Problems 2201 to 2300

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


#	ODE	CAS classiﬁcation	Solved?	time (sec)

2201	$y^{''''} - 5 y^{''} + 4 y = - 12 e^{x} + 6 e^{- x} + 10 \cos (x)$	[[_high_order, _linear, _nonhomogeneous]]	✓	0.200

2202	$y^{''''} - 4 y^{'''} + 11 y^{''} - 14 y^{'} + 10 y = - e^{x} (\sin (x) + 2 \cos (2 x))$	[[_high_order, _linear, _nonhomogeneous]]	✓	1.015

2203	$y^{''''} + 2 y^{'''} - 3 y^{''} - 4 y^{'} + 4 y = 2 e^{x} (x + 1) + e^{- 2 x}$	[[_high_order, _linear, _nonhomogeneous]]	✓	0.181

2204	$y^{''''} + 4 y = \sinh (x) \cos (x) - \cosh (x) \sin (x)$	[[_high_order, _linear, _nonhomogeneous]]	✓	1.257

2205	$y^{''''} + 5 y^{'''} + 9 y^{''} + 7 y^{'} + 2 y = e^{- x} (30 + 24 x) - e^{- 2 x}$	[[_high_order, _linear, _nonhomogeneous]]	✓	0.181

2206	$y^{''''} - 4 y^{'''} + 7 y^{''} - 6 y^{'} + 2 y = e^{x} (12 x - 2 \cos (x) + 2 \sin (x))$	[[_high_order, _linear, _nonhomogeneous]]	✓	0.951

2207	$y^{'''} - y^{''} - y^{'} + y = e^{2 x} (10 + 3 x)$	[[_3rd_order, _linear, _nonhomogeneous]]	✓	0.123

2208	$y^{'''} + y^{''} - 2 y = - e^{3 x} (17 x^{2} + 67 x + 9)$	[[_3rd_order, _linear, _nonhomogeneous]]	✓	0.134

2209	$y^{'''} - 6 y^{''} + 11 y^{'} - 6 y = e^{2 x} (- 3 x^{2} - 4 x + 5)$	[[_3rd_order, _linear, _nonhomogeneous]]	✓	0.141

2210	$y^{'''} + 2 y^{''} + y^{'} = - 2 e^{- x} (6 x^{2} - 18 x + 7)$	[[_3rd_order, _missing_y]]	✓	0.139

2211	$y^{'''} - 3 y^{''} + 3 y^{'} - y = e^{x} (x + 1)$	[[_3rd_order, _linear, _nonhomogeneous]]	✓	0.125

2212	$y^{''''} - 2 y^{''} + y = - e^{- x} (3 x^{2} - 9 x + 4)$	[[_high_order, _linear, _nonhomogeneous]]	✓	0.146

2213	$y^{'''} + 2 y^{''} - y^{'} - 2 y = e^{- 2 x} ((23 - 2 x) \cos (x) + (8 - 9 x) \sin (x))$	[[_3rd_order, _linear, _nonhomogeneous]]	✓	0.273

2214	$y^{''''} - 3 y^{'''} + 4 y^{''} - 2 y^{'} = e^{x} ((28 + 6 x) \cos (2 x) + (11 - 12 x) \sin (2 x))$	[[_high_order, _missing_y]]	✓	0.353

2215	$y^{''''} - 4 y^{'''} + 14 y^{''} - 20 y^{'} + 25 y = e^{x} ((2 + 6 x) \cos (2 x) + 3 \sin (2 x))$	[[_high_order, _linear, _nonhomogeneous]]	✓	1.438

2216	$y^{'''} - 2 y^{''} - 5 y^{'} + 6 y = 2 e^{x} (1 - 6 x)$ i.c.	[[_3rd_order, _linear, _nonhomogeneous]]	✓	0.202

2217	$y^{'''} - y^{''} - y^{'} + y = - e^{- x} (4 - 8 x)$ i.c.	[[_3rd_order, _linear, _nonhomogeneous]]	✓	0.197

2218	$4 y^{'''} - 3 y^{'} - y = e^{- \frac{x}{2}} (2 - 3 x)$ i.c.	[[_3rd_order, _linear, _nonhomogeneous]]	✓	0.203

2219	$y^{''''} + 2 y^{'''} + 2 y^{''} + 2 y^{'} + y = e^{- x} (20 - 12 x)$ i.c.	[[_high_order, _linear, _nonhomogeneous]]	✓	0.167

