2.3.235 Problems 23401 to 23500

Table 2.1043: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

23401

3431

\begin{align*} y^{\prime }&=-\frac {t}{y} \\ \end{align*}

8.188

23402

13041

\begin{align*} y^{\prime \prime \prime }-a^{2} \left ({y^{\prime }}^{5}+2 {y^{\prime }}^{3}+y^{\prime }\right )&=0 \\ \end{align*}

8.188

23403

7015

\begin{align*} x^{3} y^{\prime }-y^{2}-x^{2} y&=0 \\ \end{align*}

8.191

23404

15841

\begin{align*} y^{\prime }&=\sin \left (y\right ) \\ y \left (0\right ) &= 1 \\ \end{align*}

8.194

23405

20953

\begin{align*} y^{\prime }&=y-y^{2} \\ y \left (0\right ) &= y_{0} \\ \end{align*}

8.198

23406

26858

\begin{align*} y^{\prime } x&=x -y \\ \end{align*}

8.198

23407

19132

\begin{align*} y^{\prime }&=-x +\sqrt {x^{2}+2 y} \\ \end{align*}

8.200

23408

22389

\begin{align*} y^{\prime }&=\frac {y}{x}+\sec \left (\frac {y}{x}\right )^{2} \\ \end{align*}

8.204

23409

19815

\begin{align*} 3 x^{2} y^{\prime }+2 x^{2}-3 y^{2}&=0 \\ \end{align*}

8.210

23410

2331

\begin{align*} \left (t -\sqrt {t y}\right ) y^{\prime }&=y \\ \end{align*}

8.221

23411

16143

\begin{align*} y^{\prime \prime }+2 y^{\prime }+3 y&=\delta \left (t -1\right )-3 \delta \left (t -4\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

Using Laplace transform method.

8.222

23412

12967

\begin{align*} 4 y y^{\prime \prime }-3 {y^{\prime }}^{2}-12 y^{3}&=0 \\ \end{align*}

8.231

23413

27340

\begin{align*} y^{\prime }&=3 y^{{2}/{3}}+1 \\ \end{align*}

8.235

23414

12117

\begin{align*} y^{\prime }&=-\frac {1}{-\left (y^{3}\right )^{{2}/{3}} x -\textit {\_F1} \left (y^{3}-3 \ln \left (x \right )\right ) \left (y^{3}\right )^{{1}/{3}} x} \\ \end{align*}

8.236

23415

15877

\begin{align*} w^{\prime }&=\left (1-w\right ) \sin \left (w\right ) \\ \end{align*}

8.240

23416

23853

\begin{align*} y^{3}+y^{\prime } \sqrt {-x^{2}+1}&=0 \\ \end{align*}

8.241

23417

8743

\begin{align*} \frac {2 y y^{\prime } x}{3}&=\sqrt {x^{6}-y^{4}}+y^{2} \\ \end{align*}

8.243

23418

12701

\begin{align*} y^{\prime \prime }&=-\frac {\left (-a \cos \left (x \right )^{2} \sin \left (x \right )^{2}-m \left (m -1\right ) \sin \left (x \right )^{2}-n \left (n -1\right ) \cos \left (x \right )^{2}\right ) y}{\cos \left (x \right )^{2} \sin \left (x \right )^{2}} \\ \end{align*}

8.244

23419

25210

\begin{align*} t^{2} y^{\prime \prime }+3 y^{\prime } t -4 y&=t^{4} \\ y \left (-1\right ) &= y_{1} \\ y^{\prime }\left (-1\right ) &= y_{1} \\ \end{align*}

8.250

23420

5839

\begin{align*} a \left (1+k \right ) x^{-1+k} y+a \,x^{k} y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}

8.251

23421

6045

\begin{align*} \left (\operatorname {a1} +\operatorname {b1} \,x^{k}+\operatorname {c1} \,x^{2 k}\right ) y+x \left (\operatorname {a0} +\operatorname {b0} \,x^{k}\right ) y^{\prime }+x^{2} y^{\prime \prime }&=0 \\ \end{align*}

8.253

23422

27219

\begin{align*} 2 x^{2} y y^{\prime }+y^{2}&=2 \\ \end{align*}

8.253

23423

4905

\begin{align*} \left (x^{2}+1\right ) y^{\prime }&=x \left (x^{2}+1\right )-y x \\ \end{align*}

8.255

23424

5621

\begin{align*} {y^{\prime }}^{3}-a x y^{\prime }+x^{3}&=0 \\ \end{align*}

8.256

23425

24128

\begin{align*} 1&=b \left (\cos \left (y\right )+x \sin \left (y\right ) y^{\prime }\right ) \\ \end{align*}

