2.2.23 Problems 2201 to 2300

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

#

ODE

CAS classification

Solved?

time (sec)

2201

\[ {}y^{\prime \prime \prime \prime }-5 y^{\prime \prime }+4 y = -12 \,{\mathrm e}^{x}+6 \,{\mathrm e}^{-x}+10 \cos \left (x \right ) \]

[[_high_order, _linear, _nonhomogeneous]]

0.200

2202

\[ {}y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+11 y^{\prime \prime }-14 y^{\prime }+10 y = -{\mathrm e}^{x} \left (\sin \left (x \right )+2 \cos \left (2 x \right )\right ) \]

[[_high_order, _linear, _nonhomogeneous]]

1.015

2203

\[ {}y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }-3 y^{\prime \prime }-4 y^{\prime }+4 y = 2 \,{\mathrm e}^{x} \left (x +1\right )+{\mathrm e}^{-2 x} \]

[[_high_order, _linear, _nonhomogeneous]]

0.181

2204

\[ {}y^{\prime \prime \prime \prime }+4 y = \sinh \left (x \right ) \cos \left (x \right )-\cosh \left (x \right ) \sin \left (x \right ) \]

[[_high_order, _linear, _nonhomogeneous]]

1.257

2205

\[ {}y^{\prime \prime \prime \prime }+5 y^{\prime \prime \prime }+9 y^{\prime \prime }+7 y^{\prime }+2 y = {\mathrm e}^{-x} \left (30+24 x \right )-{\mathrm e}^{-2 x} \]

[[_high_order, _linear, _nonhomogeneous]]

0.181

2206

\[ {}y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+7 y^{\prime \prime }-6 y^{\prime }+2 y = {\mathrm e}^{x} \left (12 x -2 \cos \left (x \right )+2 \sin \left (x \right )\right ) \]

[[_high_order, _linear, _nonhomogeneous]]

0.951

2207

\[ {}y^{\prime \prime \prime }-y^{\prime \prime }-y^{\prime }+y = {\mathrm e}^{2 x} \left (10+3 x \right ) \]

[[_3rd_order, _linear, _nonhomogeneous]]

0.123

2208

\[ {}y^{\prime \prime \prime }+y^{\prime \prime }-2 y = -{\mathrm e}^{3 x} \left (17 x^{2}+67 x +9\right ) \]

[[_3rd_order, _linear, _nonhomogeneous]]

0.134

2209

\[ {}y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y = {\mathrm e}^{2 x} \left (-3 x^{2}-4 x +5\right ) \]

[[_3rd_order, _linear, _nonhomogeneous]]

0.141

2210

\[ {}y^{\prime \prime \prime }+2 y^{\prime \prime }+y^{\prime } = -2 \,{\mathrm e}^{-x} \left (6 x^{2}-18 x +7\right ) \]

[[_3rd_order, _missing_y]]

0.139

2211

\[ {}y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y = {\mathrm e}^{x} \left (x +1\right ) \]

[[_3rd_order, _linear, _nonhomogeneous]]

0.125

2212

\[ {}y^{\prime \prime \prime \prime }-2 y^{\prime \prime }+y = -{\mathrm e}^{-x} \left (3 x^{2}-9 x +4\right ) \]

[[_high_order, _linear, _nonhomogeneous]]

0.146

2213

\[ {}y^{\prime \prime \prime }+2 y^{\prime \prime }-y^{\prime }-2 y = {\mathrm e}^{-2 x} \left (\left (23-2 x \right ) \cos \left (x \right )+\left (8-9 x \right ) \sin \left (x \right )\right ) \]

[[_3rd_order, _linear, _nonhomogeneous]]

0.273

2214

\[ {}y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }+4 y^{\prime \prime }-2 y^{\prime } = {\mathrm e}^{x} \left (\left (28+6 x \right ) \cos \left (2 x \right )+\left (11-12 x \right ) \sin \left (2 x \right )\right ) \]

[[_high_order, _missing_y]]

0.353

2215

\[ {}y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+14 y^{\prime \prime }-20 y^{\prime }+25 y = {\mathrm e}^{x} \left (\left (2+6 x \right ) \cos \left (2 x \right )+3 \sin \left (2 x \right )\right ) \]

[[_high_order, _linear, _nonhomogeneous]]

1.438

2216

\[ {}y^{\prime \prime \prime }-2 y^{\prime \prime }-5 y^{\prime }+6 y = 2 \,{\mathrm e}^{x} \left (1-6 x \right ) \]
i.c.

