2.3.194 Problems 19301 to 19400

Table 2.931: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

19301

19921

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

4.413

19302

20238

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

4.414

19303

12699

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

4.417

19304

3635

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

4.420

19305

173

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

4.421

19306

7829

\begin{align*} y^{\prime \prime }+5 y^{\prime }-3 y&=\operatorname {Heaviside}\left (x -4\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

4.421

19307

11854

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

4.424

19308

5384

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

4.425

19309

5509

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

4.425

19310

14702

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

4.425

19311

4755

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

4.428

19312

5993

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

4.428

19313

21812

\begin{align*} 2 x^{2}+5 x y^{2}+\left (5 x^{2} y-2 y^{4}\right ) y^{\prime }&=0 \\ \end{align*}

4.428

19314

25467

\begin{align*} y^{\prime }&=\frac {y}{1+t}+10 \\ \end{align*}

4.428

19315

7439

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

4.429

19316

9092

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

4.430

19317

19291

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

4.431

19318

2490

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

4.432

19319

12021

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

4.432

19320

17973

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

4.434

19321

7001

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

4.435

19322

17528

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

4.435

19323

2637

\begin{align*} t \left (-2+t \right )^{2} y^{\prime \prime }+y^{\prime } t +y&=0 \\ \end{align*}
Series expansion around \(t=0\).

4.437

19324

20974

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

4.437

19325

22007

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

4.437

19326

1154

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

4.438

19327

18560

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

4.438

19328

23369

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

4.439

19329

24995

\begin{align*} y^{\prime }+a y&=t^{n} {\mathrm e}^{-a t} \\ \end{align*}

4.439

19330

5375

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

4.440

19331

5487

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

4.440

19332

19963

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

4.440

19333

8670

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

4.442

19334

1176

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

4.445

19335

20398

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

4.446

19336

4982

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

4.447

19337

13957

\begin{align*} y^{\prime \prime }+\left (a \,{\mathrm e}^{\lambda x}+b \,{\mathrm e}^{\mu x}+c \right ) y^{\prime }+\left (a b \,{\mathrm e}^{\left (\lambda +\mu \right ) x}+{\mathrm e}^{\lambda x} a c +{\mathrm e}^{\mu x} b \mu \right ) y&=0 \\ \end{align*}

4.449

19338

21790

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

4.452

19339

18059

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

4.455

19340

15963

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

4.456

19341

12038

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

4.457

19342

13019

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

4.458

19343

3051

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

4.459

19344

5448

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

4.460

19345

736

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

4.461

19346

19087

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

4.462

19347

19106

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

4.462

19348

19343

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

4.462

19349

12693

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

4.463

19350

20156

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

4.463

19351

8880

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

4.464

19352

22344

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

4.465

19353

11408

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

4.466

19354

26157

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

4.467

19355

3600

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

4.471

19356

25493

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

4.471

19357

6556

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

4.473

19358

7026

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

4.473

19359

7159

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

4.474

19360

12185

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

4.474

19361

20240

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

4.474

19362

7257

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

4.475

19363

25842

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

4.476

19364

26203

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

4.476

19365

2891

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

4.477

19366

10090

\begin{align*} y^{\prime \prime }-a x y^{\prime }-b x y-c \,x^{2}&=0 \\ \end{align*}

4.477

19367

14242

\begin{align*} x^{\prime }&=2 t^{3} x-6 \\ \end{align*}

4.481

19368

7750

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

4.483

19369

25055

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

4.486

19370

12306

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

4.487

19371

22434

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

4.487

19372

10437

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

4.488

19373

5246

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

4.489

19374

23367

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

4.490

19375

5519

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

4.494

19376

25012

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

4.494

19377

4880

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

4.495

19378

13812

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

4.495

19379

10053

\begin{align*} 3 y y^{\prime \prime }+y&=5 \\ \end{align*}

4.496

19380

4614

\begin{align*} y^{\prime }&=a +b \,{\mathrm e}^{k x}+c y \\ \end{align*}

4.497

19381

7258

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

4.497

19382

7429

\begin{align*} y^{\prime }&=x^{2} {\mathrm e}^{-4 x}-4 y \\ \end{align*}

4.497

19383

11980

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

4.497

19384

15917

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

4.498

19385

21338

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

4.499

19386

23120

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

4.501

19387

6483

\begin{align*} 2 y y^{\prime \prime }&=y^{2} \left (1-3 y^{2}\right )+6 {y^{\prime }}^{2} \\ \end{align*}

4.502

19388

12679

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

4.502

19389

2325

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

4.503

19390

3674

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

4.503

19391

4715

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

4.503

19392

14168

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

4.505

19393

22363

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

4.506

19394

5239

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

4.507

19395

11830

\begin{align*} x^{7} y^{2} {y^{\prime }}^{3}-\left (3 x^{6} y^{3}-1\right ) {y^{\prime }}^{2}+3 x^{5} y^{4} y^{\prime }-x^{4} y^{5}&=0 \\ \end{align*}

4.507

19396

25019

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

4.507

19397

12556

\begin{align*} 50 x \left (x -1\right ) y^{\prime \prime }+25 \left (2 x -1\right ) y^{\prime }-2 y&=0 \\ \end{align*}

4.508

19398

5887

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

4.509

19399

12149

\begin{align*} y^{\prime }&=\frac {-x +1-2 y+3 x^{2}-2 x^{2} y+2 x^{4}+x^{3}-2 x^{3} y+2 x^{5}}{x^{2}-y} \\ \end{align*}

4.510

19400

18590

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

4.512