2220	$y^{'''} + 2 y^{''} + y^{'} + 2 y = 30 \cos (x) - 10 \sin (x)$ i.c.	[[_3rd_order, _linear, _nonhomogeneous]]	✓	0.676

2221	$y^{''''} - 3 y^{'''} + 5 y^{''} - 2 y^{'} = - 2 e^{x} (\cos (x) - \sin (x))$ i.c.	[[_high_order, _missing_y]]	✓	2.073

2222	$x^{3} y^{'''} - 3 x^{2} y^{''} + 6 x y^{'} - 6 y = 2 x$	[[_3rd_order, _with_linear_symmetries]]	✓	0.306

2223	$4 x^{3} y^{'''} + 4 x^{2} y^{''} - 5 x y^{'} + 2 y = 30 x^{2}$	[[_3rd_order, _with_linear_symmetries]]	✓	0.341

2224	$x^{3} y^{'''} + x^{2} y^{''} - 2 x y^{'} + 2 y = x^{2}$	[[_3rd_order, _exact, _linear, _nonhomogeneous]]	✓	0.290

2225	$16 x^{4} y^{''''} + 96 x^{3} y^{'''} + 72 x^{2} y^{''} - 24 x y^{'} + 9 y = 96 x^{5 / 2}$	[[_high_order, _with_linear_symmetries]]	✓	0.358

2226	$x^{4} y^{''''} - 4 x^{3} y^{'''} + 12 x^{2} y^{''} - 24 x y^{'} + 24 y = x^{4}$	[[_high_order, _with_linear_symmetries]]	✓	0.335

2227	$x^{4} y^{''''} + 6 x^{3} y^{'''} + 2 x^{2} y^{''} - 4 x y^{'} + 4 y = 12 x^{2}$	[[_high_order, _exact, _linear, _nonhomogeneous]]	✓	0.329

2228	$x^{3} y^{'''} - 2 x^{2} y^{''} + 3 x y^{'} - 3 y = 4 x$ i.c.	[[_3rd_order, _with_linear_symmetries]]	✓	0.398

2229	$x^{3} y^{'''} - 5 x^{2} y^{''} + 14 x y^{'} - 18 y = x^{3}$ i.c.	[[_3rd_order, _with_linear_symmetries]]	✓	0.397

2230	$x^{3} y^{'''} - 6 x^{2} y^{''} + 16 x y^{'} - 16 y = 9 x^{4}$ i.c.	[[_3rd_order, _with_linear_symmetries]]	✓	0.418

2231	$x^{3} y^{'''} + x^{2} y^{''} - 2 x y^{'} + 2 y = x (x + 1)$ i.c.	[[_3rd_order, _exact, _linear, _nonhomogeneous]]	✓	0.333

2232	$x^{4} y^{''''} + 3 x^{3} y^{'''} - x^{2} y^{''} + 2 x y^{'} - 2 y = 9 x^{2}$ i.c.	[[_high_order, _exact, _linear, _nonhomogeneous]]	✓	0.433

2233	$4 x^{4} y^{''''} + 24 x^{3} y^{'''} + 23 x^{2} y^{''} - x y^{'} + y = 6 x$ i.c.	[[_high_order, _exact, _linear, _nonhomogeneous]]	✓	0.461

2234	$x^{4} y^{''''} + 5 x^{3} y^{'''} - 3 x^{2} y^{''} - 6 x y^{'} + 6 y = 40 x^{3}$ i.c.	[[_high_order, _exact, _linear, _nonhomogeneous]]	✓	0.359

2235	$y^{'''} + 2 y^{''} - y^{'} - 2 y = F (x)$	[[_3rd_order, _linear, _nonhomogeneous]]	✓	0.312

2236	$x^{3} y^{'''} + x^{2} y^{''} - 2 x y^{'} + 2 y = F (x)$	[[_3rd_order, _exact, _linear, _nonhomogeneous]]	✓	0.315

2237	$y^{''''} - 5 y^{''} + 4 y = F (x)$	[[_high_order, _linear, _nonhomogeneous]]	✓	0.343

2238	$x^{4} y^{''''} + 6 x^{3} y^{'''} + 2 x^{2} y^{''} - 4 x y^{'} + 4 y = F (x)$	[[_high_order, _exact, _linear, _nonhomogeneous]]	✓	0.365

2239	$[\begin{matrix} y_{1}^{'} = y_{1} + 2 y_{2} \\ y_{2}^{'} = 2 y_{1} + y_{2} \end{matrix}]$	system_of_ODEs	✓	0.461

