime }&=-\frac {3 x_{1}}{2}+x_{2} \\ x_{2}^{\prime }&=-\frac {x_{1}}{4}-\frac {x_{2}}{2} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.444

1419	\begin{align} x_{1}^{\prime }&=-3 x_{1}+\frac {5 x_{2}}{2} \\ x_{2}^{\prime }&=-\frac {5 x_{1}}{2}+2 x_{2} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.422

1420	\begin{align} x_{1}^{\prime }&=x_{1}+x_{2}+x_{3} \\ x_{2}^{\prime }&=2 x_{1}+x_{2}-x_{3} \\ x_{3}^{\prime }&=-x_{2}+x_{3} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.877

1421	\begin{align} x_{1}^{\prime }&=x_{2}+x_{3} \\ x_{2}^{\prime }&=x_{1}+x_{3} \\ x_{3}^{\prime }&=x_{1}+x_{2} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.669

1422	\begin{align} x_{1}^{\prime }&=x_{1}-4 x_{2} \\ x_{2}^{\prime }&=4 x_{1}-7 x_{2} \\ \end{align} With initial conditions \begin{align} x_{1} \left (0\right ) &= 3 \\ x_{2} \left (0\right ) &= 2 \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.477

1423	\begin{align} x_{1}^{\prime }&=-\frac {5 x_{1}}{2}+\frac {3 x_{2}}{2} \\ x_{2}^{\prime }&=-\frac {3 x_{1}}{2}+\frac {x_{2}}{2} \\ \end{align} With initial conditions \begin{align} x_{1} \left (0\right ) &= 3 \\ x_{2} \left (0\right ) &= -1 \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.480

1424	\begin{align} x_{1}^{\prime }&=2 x_{1}+\frac {3 x_{2}}{2} \\ x_{2}^{\prime }&=-\frac {3 x_{1}}{2}-x_{2} \\ \end{align} With initial conditions \begin{align} x_{1} \left (0\right ) &= 3 \\ x_{2} \left (0\right ) &= -2 \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.491

1425	\begin{align} x_{1}^{\prime }&=3 x_{1}+9 x_{2} \\ x_{2}^{\prime }&=-x_{1}-3 x_{2} \\ \end{align} With initial conditions \begin{align} x_{1} \left (0\right ) &= 2 \\ x_{2} \left (0\right ) &= 4 \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.450

1426	\begin{align} x_{1}^{\prime }&=x_{1} \\ x_{2}^{\prime }&=-4 x_{1}+x_{2} \\ x_{3}^{\prime }&=3 x_{1}+6 x_{2}+2 x_{3} \\ \end{align} With initial conditions \begin{align} x_{1} \left (0\right ) &= -1 \\ x_{2} \left (0\right ) &= 2 \\ x_{3} \left (0\right ) &= -30 \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.776

1427	\begin{align} x_{1}^{\prime }&=-\frac {5 x_{1}}{2}+x_{2}+x_{3} \\ x_{2}^{\prime }&=x_{1}-\frac {5 x_{2}}{2}+x_{3} \\ x_{3}^{\prime }&=x_{1}+x_{2}-\frac {5 x_{3}}{2} \\ \end{align} With initial conditions \begin{align} x_{1} \left (0\right ) &= 2 \\ x_{2} \left (0\right ) &= 3 \\ x_{3} \left (0\right ) &= -1 \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.749

1428	\begin{align} x_{1}^{\prime }&=2 x_{1}-x_{2}+{\mathrm e}^{t} \\ x_{2}^{\prime }&=3 x_{1}-2 x_{2}+t \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.928

1429	\begin{align} x_{1}^{\prime }&=x_{1}+\sqrt {3}\, x_{2}+{\mathrm e}^{t} \\ x_{2}^{\prime }&=\sqrt {3}\, x_{1}-x_{2}+\sqrt {3}\, {\mathrm e}^{-t} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	1.003

