6.224 Problems 22301 to 22400

Table 6.447: Main lookup table sequentially arranged

#

ODE

Mathematica

Maple

Sympy

22301

\[ {} y^{\prime \prime }-\left (x -2\right ) y^{\prime }+2 y = 0 \]

22302

\[ {} y^{\prime \prime }+x y^{\prime }+\left (2 x -1\right ) y = 0 \]

22303

\[ {} y^{\prime \prime }+x y^{\prime }+\left (2 x -1\right ) y = 0 \]

22304

\[ {} y^{\prime \prime }-2 x y = 0 \]

22305

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

22306

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

22307

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

22308

\[ {} n \left (n +1\right ) y-2 x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime } = 0 \]

22309

\[ {} \left (x^{2}-1\right ) y^{\prime \prime }+x y^{\prime }-y = 0 \]

22310

\[ {} y^{\prime \prime }-x y = 0 \]

22311

\[ {} y^{\prime \prime }-x y = 0 \]

22312

\[ {} y^{\prime \prime }-x^{2} y^{\prime }+\left (x +2\right ) y = 0 \]

22313

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

22314

\[ {} y^{\prime \prime }-\left (x -1\right ) y^{\prime } = x^{2}-2 x \]

22315

\[ {} y^{\prime \prime }-x y^{\prime } = {\mathrm e}^{-x} \]

22316

\[ {} y^{\prime \prime }-2 x y^{\prime }+x^{2} y = 0 \]

22317

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

22318

\[ {} 8 x^{2} y^{\prime \prime }+10 x y^{\prime }+\left (x -1\right ) y = 0 \]

22319

\[ {} 2 x^{2} y^{\prime \prime }+7 x \left (1+x \right ) y^{\prime }-3 y = 0 \]

22320

\[ {} 3 x^{2} y^{\prime \prime }-x y^{\prime }+y = 0 \]

22321

\[ {} x^{2} y^{\prime \prime }+x y^{\prime }+x^{2} y = 0 \]

22322

\[ {} x^{2} y^{\prime \prime }-x y^{\prime }+y = 0 \]

22323

\[ {} x^{2} y^{\prime \prime }+\left (x^{2}-2 x \right ) y^{\prime }+2 y = 0 \]

22324

\[ {} x^{2} y^{\prime \prime }+x y^{\prime }+y \left (x^{2}-1\right ) = 0 \]

22325

\[ {} x^{2} y^{\prime \prime }+\left (x^{2}+2 x \right ) y^{\prime }-2 y = 0 \]

22326

\[ {} x^{2} y^{\prime \prime }+x \,{\mathrm e}^{x} y^{\prime }+\left (x^{3}-1\right ) y = 0 \]

22327

\[ {} -b y a +\left (c -\left (1+a +b \right ) x \right ) y^{\prime }+\left (1-x \right ) x y^{\prime \prime } = 0 \]

22328

\[ {} 2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (1-x \right ) y = 0 \]

22329

\[ {} 2 x^{2} y^{\prime \prime }+\left (x^{2}-x \right ) y^{\prime }+y = 0 \]

22330

\[ {} 3 x^{2} y^{\prime \prime }-2 x y^{\prime }-\left (x^{2}+2\right ) y = 0 \]

22331

\[ {} -y+y^{\prime }+x y^{\prime \prime } = 0 \]

22332

\[ {} x^{2} y^{\prime \prime }+x y^{\prime }+x^{3} y = 0 \]

22333

\[ {} x^{2} y^{\prime \prime }+\left (-x^{2}+x \right ) y^{\prime }-y = 0 \]

22334

\[ {} x y^{\prime \prime }-y^{\prime } \left (1+x \right )-y = 0 \]

22335

\[ {} 4 x^{2} y^{\prime \prime }+\left (2 x^{2}+4 x \right ) y^{\prime }+\left (3 x -1\right ) y = 0 \]

22336

\[ {} x^{2} y^{\prime \prime }+\left (x^{2}-3 x \right ) y^{\prime }+\left (3 x -1\right ) y = 0 \]

22337

\[ {} x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = 0 \]