2240	$[\begin{matrix} y_{1}^{'} = - \frac{5 y_{1}}{4} + \frac{3 y_{2}}{4} \\ y_{2}^{'} = \frac{3 y_{1}}{4} - \frac{5 y_{2}}{4} \end{matrix}]$	system_of_ODEs	✓	0.464

2241	$[\begin{matrix} y_{1}^{'} = - \frac{4 y_{1}}{5} + \frac{3 y_{2}}{5} \\ y_{2}^{'} = - \frac{2 y_{1}}{5} - \frac{11 y_{2}}{5} \end{matrix}]$	system_of_ODEs	✓	0.490

2242	$[\begin{matrix} y_{1}^{'} = - y_{1} - 4 y_{2} \\ y_{2}^{'} = - y_{1} - y_{2} \end{matrix}]$	system_of_ODEs	✓	0.477

2243	$[\begin{matrix} y_{1}^{'} = 2 y_{1} - 4 y_{2} \\ y_{2}^{'} = - y_{1} - y_{2} \end{matrix}]$	system_of_ODEs	✓	0.484

2244	$[\begin{matrix} y_{1}^{'} = 4 y_{1} - 3 y_{2} \\ y_{2}^{'} = 2 y_{1} - y_{2} \end{matrix}]$	system_of_ODEs	✓	0.462

2245	$[\begin{matrix} y_{1}^{'} = - 6 y_{1} - 3 y_{2} \\ y_{2}^{'} = y_{1} - 2 y_{2} \end{matrix}]$	system_of_ODEs	✓	0.467

2246	$[\begin{matrix} y_{1}^{'} = y_{1} - y_{2} - 2 y_{3} \\ y_{2}^{'} = y_{1} - 2 y_{2} - 3 y_{3} \\ y_{3}^{'} = - 4 y_{1} + y_{2} - y_{3} \end{matrix}]$	system_of_ODEs	✓	0.548

2247	$[\begin{matrix} y_{1}^{'} = - 6 y_{1} - 4 y_{2} - 8 y_{3} \\ y_{2}^{'} = - 4 y_{1} - 4 y_{3} \\ y_{3}^{'} = - 8 y_{1} - 4 y_{2} - 6 y_{3} \end{matrix}]$	system_of_ODEs	✓	0.445

2248	$[\begin{matrix} y_{1}^{'} = 3 y_{1} + 5 y_{2} + 8 y_{3} \\ y_{2}^{'} = y_{1} - y_{2} - 2 y_{3} \\ y_{3}^{'} = - y_{1} - y_{2} - y_{3} \end{matrix}]$	system_of_ODEs	✓	0.563

2249	$[\begin{matrix} y_{1}^{'} = y_{1} - y_{2} + 2 y_{3} \\ y_{2}^{'} = 12 y_{1} - 4 y_{2} + 10 y_{3} \\ y_{3}^{'} = - 6 y_{1} + y_{2} - 7 y_{3} \end{matrix}]$	system_of_ODEs	✓	0.497

2250	$[\begin{matrix} y_{1}^{'} = 4 y_{1} - y_{2} - 4 y_{3} \\ y_{2}^{'} = 4 y_{1} - 3 y_{2} - 2 y_{3} \\ y_{3}^{'} = y_{1} - y_{2} - y_{3} \end{matrix}]$	system_of_ODEs	✓	0.521

2251	$[\begin{matrix} y_{1}^{'} = - 2 y_{1} + 2 y_{2} - 6 y_{3} \\ y_{2}^{'} = 2 y_{1} + 6 y_{2} + 2 y_{3} \\ y_{3}^{'} = - 2 y_{1} - 2 y_{2} + 2 y_{3} \end{matrix}]$	system_of_ODEs	✓	0.495

2252	$[\begin{matrix} y_{1}^{'} = 3 y_{1} + 2 y_{2} - 2 y_{3} \\ y_{2}^{'} = - 2 y_{1} + 7 y_{2} - 2 y_{3} \\ y_{3}^{'} = - 10 y_{1} + 10 y_{2} - 5 y_{3} \end{matrix}]$	system_of_ODEs	✓	0.424

2253	$[\begin{matrix} y_{1}^{'} = 3 y_{1} + y_{2} - y_{3} \\ y_{2}^{'} = 3 y_{1} + 5 y_{2} + y_{3} \\ y_{3}^{'} = - 6 y_{1} + 2 y_{2} + 4 y_{3} \end{matrix}]$	system_of_ODEs	✓	0.413