1430	\begin{align} x_{1}^{\prime }&=2 x_{1}-5 x_{2}-\cos \left (t \right ) \\ x_{2}^{\prime }&=x_{1}-2 x_{2}+\sin \left (t \right ) \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.986

1431	\begin{align} x_{1}^{\prime }&=x_{1}+x_{2}+{\mathrm e}^{-2 t} \\ x_{2}^{\prime }&=4 x_{1}-2 x_{2}-2 \,{\mathrm e}^{t} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.807

1432	\begin{align} x_{1}^{\prime }&=4 x_{1}-2 x_{2}+\frac {1}{t^{3}} \\ x_{2}^{\prime }&=8 x_{1}-4 x_{2}-\frac {1}{t^{2}} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.674

1433	\begin{align} x_{1}^{\prime }&=-4 x_{1}+2 x_{2}+\frac {1}{t} \\ x_{2}^{\prime }&=2 x_{1}-x_{2}+\frac {2}{t}+4 \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.786

1434	\begin{align} x_{1}^{\prime }&=x_{1}+x_{2}+2 \,{\mathrm e}^{t} \\ x_{2}^{\prime }&=4 x_{1}+x_{2}-{\mathrm e}^{t} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.789

1435	\begin{align} x_{1}^{\prime }&=2 x_{1}-x_{2}+{\mathrm e}^{t} \\ x_{2}^{\prime }&=3 x_{1}-2 x_{2}-{\mathrm e}^{t} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.807

1436	\begin{align} x_{1}^{\prime }&=-\frac {5 x_{1}}{4}+\frac {3 x_{2}}{4}+2 t \\ x_{2}^{\prime }&=\frac {3 x_{1}}{4}-\frac {5 x_{2}}{4}+{\mathrm e}^{t} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.820

1437	\begin{align} x_{1}^{\prime }&=-3 x_{1}+\sqrt {2}\, x_{2}+{\mathrm e}^{-t} \\ x_{2}^{\prime }&=\sqrt {2}\, x_{1}-2 x_{2}-{\mathrm e}^{-t} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.934

1438	\begin{align} x_{1}^{\prime }&=2 x_{1}-5 x_{2} \\ x_{2}^{\prime }&=x_{1}-2 x_{2}+\cos \left (t \right ) \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.960

1439	\begin{align} x_{1}^{\prime }&=2 x_{1}-5 x_{2}+\csc \left (t \right ) \\ x_{2}^{\prime }&=x_{1}-2 x_{2}+\sec \left (t \right ) \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	1.457

1440	\begin{align} x_{1}^{\prime }&=-\frac {x_{1}}{2}-\frac {x_{2}}{8}+\frac {{\mathrm e}^{-\frac {t}{2}}}{2} \\ x_{2}^{\prime }&=2 x_{1}-\frac {x_{2}}{2} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.807

1441	\begin{align} x_{1}^{\prime }&=-2 x_{1}+x_{2}+2 \,{\mathrm e}^{-t} \\ x_{2}^{\prime }&=x_{1}-2 x_{2}+3 t \\ \end{align} With initial conditions \begin{align} x_{1} \left (0\right ) &= \alpha _{1} \\ x_{2} \left (0\right ) &= \alpha _{2} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.854

1442	\begin{align} x_{1}^{\prime }&=3 x_{1}-2 x_{2} \\ x_{2}^{\prime }&=2 x_{1}-2 x_{2} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.509

1443	\begin{align} x_{1}^{\prime }&=5 x_{1}-x_{2} \\ x_{2}^{\prime }&=3 x_{1}+x_{2} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.497

1444	\begin{align} x_{1}^{\prime }&=2 x_{1}-x_{2} \\ x_{2}^{\prime }&=3 x_{1}-2 x_{2} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.491

1445	\begin{align} x_{1}^{\prime }&=x_{1}-4 x_{2} \\ x_{2}^{\prime }&=4 x_{1}-7 x_{2} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.404