[[_3rd_order, _linear, _nonhomogeneous]]

0.202

2217

\[ {}y^{\prime \prime \prime }-y^{\prime \prime }-y^{\prime }+y = -{\mathrm e}^{-x} \left (4-8 x \right ) \]
i.c.

[[_3rd_order, _linear, _nonhomogeneous]]

0.197

2218

\[ {}4 y^{\prime \prime \prime }-3 y^{\prime }-y = {\mathrm e}^{-\frac {x}{2}} \left (2-3 x \right ) \]
i.c.

[[_3rd_order, _linear, _nonhomogeneous]]

0.203

2219

\[ {}y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+2 y^{\prime \prime }+2 y^{\prime }+y = {\mathrm e}^{-x} \left (20-12 x \right ) \]
i.c.

[[_high_order, _linear, _nonhomogeneous]]

0.167

2220

\[ {}y^{\prime \prime \prime }+2 y^{\prime \prime }+y^{\prime }+2 y = 30 \cos \left (x \right )-10 \sin \left (x \right ) \]
i.c.

[[_3rd_order, _linear, _nonhomogeneous]]

0.676

2221

\[ {}y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }+5 y^{\prime \prime }-2 y^{\prime } = -2 \,{\mathrm e}^{x} \left (\cos \left (x \right )-\sin \left (x \right )\right ) \]
i.c.

[[_high_order, _missing_y]]

2.073

2222

\[ {}x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 x y^{\prime }-6 y = 2 x \]

[[_3rd_order, _with_linear_symmetries]]

0.306

2223

\[ {}4 x^{3} y^{\prime \prime \prime }+4 x^{2} y^{\prime \prime }-5 x y^{\prime }+2 y = 30 x^{2} \]

[[_3rd_order, _with_linear_symmetries]]

0.341

2224

\[ {}x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = x^{2} \]

[[_3rd_order, _exact, _linear, _nonhomogeneous]]

0.290

2225

\[ {}16 x^{4} y^{\prime \prime \prime \prime }+96 x^{3} y^{\prime \prime \prime }+72 x^{2} y^{\prime \prime }-24 x y^{\prime }+9 y = 96 x^{{5}/{2}} \]

[[_high_order, _with_linear_symmetries]]

0.358

2226

\[ {}x^{4} y^{\prime \prime \prime \prime }-4 x^{3} y^{\prime \prime \prime }+12 x^{2} y^{\prime \prime }-24 x y^{\prime }+24 y = x^{4} \]

[[_high_order, _with_linear_symmetries]]

0.335

2227

\[ {}x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-4 x y^{\prime }+4 y = 12 x^{2} \]

[[_high_order, _exact, _linear, _nonhomogeneous]]

0.329

2228

\[ {}x^{3} y^{\prime \prime \prime }-2 x^{2} y^{\prime \prime }+3 x y^{\prime }-3 y = 4 x \]
i.c.

[[_3rd_order, _with_linear_symmetries]]

0.398

2229

\[ {}x^{3} y^{\prime \prime \prime }-5 x^{2} y^{\prime \prime }+14 x y^{\prime }-18 y = x^{3} \]
i.c.

[[_3rd_order, _with_linear_symmetries]]

0.397

2230

\[ {}x^{3} y^{\prime \prime \prime }-6 x^{2} y^{\prime \prime }+16 x y^{\prime }-16 y = 9 x^{4} \]
i.c.

[[_3rd_order, _with_linear_symmetries]]

0.418

2231

\[ {}x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = x \left (x +1\right ) \]
i.c.

[[_3rd_order, _exact, _linear, _nonhomogeneous]]

0.333

2232

\[ {}x^{4} y^{\prime \prime \prime \prime }+3 x^{3} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }+2 x y^{\prime }-2 y = 9 x^{2} \]
i.c.