22338

\[ {} x^{2} y^{\prime \prime }+x y^{\prime }+x^{2} y = 0 \]

22339

\[ {} x^{2} y^{\prime \prime }+x y^{\prime }+y \left (x^{2}-1\right ) = 0 \]

22340

\[ {} x^{2} y^{\prime \prime }+\left (x^{2}-2\right ) y = 0 \]

22341

\[ {} x^{2} y^{\prime \prime }-x y^{\prime }+\left (-n^{2}+x^{2}+1\right ) y = 0 \]

22342

\[ {} x y^{\prime \prime }-3 y^{\prime }+x y = 0 \]

22343

\[ {} y^{\prime }-5 y = 0 \]

22344

\[ {} y^{\prime }-5 y = {\mathrm e}^{5 x} \]

22345

\[ {} y^{\prime }-5 y = 0 \]

22346

\[ {} y^{\prime }+y = \sin \left (x \right ) \]

22347

\[ {} 4 y+y^{\prime \prime } = 0 \]

22348

\[ {} y^{\prime \prime }-3 y^{\prime }+4 y = 0 \]

22349

\[ {} y^{\prime \prime }-y^{\prime }-2 y = 4 t^{2} \]

22350

\[ {} y^{\prime \prime }+4 y^{\prime }+8 y = \sin \left (t \right ) \]

22351

\[ {} y^{\prime \prime }-3 y^{\prime }+2 y = {\mathrm e}^{-t} \]

22352

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

22353

\[ {} y^{\prime \prime }+y = \left \{\begin {array}{cc} 0 & t <1 \\ 2 & 1\le t \end {array}\right . \]

22354

\[ {} y^{\prime \prime \prime }+y^{\prime } = {\mathrm e}^{t} \]

22355

\[ {} y^{\prime }+2 y = 0 \]

22356

\[ {} y^{\prime }+2 y = 2 \]

22357

\[ {} y^{\prime }+2 y = {\mathrm e}^{t} \]

22358

\[ {} y^{\prime }+2 y = 0 \]

22359

\[ {} y^{\prime }+5 y = 0 \]

22360

\[ {} y^{\prime \prime }-y = 0 \]

22361

\[ {} y^{\prime \prime }-y = \sin \left (t \right ) \]

22362

\[ {} y^{\prime \prime }-y = {\mathrm e}^{t} \]

22363

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

22364

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

22365

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

22366

\[ {} y^{\prime \prime }+2 y^{\prime }+5 y = 3 \,{\mathrm e}^{-2 t} \]

22367

\[ {} y^{\prime \prime }+5 y^{\prime }-3 y = \operatorname {Heaviside}\left (t -4\right ) \]

22368

\[ {} y^{\prime \prime }+y = 0 \]

22369

\[ {} y^{\prime \prime \prime }-y = 5 \]

22370

\[ {} y^{\prime \prime \prime \prime }-y = 0 \]

22371

\[ {} [y^{\prime }\left (t \right )+z \left (t \right ) = t, z^{\prime }\left (t \right )+4 y \left (t \right ) = 0] \]

22372

\[ {} [w^{\prime }\left (t \right )+y \left (t \right ) = \sin \left (t \right ), y^{\prime }\left (t \right )-z \left (t \right ) = {\mathrm e}^{t}, w \left (t \right )+y \left (t \right )+z^{\prime }\left (t \right ) = 1] \]

22373

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

22374

\[ {} [z^{\prime \prime }\left (t \right )+y^{\prime }\left (t \right ) = \cos \left (t \right ), y^{\prime \prime }\left (t \right )-z \left (t \right ) = \sin \left (t \right )] \]

22375

\[ {} [w^{\prime \prime }\left (t \right )-y \left (t \right )+2 z \left (t \right ) = 3 \,{\mathrm e}^{-t}, -2 w^{\prime }\left (t \right )+2 y^{\prime }\left (t \right )+z \left (t \right ) = 0, 2 w^{\prime }\left (t \right )-2 y \left (t \right )+z^{\prime }\left (t \right )+2 z^{\prime \prime }\left (t \right ) = 0] \]