1446	\begin{align} x_{1}^{\prime }&=x_{1}-5 x_{2} \\ x_{2}^{\prime }&=x_{1}-3 x_{2} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.575

1447	\begin{align} x_{1}^{\prime }&=2 x_{1}-5 x_{2} \\ x_{2}^{\prime }&=x_{1}-2 x_{2} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.491

1448	\begin{align} x_{1}^{\prime }&=3 x_{1}-2 x_{2} \\ x_{2}^{\prime }&=4 x_{1}-x_{2} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.610

1449	\begin{align} x_{1}^{\prime }&=-x_{1}-x_{2} \\ x_{2}^{\prime }&=-\frac {5 x_{2}}{2} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.456

1450	\begin{align} x_{1}^{\prime }&=3 x_{1}-4 x_{2} \\ x_{2}^{\prime }&=x_{1}-x_{2} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.417

1451	\begin{align} x_{1}^{\prime }&=x_{1}+2 x_{2} \\ x_{2}^{\prime }&=-5 x_{1} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	1.168

1452	\begin{align} x_{1}^{\prime }&=-x_{1} \\ x_{2}^{\prime }&=-x_{2} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.311

1453	\begin{align} x_{1}^{\prime }&=2 x_{1}-\frac {5 x_{2}}{2} \\ x_{2}^{\prime }&=\frac {9 x_{1}}{5}-x_{2} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.618

1454	\begin{align} x_{1}^{\prime }&=x_{1}+x_{2}-2 \\ x_{2}^{\prime }&=x_{1}-x_{2} \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.934

1455	\begin{align} x_{1}^{\prime }&=-2 x_{1}+x_{2}-2 \\ x_{2}^{\prime }&=x_{1}-2 x_{2}+1 \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.694

1456	\begin{align} x_{1}^{\prime }&=-x_{1}-x_{2}-1 \\ x_{2}^{\prime }&=2 x_{1}-x_{2}+5 \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.997

1457	\begin{align} x^{\prime }&=-x \\ y^{\prime }&=-2 y \\ \end{align} With initial conditions \begin{align} x \left (0\right ) &= 4 \\ y \left (0\right ) &= 2 \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.424

1458	\begin{align} x^{\prime }&=-x \\ y^{\prime }&=2 y \\ \end{align} With initial conditions \begin{align} x \left (0\right ) &= 4 \\ y \left (0\right ) &= 2 \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.417

1459	\begin{align} x^{\prime }&=-x \\ y^{\prime }&=2 y \\ \end{align} With initial conditions \begin{align} x \left (0\right ) &= 4 \\ y \left (0\right ) &= 0 \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.407

1460	\begin{align} x^{\prime }&=-y \\ y^{\prime }&=x \\ \end{align} With initial conditions \begin{align} x \left (0\right ) &= 4 \\ y \left (0\right ) &= 0 \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.480

1461	\begin{align} x^{\prime }&=-y \\ y^{\prime }&=x \\ \end{align} With initial conditions \begin{align} x \left (0\right ) &= 0 \\ y \left (0\right ) &= 4 \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.462

1462	\begin{align} y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+3 y&=t \\ \end{align}	[[_high_order, _with_linear_symmetries]]	✓	✓	✓	✓	0.200

1463	\begin{align} t \left (t -1\right ) y^{\prime \prime \prime \prime }+{\mathrm e}^{t} y^{\prime \prime }+4 t^{2} y&=0 \\ \end{align}	[[_high_order, _with_linear_symmetries]]	✗	✗	✗	✗	0.056

1464	\begin{align} y^{\prime \prime \prime \prime }+y^{\prime \prime }&=0 \\ \end{align}	[[_high_order, _missing_x]]	✓	✓	✓	✓	0.060