[[_high_order, _exact, _linear, _nonhomogeneous]]

0.433

2233

\[ {}4 x^{4} y^{\prime \prime \prime \prime }+24 x^{3} y^{\prime \prime \prime }+23 x^{2} y^{\prime \prime }-x y^{\prime }+y = 6 x \]
i.c.

[[_high_order, _exact, _linear, _nonhomogeneous]]

0.461

2234

\[ {}x^{4} y^{\prime \prime \prime \prime }+5 x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }-6 x y^{\prime }+6 y = 40 x^{3} \]
i.c.

[[_high_order, _exact, _linear, _nonhomogeneous]]

0.359

2235

\[ {}y^{\prime \prime \prime }+2 y^{\prime \prime }-y^{\prime }-2 y = F \left (x \right ) \]

[[_3rd_order, _linear, _nonhomogeneous]]

0.312

2236

\[ {}x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = F \left (x \right ) \]

[[_3rd_order, _exact, _linear, _nonhomogeneous]]

0.315

2237

\[ {}y^{\prime \prime \prime \prime }-5 y^{\prime \prime }+4 y = F \left (x \right ) \]

[[_high_order, _linear, _nonhomogeneous]]

0.343

2238

\[ {}x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-4 x y^{\prime }+4 y = F \left (x \right ) \]

[[_high_order, _exact, _linear, _nonhomogeneous]]

0.365

2239

\[ {}\left [\begin {array}{c} y_{1}^{\prime }=y_{1}+2 y_{2} \\ y_{2}^{\prime }=2 y_{1}+y_{2} \end {array}\right ] \]

system_of_ODEs

0.461

2240

\[ {}\left [\begin {array}{c} y_{1}^{\prime }=-\frac {5 y_{1}}{4}+\frac {3 y_{2}}{4} \\ y_{2}^{\prime }=\frac {3 y_{1}}{4}-\frac {5 y_{2}}{4} \end {array}\right ] \]

system_of_ODEs

0.464

2241

\[ {}\left [\begin {array}{c} y_{1}^{\prime }=-\frac {4 y_{1}}{5}+\frac {3 y_{2}}{5} \\ y_{2}^{\prime }=-\frac {2 y_{1}}{5}-\frac {11 y_{2}}{5} \end {array}\right ] \]

system_of_ODEs

0.490

2242

\[ {}\left [\begin {array}{c} y_{1}^{\prime }=-y_{1}-4 y_{2} \\ y_{2}^{\prime }=-y_{1}-y_{2} \end {array}\right ] \]

system_of_ODEs

0.477

2243

\[ {}\left [\begin {array}{c} y_{1}^{\prime }=2 y_{1}-4 y_{2} \\ y_{2}^{\prime }=-y_{1}-y_{2} \end {array}\right ] \]

system_of_ODEs

0.484

2244

\[ {}\left [\begin {array}{c} y_{1}^{\prime }=4 y_{1}-3 y_{2} \\ y_{2}^{\prime }=2 y_{1}-y_{2} \end {array}\right ] \]

system_of_ODEs

0.462

2245

\[ {}\left [\begin {array}{c} y_{1}^{\prime }=-6 y_{1}-3 y_{2} \\ y_{2}^{\prime }=y_{1}-2 y_{2} \end {array}\right ] \]

system_of_ODEs

0.467

2246

\[ {}\left [\begin {array}{c} y_{1}^{\prime }=y_{1}-y_{2}-2 y_{3} \\ y_{2}^{\prime }=y_{1}-2 y_{2}-3 y_{3} \\ y_{3}^{\prime }=-4 y_{1}+y_{2}-y_{3} \end {array}\right ] \]

system_of_ODEs

0.548

2247

\[ {}\left [\begin {array}{c} y_{1}^{\prime }=-6 y_{1}-4 y_{2}-8 y_{3} \\ y_{2}^{\prime }=-4 y_{1}-4 y_{3} \\ y_{3}^{\prime }=-8 y_{1}-4 y_{2}-6 y_{3} \end {array}\right ] \]