8.256

23426

738

\begin{align*} y y^{\prime } x&=x^{2}+3 y^{2} \\ \end{align*}

8.257

23427

12201

\begin{align*} y^{\prime }&=-\left (-\frac {\ln \left (y\right )}{x}+\frac {\ln \left (y\right )}{x \ln \left (x \right )}-\textit {\_F1} \left (x \right )\right ) y \\ \end{align*}

8.257

23428

20776

\begin{align*} y y^{\prime \prime }-{y^{\prime }}^{2}&=\ln \left (y\right ) y^{2} \\ \end{align*}

8.257

23429

9116

\begin{align*} y^{\prime } x +y&=x^{4} y^{3} \\ \end{align*}

8.263

23430

22426

\begin{align*} y+\left (4 x -y^{2}\right ) y^{\prime }&=0 \\ \end{align*}

8.270

23431

11518

\begin{align*} \left (x +2 y+1\right ) y^{\prime }+1-x -2 y&=0 \\ \end{align*}

8.271

23432

12225

\begin{align*} y^{\prime }&=\frac {-32 y x -8 x^{3}-16 a \,x^{2}-32 x +64 y^{3}+48 y^{2} x^{2}+96 a x y^{2}+12 x^{4} y+48 y a \,x^{3}+48 y a^{2} x^{2}+x^{6}+6 x^{5} a +12 a^{2} x^{4}+8 a^{3} x^{3}}{64 y+16 x^{2}+32 a x +64} \\ \end{align*}

8.273

23433

21403

\begin{align*} \left (2+3 x -y x \right ) y^{\prime }+y&=0 \\ \end{align*}

8.273

23434

12397

\begin{align*} 2 y^{\prime \prime } x -\left (x -1\right ) y^{\prime }+a y&=0 \\ \end{align*}

8.280

23435

6123

\begin{align*} 2 y-4 \left (1-x \right ) y^{\prime }+\left (1-x \right )^{2} y^{\prime \prime }&=\cos \left (x \right ) \\ \end{align*}

8.283

23436

9336

\begin{align*} x^{2} y^{\prime \prime }+3 y^{\prime } x +y&=\frac {2}{x} \\ \end{align*}

8.290

23437

5131

\begin{align*} y y^{\prime } x&=a \,x^{n}+b y^{2} \\ \end{align*}

8.294

23438

8403

\begin{align*} y^{\prime }&=x \sqrt {y} \\ \end{align*}

8.294

23439

15137

\begin{align*} 2 y^{\prime \prime }+3 y^{\prime }+4 x^{2} y&=1 \\ \end{align*}

8.295

23440

734

\begin{align*} \left (x +2 y\right ) y^{\prime }&=y \\ \end{align*}

8.303

23441

8787

\begin{align*} y^{\prime }&=-\frac {2}{t}+\frac {y}{t}+\frac {y^{2}}{t} \\ \end{align*}

8.305

23442

20216

\begin{align*} y^{\prime } x +x +y&=0 \\ \end{align*}

8.310

23443

5763

\begin{align*} \left (a +b \cosh \left (x \right )^{2}\right ) y+y^{\prime \prime }&=0 \\ \end{align*}

8.311

23444

26174

\begin{align*} y^{\prime }&=x^{2}+y^{2} \\ \end{align*}

8.311

23445

12202

\begin{align*} y^{\prime }&=\frac {y^{2}}{y^{2}+y^{{3}/{2}}+\sqrt {y}\, x^{2}-2 y^{{3}/{2}} x +y^{{5}/{2}}+x^{3}-3 x^{2} y+3 x y^{2}-y^{3}} \\ \end{align*}

8.319

23446

12824

\begin{align*} y^{\left (6\right )}+y-\sin \left (\frac {3 x}{2}\right ) \sin \left (\frac {x}{2}\right )&=0 \\ \end{align*}

8.319

23447

7014

\begin{align*} y^{\prime } x -y \left (\ln \left (y x \right )-1\right )&=0 \\ \end{align*}

8.323

23448

17097

\begin{align*} y^{\prime }&=t^{2} y^{2}+y^{2}-t^{2}-1 \\ \end{align*}

8.323

23449

5276

\begin{align*} \left (1-y^{2} x^{2}\right ) y^{\prime }&=x y^{3} \\ \end{align*}

8.329

23450

9007

\begin{align*} y y^{\prime }&=x \\ \end{align*}

8.332

23451

3456

\begin{align*} y^{\prime }-x y^{3}&=0 \\ \end{align*}

8.338

23452

12191

\begin{align*} y^{\prime }&=-\left (-\frac {\ln \left (y\right )}{x}+\frac {\cos \left (x \right ) \ln \left (y\right )}{\sin \left (x \right )}-\textit {\_F1} \left (x \right )\right ) y \\ \end{align*}