2254	$[\begin{matrix} y_{1}^{'} = 3 y_{1} + 4 y_{2} \\ y_{2}^{'} = - y_{1} + 7 y_{2} \end{matrix}]$	system_of_ODEs	✓	0.440

2255	$[\begin{matrix} y_{1}^{'} = - y_{2} \\ y_{2}^{'} = y_{1} - 2 y_{2} \end{matrix}]$	system_of_ODEs	✓	0.433

2256	$[\begin{matrix} y_{1}^{'} = - 7 y_{1} + 4 y_{2} \\ y_{2}^{'} = - y_{1} - 11 y_{2} \end{matrix}]$	system_of_ODEs	✓	0.458

2257	$[\begin{matrix} y_{1}^{'} = 3 y_{1} + y_{2} \\ y_{2}^{'} = - y_{1} + y_{2} \end{matrix}]$	system_of_ODEs	✓	0.448

2258	$[\begin{matrix} y_{1}^{'} = 4 y_{1} + 12 y_{2} \\ y_{2}^{'} = - 3 y_{1} - 8 y_{2} \end{matrix}]$	system_of_ODEs	✓	0.449

2259	$[\begin{matrix} y_{1}^{'} = - 10 y_{1} + 9 y_{2} \\ y_{2}^{'} = - 4 y_{1} + 2 y_{2} \end{matrix}]$	system_of_ODEs	✓	0.453

2260	$[\begin{matrix} y_{1}^{'} = - 13 y_{1} + 16 y_{2} \\ y_{2}^{'} = - 9 y_{1} + 11 y_{2} \end{matrix}]$	system_of_ODEs	✓	0.457

2261	$[\begin{matrix} y_{1}^{'} = 2 y_{2} + y_{3} \\ y_{2}^{'} = - 4 y_{1} + 6 y_{2} + y_{3} \\ y_{3}^{'} = 4 y_{2} + 2 y_{3} \end{matrix}]$	system_of_ODEs	✓	0.425

2262	$[\begin{matrix} y_{1}^{'} = \frac{y_{1}}{3} + \frac{y_{2}}{3} - y_{3} \\ y_{2}^{'} = - \frac{4 y_{1}}{3} - \frac{4 y_{2}}{3} + y_{3} \\ y_{3}^{'} = - \frac{2 y_{1}}{3} + \frac{y_{2}}{3} \end{matrix}]$	system_of_ODEs	✓	0.461

2263	$[\begin{matrix} y_{1}^{'} = - y_{1} + y_{2} - y_{3} \\ y_{2}^{'} = - 2 y_{1} + 2 y_{3} \\ y_{3}^{'} = - y_{1} + 3 y_{2} - y_{3} \end{matrix}]$	system_of_ODEs	✓	0.449

2264	$[\begin{matrix} y_{1}^{'} = 4 y_{1} - 2 y_{2} - 2 y_{3} \\ y_{2}^{'} = - 2 y_{1} + 3 y_{2} - y_{3} \\ y_{3}^{'} = 2 y_{1} - y_{2} + 3 y_{3} \end{matrix}]$	system_of_ODEs	✓	0.451

2265	$[\begin{matrix} y_{1}^{'} = 6 y_{1} - 5 y_{2} + 3 y_{3} \\ y_{2}^{'} = 2 y_{1} - y_{2} + 3 y_{3} \\ y_{3}^{'} = 2 y_{1} + y_{2} + y_{3} \end{matrix}]$	system_of_ODEs	✓	0.463

2266	$[\begin{matrix} y_{1}^{'} = - 11 y_{1} + 8 y_{2} \\ y_{2}^{'} = - 2 y_{1} - 3 y_{2} \end{matrix}]$ i.c.	system_of_ODEs	✓	0.585

2267	$[\begin{matrix} y_{1}^{'} = 15 y_{1} - 9 y_{2} \\ y_{2}^{'} = 16 y_{1} - 9 y_{2} \end{matrix}]$ i.c.	system_of_ODEs	✓	0.639

2268	$[\begin{matrix} y_{1}^{'} = - 3 y_{1} - 4 y_{2} \\ y_{2}^{'} = y_{1} - 7 y_{2} \end{matrix}]$ i.c.	system_of_ODEs	✓	0.561