system_of_ODEs

0.445

2248

\[ {}\left [\begin {array}{c} y_{1}^{\prime }=3 y_{1}+5 y_{2}+8 y_{3} \\ y_{2}^{\prime }=y_{1}-y_{2}-2 y_{3} \\ y_{3}^{\prime }=-y_{1}-y_{2}-y_{3} \end {array}\right ] \]

system_of_ODEs

0.563

2249

\[ {}\left [\begin {array}{c} y_{1}^{\prime }=y_{1}-y_{2}+2 y_{3} \\ y_{2}^{\prime }=12 y_{1}-4 y_{2}+10 y_{3} \\ y_{3}^{\prime }=-6 y_{1}+y_{2}-7 y_{3} \end {array}\right ] \]

system_of_ODEs

0.497

2250

\[ {}\left [\begin {array}{c} y_{1}^{\prime }=4 y_{1}-y_{2}-4 y_{3} \\ y_{2}^{\prime }=4 y_{1}-3 y_{2}-2 y_{3} \\ y_{3}^{\prime }=y_{1}-y_{2}-y_{3} \end {array}\right ] \]

system_of_ODEs

0.521

2251

\[ {}\left [\begin {array}{c} y_{1}^{\prime }=-2 y_{1}+2 y_{2}-6 y_{3} \\ y_{2}^{\prime }=2 y_{1}+6 y_{2}+2 y_{3} \\ y_{3}^{\prime }=-2 y_{1}-2 y_{2}+2 y_{3} \end {array}\right ] \]

system_of_ODEs

0.495

2252

\[ {}\left [\begin {array}{c} y_{1}^{\prime }=3 y_{1}+2 y_{2}-2 y_{3} \\ y_{2}^{\prime }=-2 y_{1}+7 y_{2}-2 y_{3} \\ y_{3}^{\prime }=-10 y_{1}+10 y_{2}-5 y_{3} \end {array}\right ] \]

system_of_ODEs

0.424

2253

\[ {}\left [\begin {array}{c} y_{1}^{\prime }=3 y_{1}+y_{2}-y_{3} \\ y_{2}^{\prime }=3 y_{1}+5 y_{2}+y_{3} \\ y_{3}^{\prime }=-6 y_{1}+2 y_{2}+4 y_{3} \end {array}\right ] \]

system_of_ODEs

0.413

2254

\[ {}\left [\begin {array}{c} y_{1}^{\prime }=3 y_{1}+4 y_{2} \\ y_{2}^{\prime }=-y_{1}+7 y_{2} \end {array}\right ] \]

system_of_ODEs

0.440

2255

\[ {}\left [\begin {array}{c} y_{1}^{\prime }=-y_{2} \\ y_{2}^{\prime }=y_{1}-2 y_{2} \end {array}\right ] \]

system_of_ODEs

0.433

2256

\[ {}\left [\begin {array}{c} y_{1}^{\prime }=-7 y_{1}+4 y_{2} \\ y_{2}^{\prime }=-y_{1}-11 y_{2} \end {array}\right ] \]

system_of_ODEs

0.458

2257

\[ {}\left [\begin {array}{c} y_{1}^{\prime }=3 y_{1}+y_{2} \\ y_{2}^{\prime }=-y_{1}+y_{2} \end {array}\right ] \]

system_of_ODEs

0.448

2258

\[ {}\left [\begin {array}{c} y_{1}^{\prime }=4 y_{1}+12 y_{2} \\ y_{2}^{\prime }=-3 y_{1}-8 y_{2} \end {array}\right ] \]

system_of_ODEs

0.449

2259

\[ {}\left [\begin {array}{c} y_{1}^{\prime }=-10 y_{1}+9 y_{2} \\ y_{2}^{\prime }=-4 y_{1}+2 y_{2} \end {array}\right ] \]

system_of_ODEs

0.453

2260

\[ {}\left [\begin {array}{c} y_{1}^{\prime }=-13 y_{1}+16 y_{2} \\ y_{2}^{\prime }=-9 y_{1}+11 y_{2} \end {array}\right ] \]