1465	\begin{align} y^{\prime \prime \prime }+2 y^{\prime \prime }-y^{\prime }-2 y&=0 \\ \end{align}	[[_3rd_order, _missing_x]]	✓	✓	✓	✓	0.066

1466	\begin{align} x y^{\prime \prime \prime }-y^{\prime \prime }&=0 \\ \end{align}	[[_3rd_order, _missing_y]]	✓	✓	✓	✓	0.300

1467	\begin{align} x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\ \end{align}	[[_3rd_order, _exact, _linear, _homogeneous]]	✓	✓	✓	✓	0.178

1468	\begin{align} y^{\prime \prime \prime }+2 y^{\prime \prime }-y^{\prime }-3 y&=0 \\ \end{align}	[[_3rd_order, _missing_x]]	✓	✓	✓	✓	0.105

1469	\begin{align} t y^{\prime \prime \prime }+2 y^{\prime \prime }-y^{\prime }+t y&=0 \\ \end{align}	[[_3rd_order, _with_linear_symmetries]]	✗	✓	✓	✗	0.049

1470	\begin{align} \left (2-t \right ) y^{\prime \prime \prime }+\left (2 t -3\right ) y^{\prime \prime }-y^{\prime } t +y&=0 \\ \end{align}	[[_3rd_order, _with_linear_symmetries]]	✗	✓	✓	✗	0.051

1471	\begin{align} t^{2} \left (t +3\right ) y^{\prime \prime \prime }-3 t \left (t +2\right ) y^{\prime \prime }+6 \left (1+t \right ) y^{\prime }-6 y&=0 \\ \end{align}	[[_3rd_order, _with_linear_symmetries]]	✗	✓	✓	✗	0.056

1472	\begin{align} y^{\prime \prime \prime }-y^{\prime \prime }-y^{\prime }+y&=0 \\ \end{align}	[[_3rd_order, _missing_x]]	✓	✓	✓	✓	0.069

1473	\begin{align} y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }+y&=0 \\ \end{align}	[[_3rd_order, _missing_x]]	✓	✓	✓	✓	0.085

1474	\begin{align} y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+4 y^{\prime \prime }&=0 \\ \end{align}	[[_high_order, _missing_x]]	✓	✓	✓	✓	0.070

1475	\begin{align} y^{\left (6\right )}+y&=0 \\ \end{align}	[[_high_order, _missing_x]]	✓	✓	✓	✓	0.112

1476	\begin{align} y^{\left (6\right )}-3 y^{\prime \prime \prime \prime }+3 y^{\prime \prime }-y&=0 \\ \end{align}	[[_high_order, _missing_x]]	✓	✓	✓	✓	0.092

1477	\begin{align} y^{\left (6\right )}-y^{\prime \prime }&=0 \\ \end{align}	[[_high_order, _missing_x]]	✓	✓	✓	✓	0.081

1478	\begin{align} y^{\left (5\right )}-3 y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime }-3 y^{\prime \prime }+2 y^{\prime }&=0 \\ \end{align}	[[_high_order, _missing_x]]	✓	✓	✓	✓	0.085

1479	\begin{align} y^{\left (8\right )}+8 y^{\prime \prime \prime \prime }+16 y&=0 \\ \end{align}	[[_high_order, _missing_x]]	✓	✓	✓	✓	0.123

1480	\begin{align} y^{\prime \prime \prime \prime }+2 y^{\prime \prime }+y&=0 \\ \end{align}	[[_high_order, _missing_x]]	✓	✓	✓	✓	0.079

1481	\begin{align} y^{\prime \prime \prime }+5 y^{\prime \prime }+6 y^{\prime }+2 y&=0 \\ \end{align}	[[_3rd_order, _missing_x]]	✓	✓	✓	✓	0.075

1482	\begin{align} y^{\prime \prime \prime \prime }-7 y^{\prime \prime \prime }+6 y^{\prime \prime }+30 y^{\prime }-36 y&=0 \\ \end{align}	[[_high_order, _missing_x]]	✓	✓	✓	✓	0.085