2269	$[\begin{matrix} y_{1}^{'} = - 7 y_{1} + 24 y_{2} \\ y_{2}^{'} = - 6 y_{1} + 17 y_{2} \end{matrix}]$ i.c.	system_of_ODEs	✓	0.582

2270	$[\begin{matrix} y_{1}^{'} = - 7 y_{1} + 3 y_{2} \\ y_{2}^{'} = - 3 y_{1} - y_{2} \end{matrix}]$ i.c.	system_of_ODEs	✓	0.550

2271	$[\begin{matrix} y_{1}^{'} = - y_{1} + y_{2} \\ y_{2}^{'} = y_{1} - y_{2} - 2 y_{3} \\ y_{3}^{'} = - y_{1} - y_{2} - y_{3} \end{matrix}]$ i.c.	system_of_ODEs	✓	0.505

2272	$[\begin{matrix} y_{1}^{'} = - 2 y_{1} + 2 y_{2} + y_{3} \\ y_{2}^{'} = - 2 y_{1} + 2 y_{2} + y_{3} \\ y_{3}^{'} = - 3 y_{1} + 3 y_{2} + 2 y_{3} \end{matrix}]$ i.c.	system_of_ODEs	✓	0.412

2273	$[\begin{matrix} y_{1}^{'} = - 7 y_{1} - 4 y_{2} + 4 y_{3} \\ y_{2}^{'} = y_{1} + y_{3} \\ y_{3}^{'} = - 9 y_{1} - 5 y_{2} + 6 y_{3} \end{matrix}]$ i.c.	system_of_ODEs	✓	0.829

2274	$[\begin{matrix} y_{1}^{'} = - y_{1} - 4 y_{2} - y_{3} \\ y_{2}^{'} = 3 y_{1} + 6 y_{2} + y_{3} \\ y_{3}^{'} = - 3 y_{1} - 2 y_{2} + 3 y_{3} \end{matrix}]$ i.c.	system_of_ODEs	✓	0.485

2275	$[\begin{matrix} y_{1}^{'} = 4 y_{1} - 8 y_{2} - 4 y_{3} \\ y_{2}^{'} = - 3 y_{1} - y_{2} - 4 y_{3} \\ y_{3}^{'} = y_{1} - y_{2} + 9 y_{3} \end{matrix}]$ i.c.	system_of_ODEs	✓	0.645

2276	$[\begin{matrix} y_{1}^{'} = - 5 y_{1} - y_{2} + 11 y_{3} \\ y_{2}^{'} = - 7 y_{1} + y_{2} + 13 y_{3} \\ y_{3}^{'} = - 4 y_{1} + 8 y_{3} \end{matrix}]$ i.c.	system_of_ODEs	✓	0.425

2277	$[\begin{matrix} y_{1}^{'} = 5 y_{1} - y_{2} + y_{3} \\ y_{2}^{'} = - y_{1} + 9 y_{2} - 3 y_{3} \\ y_{3}^{'} = - 2 y_{1} + 2 y_{2} + 4 y_{3} \end{matrix}]$	system_of_ODEs	✓	0.429

2278	$[\begin{matrix} y_{1}^{'} = y_{1} + 10 y_{2} - 12 y_{3} \\ y_{2}^{'} = 2 y_{1} + 2 y_{2} + 3 y_{3} \\ y_{3}^{'} = 2 y_{1} - y_{2} + 6 y_{3} \end{matrix}]$	system_of_ODEs	✓	0.434

2279	$[\begin{matrix} y_{1}^{'} = - 6 y_{1} - 4 y_{2} - 4 y_{3} \\ y_{2}^{'} = 2 y_{1} - y_{2} + y_{3} \\ y_{3}^{'} = 2 y_{1} + 3 y_{2} + y_{3} \end{matrix}]$	system_of_ODEs	✓	0.427

2280	$[\begin{matrix} y_{1}^{'} = 2 y_{2} - 2 y_{3} \\ y_{2}^{'} = - y_{1} + 5 y_{2} - 3 y_{3} \\ y_{3}^{'} = y_{1} + y_{2} + y_{3} \end{matrix}]$	system_of_ODEs	✓	0.427

2281	$[\begin{matrix} y_{1}^{'} = - 2 y_{1} - 12 y_{2} + 10 y_{3} \\ y_{2}^{'} = 2 y_{1} - 24 y_{2} + 11 y_{3} \\ y_{3}^{'} = 2 y_{1} - 24 y_{2} + 8 y_{3} \end{matrix}]$	system_of_ODEs	✓	0.533