system_of_ODEs

0.457

2261

\[ {}\left [\begin {array}{c} y_{1}^{\prime }=2 y_{2}+y_{3} \\ y_{2}^{\prime }=-4 y_{1}+6 y_{2}+y_{3} \\ y_{3}^{\prime }=4 y_{2}+2 y_{3} \end {array}\right ] \]

system_of_ODEs

0.425

2262

\[ {}\left [\begin {array}{c} y_{1}^{\prime }=\frac {y_{1}}{3}+\frac {y_{2}}{3}-y_{3} \\ y_{2}^{\prime }=-\frac {4 y_{1}}{3}-\frac {4 y_{2}}{3}+y_{3} \\ y_{3}^{\prime }=-\frac {2 y_{1}}{3}+\frac {y_{2}}{3} \end {array}\right ] \]

system_of_ODEs

0.461

2263

\[ {}\left [\begin {array}{c} y_{1}^{\prime }=-y_{1}+y_{2}-y_{3} \\ y_{2}^{\prime }=-2 y_{1}+2 y_{3} \\ y_{3}^{\prime }=-y_{1}+3 y_{2}-y_{3} \end {array}\right ] \]

system_of_ODEs

0.449

2264

\[ {}\left [\begin {array}{c} y_{1}^{\prime }=4 y_{1}-2 y_{2}-2 y_{3} \\ y_{2}^{\prime }=-2 y_{1}+3 y_{2}-y_{3} \\ y_{3}^{\prime }=2 y_{1}-y_{2}+3 y_{3} \end {array}\right ] \]

system_of_ODEs

0.451

2265

\[ {}\left [\begin {array}{c} y_{1}^{\prime }=6 y_{1}-5 y_{2}+3 y_{3} \\ y_{2}^{\prime }=2 y_{1}-y_{2}+3 y_{3} \\ y_{3}^{\prime }=2 y_{1}+y_{2}+y_{3} \end {array}\right ] \]

system_of_ODEs

0.463

2266

\[ {}\left [\begin {array}{c} y_{1}^{\prime }=-11 y_{1}+8 y_{2} \\ y_{2}^{\prime }=-2 y_{1}-3 y_{2} \end {array}\right ] \]
i.c.

system_of_ODEs

0.585

2267

\[ {}\left [\begin {array}{c} y_{1}^{\prime }=15 y_{1}-9 y_{2} \\ y_{2}^{\prime }=16 y_{1}-9 y_{2} \end {array}\right ] \]
i.c.

system_of_ODEs

0.639

2268

\[ {}\left [\begin {array}{c} y_{1}^{\prime }=-3 y_{1}-4 y_{2} \\ y_{2}^{\prime }=y_{1}-7 y_{2} \end {array}\right ] \]
i.c.

system_of_ODEs

0.561

2269

\[ {}\left [\begin {array}{c} y_{1}^{\prime }=-7 y_{1}+24 y_{2} \\ y_{2}^{\prime }=-6 y_{1}+17 y_{2} \end {array}\right ] \]
i.c.

system_of_ODEs

0.582

2270

\[ {}\left [\begin {array}{c} y_{1}^{\prime }=-7 y_{1}+3 y_{2} \\ y_{2}^{\prime }=-3 y_{1}-y_{2} \end {array}\right ] \]
i.c.

system_of_ODEs

0.550

2271

\[ {}\left [\begin {array}{c} y_{1}^{\prime }=-y_{1}+y_{2} \\ y_{2}^{\prime }=y_{1}-y_{2}-2 y_{3} \\ y_{3}^{\prime }=-y_{1}-y_{2}-y_{3} \end {array}\right ] \]
i.c.

system_of_ODEs

0.505

2272

\[ {}\left [\begin {array}{c} y_{1}^{\prime }=-2 y_{1}+2 y_{2}+y_{3} \\ y_{2}^{\prime }=-2 y_{1}+2 y_{2}+y_{3} \\ y_{3}^{\prime }=-3 y_{1}+3 y_{2}+2 y_{3} \end {array}\right ] \]
i.c.