22376

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

22377

\[ {} [y^{\prime }\left (t \right )-z \left (t \right ) = 0, y \left (t \right )-z^{\prime }\left (t \right ) = 0] \]

22378

\[ {} [w^{\prime }\left (t \right )-w \left (t \right )-2 y \left (t \right ) = 1, y^{\prime }\left (t \right )-4 w \left (t \right )-3 y \left (t \right ) = -1] \]

22379

\[ {} [w^{\prime }\left (t \right )-y \left (t \right ) = 0, w \left (t \right )+y^{\prime }\left (t \right )+z \left (t \right ) = 1, w \left (t \right )-y \left (t \right )+z^{\prime }\left (t \right ) = 2 \sin \left (t \right )] \]

22380

\[ {} [u^{\prime \prime }\left (t \right )-2 v \left (t \right ) = 2, u \left (t \right )+v^{\prime }\left (t \right ) = 5 \,{\mathrm e}^{2 t}+1] \]

22381

\[ {} [w^{\prime \prime }\left (t \right )-2 z \left (t \right ) = 0, w^{\prime }\left (t \right )+y^{\prime }\left (t \right )-z \left (t \right ) = 2 t, w^{\prime }\left (t \right )-2 y \left (t \right )+z^{\prime \prime }\left (t \right ) = 0] \]

22382

\[ {} [w^{\prime \prime }\left (t \right )+y \left (t \right )+z \left (t \right ) = -1, w \left (t \right )+y^{\prime \prime }\left (t \right )-z \left (t \right ) = 0, -w \left (t \right )-y^{\prime }\left (t \right )+z^{\prime \prime }\left (t \right ) = 0] \]

22383

\[ {} [x^{\prime }\left (t \right ) = y \left (t \right ), y^{\prime }\left (t \right ) = 8 x \left (t \right )-2 y \left (t \right )] \]

22384

\[ {} [x^{\prime }\left (t \right ) = y \left (t \right ), y^{\prime }\left (t \right ) = 8 x \left (t \right )-2 y \left (t \right )+{\mathrm e}^{t}] \]

22385

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

22386

\[ {} [x^{\prime }\left (t \right ) = y \left (t \right ), y^{\prime }\left (t \right ) = -9 x \left (t \right )+6 y \left (t \right )+t] \]

22387

\[ {} [x^{\prime }\left (t \right ) = y \left (t \right ), y^{\prime }\left (t \right ) = -2 y \left (t \right )-5 z \left (t \right )+3, z^{\prime }\left (t \right ) = y \left (t \right )+2 z \left (t \right )] \]

22388

\[ {} [x^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = 9 x \left (t \right )+y \left (t \right )] \]

22389

\[ {} [x_{1}^{\prime }\left (t \right ) = x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 6 x_{1} \left (t \right )] \]

22390

\[ {} [x_{1}^{\prime }\left (t \right ) = x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 6 x_{1} \left (t \right )+4] \]

22391

\[ {} [x_{1}^{\prime }\left (t \right ) = x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 6 x_{1} \left (t \right )+4] \]

22392

\[ {} [x_{1}^{\prime }\left (t \right ) = x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 6 x_{1} \left (t \right )+4] \]

22393

\[ {} [x_{1}^{\prime }\left (t \right ) = x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 6 x_{1} \left (t \right )+9 \,{\mathrm e}^{-t}] \]

22394

\[ {} [x^{\prime }\left (t \right ) = x \left (t \right )+2 y \left (t \right ), y^{\prime }\left (t \right ) = 4 x \left (t \right )+3 y \left (t \right )] \]

22395

\[ {} [x_{1}^{\prime }\left (t \right ) = x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 6 t] \]

22396

\[ {} y^{\prime \prime }+2 y^{\prime }-3 y = 0 \]

22397

\[ {} y^{\prime \prime }+2 y^{\prime }-3 y = 9 x \]

22398

\[ {} y^{\prime \prime }+y = 0 \]

22399

\[ {} y^{\prime \prime }+y = x \]

22400

\[ {} y^{\prime \prime }+y = 0 \]