2282	$[\begin{matrix} y_{1}^{'} = - y_{1} - 12 y_{2} + 8 y_{3} \\ y_{2}^{'} = y_{1} - 9 y_{2} + 4 y_{3} \\ y_{3}^{'} = y_{1} - 6 y_{2} + y_{3} \end{matrix}]$	system_of_ODEs	✓	0.436

2283	$[\begin{matrix} y_{1}^{'} = - 4 y_{1} - y_{3} \\ y_{2}^{'} = - y_{1} - 3 y_{2} - y_{3} \\ y_{3}^{'} = y_{1} - 2 y_{3} \end{matrix}]$	system_of_ODEs	✓	0.374

2284	$[\begin{matrix} y_{1}^{'} = - 3 y_{1} - 3 y_{2} + 4 y_{3} \\ y_{2}^{'} = 4 y_{1} + 5 y_{2} - 8 y_{3} \\ y_{3}^{'} = 2 y_{1} + 3 y_{2} - 5 y_{3} \end{matrix}]$	system_of_ODEs	✓	0.429

2285	$[\begin{matrix} y_{1}^{'} = - 3 y_{1} - y_{2} \\ y_{2}^{'} = y_{1} - y_{2} \\ y_{3}^{'} = - y_{1} - y_{2} - 2 y_{3} \end{matrix}]$	system_of_ODEs	✓	0.375

2286	$[\begin{matrix} y_{1}^{'} = - y_{1} + 2 y_{2} \\ y_{2}^{'} = - 5 y_{1} + 5 y_{2} \end{matrix}]$	system_of_ODEs	✓	0.549

2287	$[\begin{matrix} y_{1}^{'} = - 11 y_{1} + 4 y_{2} \\ y_{2}^{'} = - 26 y_{1} + 9 y_{2} \end{matrix}]$	system_of_ODEs	✓	0.566

2288	$[\begin{matrix} y_{1}^{'} = y_{1} + 2 y_{2} \\ y_{2}^{'} = - 4 y_{1} + 5 y_{2} \end{matrix}]$	system_of_ODEs	✓	0.617

2289	$[\begin{matrix} y_{1}^{'} = 5 y_{1} - 6 y_{2} \\ y_{2}^{'} = 3 y_{1} - y_{2} \end{matrix}]$	system_of_ODEs	✓	0.547

2290	$[\begin{matrix} y_{1}^{'} = - 3 y_{1} - 3 y_{2} + y_{3} \\ y_{2}^{'} = 2 y_{2} + 2 y_{3} \\ y_{3}^{'} = 5 y_{1} + y_{2} + y_{3} \end{matrix}]$	system_of_ODEs	✓	9.546

2291	$[\begin{matrix} y_{1}^{'} = - 3 y_{1} + 3 y_{2} + y_{3} \\ y_{2}^{'} = y_{1} - 5 y_{2} - 3 y_{3} \\ y_{3}^{'} = - 3 y_{1} + 7 y_{2} + 3 y_{3} \end{matrix}]$	system_of_ODEs	✓	0.759

2292	$[\begin{matrix} y_{1}^{'} = 2 y_{1} + y_{2} - y_{3} \\ y_{2}^{'} = y_{2} + y_{3} \\ y_{3}^{'} = y_{1} + y_{3} \end{matrix}]$	system_of_ODEs	✓	0.604

2293	$[\begin{matrix} y_{1}^{'} = - 3 y_{1} + y_{2} - 3 y_{3} \\ y_{2}^{'} = 4 y_{1} - y_{2} + 2 y_{3} \\ y_{3}^{'} = 4 y_{1} - 2 y_{2} + 3 y_{3} \end{matrix}]$	system_of_ODEs	✓	0.747

2294	$y^{'} + \sin (t) y = 0$ i.c.	[_separable]	✓	0.464

2295	$y^{'} + e^{t^{2}} y = 0$ i.c.	[_separable]	✓	0.408

2296	$y^{'} - 2 t y = t$	[_separable]	✓	0.251

2297	$2 t y + y^{'} = t$ i.c.	[_separable]	✓	0.460

2298	$y^{'} + y = \frac{1}{t^{2} + 1}$ i.c.	[_linear]	✓	0.572

2299	$\cos (t) y + y^{'} = 0$	[_separable]	✓	2.009

2300	$\sqrt{t} \sin (t) y + y^{'} = 0$	[_separable]	✓	2.035

2.2.23 Problems 2201 to 2300