8.338

23453

5917

\begin{align*} b y+\left (a +x \right ) y^{\prime }+y^{\prime \prime } x&=0 \\ \end{align*}

8.343

23454

19799

\begin{align*} y^{\prime }+\cos \left (x \right ) y&=y^{n} \sin \left (2 x \right ) \\ \end{align*}

8.343

23455

6845

\begin{align*} z^{\prime }+z \cos \left (x \right )&=z^{n} \sin \left (2 x \right ) \\ \end{align*}

8.345

23456

6567

\begin{align*} \operatorname {f3} \left (y\right )+\operatorname {f2} \left (y\right ) y^{\prime }+\operatorname {f1} \left (y\right ) {y^{\prime }}^{2}+\operatorname {f0} \left (y\right ) y^{\prime \prime }&=0 \\ \end{align*}

8.347

23457

12205

\begin{align*} y^{\prime }&=\frac {y^{2}+2 y x +x^{2}+{\mathrm e}^{2 \left (x -y\right )^{2} \left (x +y\right )^{2}}}{y^{2}+2 y x +x^{2}-{\mathrm e}^{2 \left (x -y\right )^{2} \left (x +y\right )^{2}}} \\ \end{align*}

8.350

23458

9997

\begin{align*} y^{\prime }&=x +\frac {\sec \left (x \right ) y}{x} \\ \end{align*}

8.352

23459

27223

\begin{align*} x x^{\prime }+t&=1 \\ \end{align*}

8.352

23460

13902

\begin{align*} x^{n} y^{\prime \prime }+a x y^{\prime }-\left (b^{2} x^{n}+2 b \,x^{n -1}+a b x +a \right ) y&=0 \\ \end{align*}

8.356

23461

13301

\begin{align*} y^{\prime }&=y^{2}+a x \,{\mathrm e}^{\lambda x} y+a \,{\mathrm e}^{\lambda x} \\ \end{align*}

8.358

23462

3056

\begin{align*} 2 \left (x^{2}+1\right ) y^{\prime }&=\left (2 y^{2}-1\right ) x y \\ y \left (0\right ) &= 1 \\ \end{align*}

8.359

23463

10114

\begin{align*} y^{\prime \prime }-x^{2} y-x^{3}&=0 \\ \end{align*}

8.362

23464

12260

\begin{align*} y^{\prime }&=\frac {x^{3} y^{3}+6 y^{2} x^{2}+12 y x +8+2 x}{x^{3}} \\ \end{align*}

8.364

23465

27554

\begin{align*} y y^{\prime \prime }+y&={y^{\prime }}^{2} \\ \end{align*}

8.371

23466

16316

\begin{align*} 2 x y^{3}+4 x^{3}+3 x^{2} y^{2} y^{\prime }&=0 \\ \end{align*}

8.376

23467

19321

\begin{align*} x +3 y^{2}+2 y y^{\prime } x&=0 \\ \end{align*}

8.377

23468

5318

\begin{align*} \left (x^{2}-y^{4}\right ) y^{\prime }&=y x \\ \end{align*}

8.378

23469

11522

\begin{align*} \left (3+2 x +4 y\right ) y^{\prime }-2 y-x -1&=0 \\ \end{align*}

8.380

23470

4726

\begin{align*} y^{\prime }&=\tan \left (x \right ) \left (\tan \left (y\right )+\sec \left (x \right ) \sec \left (y\right )\right ) \\ \end{align*}

8.386

23471

25879

\begin{align*} 3 x +2 y+1-\left (3 x +2 y-1\right ) y^{\prime }&=0 \\ \end{align*}

8.387

23472

26404

\begin{align*} \left (x -1\right ) \left (y^{2}-y+1\right )&=\left (1+y\right ) \left (x^{2}+x +1\right ) y^{\prime } \\ \end{align*}

8.388

23473

5678

\begin{align*} {y^{\prime }}^{6}+f \left (x \right ) \left (y-a \right )^{4} \left (y-b \right )^{3}&=0 \\ \end{align*}

8.390

23474

5188

\begin{align*} \left (x^{2}+1\right ) y y^{\prime }+x \left (1-y^{2}\right )&=0 \\ \end{align*}

8.392

23475

11962

\begin{align*} y^{\prime }&=\frac {y+x^{3} \ln \left (x \right )+x^{4}+x^{3}+7 x y^{2} \ln \left (x \right )+7 y^{2} x^{2}+7 x y^{2}}{x} \\ \end{align*}