system_of_ODEs

0.412

2273

\[ {}\left [\begin {array}{c} y_{1}^{\prime }=-7 y_{1}-4 y_{2}+4 y_{3} \\ y_{2}^{\prime }=y_{1}+y_{3} \\ y_{3}^{\prime }=-9 y_{1}-5 y_{2}+6 y_{3} \end {array}\right ] \]
i.c.

system_of_ODEs

0.829

2274

\[ {}\left [\begin {array}{c} y_{1}^{\prime }=-y_{1}-4 y_{2}-y_{3} \\ y_{2}^{\prime }=3 y_{1}+6 y_{2}+y_{3} \\ y_{3}^{\prime }=-3 y_{1}-2 y_{2}+3 y_{3} \end {array}\right ] \]
i.c.

system_of_ODEs

0.485

2275

\[ {}\left [\begin {array}{c} y_{1}^{\prime }=4 y_{1}-8 y_{2}-4 y_{3} \\ y_{2}^{\prime }=-3 y_{1}-y_{2}-4 y_{3} \\ y_{3}^{\prime }=y_{1}-y_{2}+9 y_{3} \end {array}\right ] \]
i.c.

system_of_ODEs

0.645

2276

\[ {}\left [\begin {array}{c} y_{1}^{\prime }=-5 y_{1}-y_{2}+11 y_{3} \\ y_{2}^{\prime }=-7 y_{1}+y_{2}+13 y_{3} \\ y_{3}^{\prime }=-4 y_{1}+8 y_{3} \end {array}\right ] \]
i.c.

system_of_ODEs

0.425

2277

\[ {}\left [\begin {array}{c} y_{1}^{\prime }=5 y_{1}-y_{2}+y_{3} \\ y_{2}^{\prime }=-y_{1}+9 y_{2}-3 y_{3} \\ y_{3}^{\prime }=-2 y_{1}+2 y_{2}+4 y_{3} \end {array}\right ] \]

system_of_ODEs

0.429

2278

\[ {}\left [\begin {array}{c} y_{1}^{\prime }=y_{1}+10 y_{2}-12 y_{3} \\ y_{2}^{\prime }=2 y_{1}+2 y_{2}+3 y_{3} \\ y_{3}^{\prime }=2 y_{1}-y_{2}+6 y_{3} \end {array}\right ] \]

system_of_ODEs

0.434

2279

\[ {}\left [\begin {array}{c} y_{1}^{\prime }=-6 y_{1}-4 y_{2}-4 y_{3} \\ y_{2}^{\prime }=2 y_{1}-y_{2}+y_{3} \\ y_{3}^{\prime }=2 y_{1}+3 y_{2}+y_{3} \end {array}\right ] \]

system_of_ODEs

0.427

2280

\[ {}\left [\begin {array}{c} y_{1}^{\prime }=2 y_{2}-2 y_{3} \\ y_{2}^{\prime }=-y_{1}+5 y_{2}-3 y_{3} \\ y_{3}^{\prime }=y_{1}+y_{2}+y_{3} \end {array}\right ] \]

system_of_ODEs

0.427

2281

\[ {}\left [\begin {array}{c} y_{1}^{\prime }=-2 y_{1}-12 y_{2}+10 y_{3} \\ y_{2}^{\prime }=2 y_{1}-24 y_{2}+11 y_{3} \\ y_{3}^{\prime }=2 y_{1}-24 y_{2}+8 y_{3} \end {array}\right ] \]

system_of_ODEs

0.533

2282

\[ {}\left [\begin {array}{c} y_{1}^{\prime }=-y_{1}-12 y_{2}+8 y_{3} \\ y_{2}^{\prime }=y_{1}-9 y_{2}+4 y_{3} \\ y_{3}^{\prime }=y_{1}-6 y_{2}+y_{3} \end {array}\right ] \]

system_of_ODEs

0.436

2283

\[ {}\left [\begin {array}{c} y_{1}^{\prime }=-4 y_{1}-y_{3} \\ y_{2}^{\prime }=-y_{1}-3 y_{2}-y_{3} \\ y_{3}^{\prime }=y_{1}-2 y_{3} \end {array}\right ] \]