1483	\begin{align} y^{\prime \prime }-y^{\prime }-6 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align} Using Laplace transform method.	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.282

1484	\begin{align} y^{\prime \prime }+3 y^{\prime }+2 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align} Using Laplace transform method.	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.217

1485	\begin{align} y^{\prime \prime }-2 y^{\prime }+2 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align} Using Laplace transform method.	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.228

1486	\begin{align} y^{\prime \prime }-2 y^{\prime }+4 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align} Using Laplace transform method.	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.259

1487	\begin{align} y^{\prime \prime }+2 y^{\prime }+5 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align} Using Laplace transform method.	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.241

1488	\begin{align} y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+6 y^{\prime \prime }-4 y^{\prime }+y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ y^{\prime \prime \prime }\left (0\right ) &= 1 \\ \end{align} Using Laplace transform method.	[[_high_order, _missing_x]]	✓	✓	✓	✓	0.296

1489	\begin{align} y^{\prime \prime \prime \prime }-4 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 1 \\ y^{\prime \prime \prime }\left (0\right ) &= 0 \\ \end{align} Using Laplace transform method.	[[_high_order, _missing_x]]	✓	✓	✓	✓	0.323

1490	\begin{align} y^{\prime \prime }+\omega ^{2} y&=\cos \left (2 t \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align} Using Laplace transform method.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓	0.340

1491	\begin{align} y^{\prime \prime }-2 y^{\prime }+2 y&={\mathrm e}^{-t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align} Using Laplace transform method.	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓	0.277

1492	\begin{align} y^{\prime \prime }+4 y&=\left \{\begin {array}{cc} 1 & 0\le t <\pi \\ 0 & \pi \le t <\infty \end {array}\right . \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align} Using Laplace transform method.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓	1.175

1493	\begin{align} y^{\prime \prime }+4 y&=\left \{\begin {array}{cc} 1 & 0\le t <1 \\ 0 & 1\le t <\infty \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align} Using Laplace transform method.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓	1.300

1494	\begin{align} y^{\prime \prime }+y&=\left \{\begin {array}{cc} t & 0\le t <1 \\ 2-t & 1\le t <2 \\ 0 & 2\le t <\infty \end {array}\right . \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align} Using Laplace transform method.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓	1.073

1495	\begin{align} y^{\prime \prime }+y&=\left \{\begin {array}{cc} 1 & 0\le t <3 \pi \\ 0 & 3 \pi \le t <\infty \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align} Using Laplace transform method.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓	1.029

1496	\begin{align} y^{\prime \prime }+2 y^{\prime }+2 y&=\left \{\begin {array}{cc} 1 & \pi \le t <2 \pi \\ 0 & \operatorname {otherwise} \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align} Using Laplace transform method.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✗	2.784

1497	\begin{align} y^{\prime \prime }+4 y&=\sin \left (t \right )-\operatorname {Heaviside}\left (t -2 \pi \right ) \sin \left (t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align} Using Laplace transform method.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓	0.667

1498	\begin{align} y^{\prime \prime }+3 y^{\prime }+2 y&=\left \{\begin {array}{cc} 1 & 0\le t <10 \\ 0 & \operatorname {otherwise} \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align} Using Laplace transform method.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✗	1.998

1499	\begin{align} y^{\prime \prime }+y^{\prime }+\frac {5 y}{4}&=t -\operatorname {Heaviside}\left (t -\frac {\pi }{2}\right ) \left (t -\frac {\pi }{2}\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align} Using Laplace transform method.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓	2.218

1500	\begin{align} y^{\prime \prime }+y^{\prime }+\frac {5 y}{4}&=\left \{\begin {array}{cc} \sin \left (t \right ) & 0\le t <\pi \\ 0 & \operatorname {otherwise} \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align} Using Laplace transform method.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✗	2.295

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