8.395

23476

5918

\begin{align*} -a y+\left (c -x \right ) y^{\prime }+y^{\prime \prime } x&=0 \\ \end{align*}

8.398

23477

4404

\begin{align*} -y+y^{\prime } x&=x \tan \left (\frac {y}{x}\right ) \\ \end{align*}

8.408

23478

7220

\begin{align*} y y^{\prime } x +1+y^{2}&=0 \\ y \left (5\right ) &= 0 \\ \end{align*}

8.409

23479

11445

\begin{align*} x^{2} y^{\prime }+x y^{3}+a y^{2}&=0 \\ \end{align*}

8.413

23480

17209

\begin{align*} \frac {3 t^{2}}{y}-\frac {t^{3} y^{\prime }}{y^{2}}&=0 \\ \end{align*}

8.419

23481

4831

\begin{align*} y^{\prime } x&=y-2 x \tanh \left (\frac {y}{x}\right ) \\ \end{align*}

8.420

23482

22540

\begin{align*} 3 x y^{2}+2+2 x^{2} y y^{\prime }&=0 \\ \end{align*}

8.421

23483

27462

\begin{align*} 1-x^{2} y+x^{2} \left (-x +y\right ) y^{\prime }&=0 \\ \end{align*}

8.422

23484

25787

\begin{align*} y y^{\prime }&=-x \\ y \left (1\right ) &= 1 \\ \end{align*}

8.423

23485

11960

\begin{align*} y^{\prime }&=\frac {y+x^{3} a \ln \left (x +1\right )+a \,x^{4}+a \,x^{3}-x y^{2} \ln \left (x +1\right )-y^{2} x^{2}-x y^{2}}{x} \\ \end{align*}

8.427

23486

6806

\begin{align*} {y^{\prime }}^{3} y^{\prime \prime \prime }&=1 \\ \end{align*}

8.434

23487

1582

\begin{align*} x^{2} y y^{\prime }&=\left (-1+y^{2}\right )^{{3}/{2}} \\ \end{align*}

8.437

23488

7467

\begin{align*} {\mathrm e}^{t} y+t \,{\mathrm e}^{t} y+\left ({\mathrm e}^{t} t +2\right ) y^{\prime }&=0 \\ y \left (0\right ) &= -1 \\ \end{align*}

8.437

23489

2332

\begin{align*} y^{\prime }&=\frac {y+t}{t -y} \\ \end{align*}

8.440

23490

26288

\begin{align*} x \ln \left (x \right ) y^{\prime }-\left (1+\ln \left (x \right )\right ) y+\frac {\sqrt {x}\, \left (2+\ln \left (x \right )\right )}{2}&=0 \\ \end{align*}

8.448

23491

20969

\begin{align*} y^{\prime }&=\frac {{\mathrm e}^{-y^{2}}}{y \left (x^{2}+2 x \right )} \\ y \left (2\right ) &= 0 \\ \end{align*}

8.453

23492

1351

\begin{align*} t^{2} y^{\prime \prime }-2 y^{\prime } t +2 y&=4 t^{2} \\ \end{align*}

8.457

23493

3288

\begin{align*} \left (1-y^{2}\right ) {y^{\prime }}^{2}&=1 \\ \end{align*}

8.471

23494

11985

\begin{align*} y^{\prime }&=\frac {-{\mathrm e}^{x} y+y x -x^{3} \ln \left (x \right )-x^{3}-x y^{2} \ln \left (x \right )-x y^{2}}{\left (x -{\mathrm e}^{x}\right ) x} \\ \end{align*}

8.471

23495

19802

\begin{align*} y \sqrt {x^{2}-1}+x \sqrt {-1+y^{2}}\, y^{\prime }&=0 \\ \end{align*}

8.472

23496

5608

\begin{align*} {y^{\prime }}^{3}&=a \,x^{n} \\ \end{align*}

8.475

23497

17205

\begin{align*} {\mathrm e}^{t y}+\frac {t \,{\mathrm e}^{t y} y^{\prime }}{y}&=0 \\ \end{align*}

8.477

23498

12228

\begin{align*} y^{\prime }&=-\frac {216 y}{-216 y^{4}-252 y^{3}-396 y^{2}-216 y+36 x^{2}-72 y x +60 y^{5}-36 x y^{3}-72 x y^{2}-24 y^{4} x +4 y^{8}+12 y^{7}+33 y^{6}} \\ \end{align*}

8.485

23499

20310

\begin{align*} y y^{\prime }+b y^{2}&=a \cos \left (x \right ) \\ \end{align*}

8.487

23500

19939

\begin{align*} y^{2}+x y^{2}+\left (x^{2}-x^{2} y\right ) y^{\prime }&=0 \\ \end{align*}

8.490