system_of_ODEs

0.374

2284

\[ {}\left [\begin {array}{c} y_{1}^{\prime }=-3 y_{1}-3 y_{2}+4 y_{3} \\ y_{2}^{\prime }=4 y_{1}+5 y_{2}-8 y_{3} \\ y_{3}^{\prime }=2 y_{1}+3 y_{2}-5 y_{3} \end {array}\right ] \]

system_of_ODEs

0.429

2285

\[ {}\left [\begin {array}{c} y_{1}^{\prime }=-3 y_{1}-y_{2} \\ y_{2}^{\prime }=y_{1}-y_{2} \\ y_{3}^{\prime }=-y_{1}-y_{2}-2 y_{3} \end {array}\right ] \]

system_of_ODEs

0.375

2286

\[ {}\left [\begin {array}{c} y_{1}^{\prime }=-y_{1}+2 y_{2} \\ y_{2}^{\prime }=-5 y_{1}+5 y_{2} \end {array}\right ] \]

system_of_ODEs

0.549

2287

\[ {}\left [\begin {array}{c} y_{1}^{\prime }=-11 y_{1}+4 y_{2} \\ y_{2}^{\prime }=-26 y_{1}+9 y_{2} \end {array}\right ] \]

system_of_ODEs

0.566

2288

\[ {}\left [\begin {array}{c} y_{1}^{\prime }=y_{1}+2 y_{2} \\ y_{2}^{\prime }=-4 y_{1}+5 y_{2} \end {array}\right ] \]

system_of_ODEs

0.617

2289

\[ {}\left [\begin {array}{c} y_{1}^{\prime }=5 y_{1}-6 y_{2} \\ y_{2}^{\prime }=3 y_{1}-y_{2} \end {array}\right ] \]

system_of_ODEs

0.547

2290

\[ {}\left [\begin {array}{c} y_{1}^{\prime }=-3 y_{1}-3 y_{2}+y_{3} \\ y_{2}^{\prime }=2 y_{2}+2 y_{3} \\ y_{3}^{\prime }=5 y_{1}+y_{2}+y_{3} \end {array}\right ] \]

system_of_ODEs

9.546

2291

\[ {}\left [\begin {array}{c} y_{1}^{\prime }=-3 y_{1}+3 y_{2}+y_{3} \\ y_{2}^{\prime }=y_{1}-5 y_{2}-3 y_{3} \\ y_{3}^{\prime }=-3 y_{1}+7 y_{2}+3 y_{3} \end {array}\right ] \]

system_of_ODEs

0.759

2292

\[ {}\left [\begin {array}{c} y_{1}^{\prime }=2 y_{1}+y_{2}-y_{3} \\ y_{2}^{\prime }=y_{2}+y_{3} \\ y_{3}^{\prime }=y_{1}+y_{3} \end {array}\right ] \]

system_of_ODEs

0.604

2293

\[ {}\left [\begin {array}{c} y_{1}^{\prime }=-3 y_{1}+y_{2}-3 y_{3} \\ y_{2}^{\prime }=4 y_{1}-y_{2}+2 y_{3} \\ y_{3}^{\prime }=4 y_{1}-2 y_{2}+3 y_{3} \end {array}\right ] \]

system_of_ODEs

0.747

2294

\[ {}y^{\prime }+\sin \left (t \right ) y = 0 \]
i.c.

[_separable]

0.464

2295

\[ {}y^{\prime }+{\mathrm e}^{t^{2}} y = 0 \]
i.c.

[_separable]

0.408

2296

\[ {}y^{\prime }-2 t y = t \]

[_separable]

0.251

2297

\[ {}2 t y+y^{\prime } = t \]
i.c.

[_separable]

0.460

2298

\[ {}y^{\prime }+y = \frac {1}{t^{2}+1} \]
i.c.

[_linear]

0.572

2299

\[ {}\cos \left (t \right ) y+y^{\prime } = 0 \]

[_separable]

2.009

2300

\[ {}\sqrt {t}\, \sin \left (t \right ) y+y^{\prime } = 0 \]

[_separable]

2.035