2.3.245 Problems 24401 to 24500

Table 2.1021: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

24401

14107

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

48.868

24402

17522

\begin{align*} y^{\prime \prime }-16 y&=16 t \,{\mathrm e}^{-4 t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

48.911

24403

17912

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

48.946

24404

6287

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

48.953

24405

13401

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

49.026

24406

13439

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

49.038

24407

14109

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

49.056

24408

12612

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

49.106

24409

17891

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

49.110

24410

4140

\begin{align*} y^{\prime \prime }+2 n y^{\prime }+n^{2} y&=A \cos \left (p x \right ) \\ y \left (0\right ) &= 9 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

49.183

24411

19698

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

49.198

24412

13614

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

49.222

24413

19817

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

49.236

24414

24326

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

49.255

24415

25445

\begin{align*} z^{\prime }+4 z&={\mathrm e}^{8 i t} \\ \end{align*}

49.280

24416

12702

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

49.359

24417

13997

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

49.369

24418

25447

\begin{align*} z^{\prime }+4 i z&={\mathrm e}^{8 t} \\ \end{align*}

49.383

24419

12146

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

49.426

24420

13985

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

49.435

24421

9661

\begin{align*} x^{\prime }&=7 x+5 y-9 z-8 \,{\mathrm e}^{-2 t} \\ y^{\prime }&=4 x+y+z+2 \,{\mathrm e}^{5 t} \\ z^{\prime }&=-2 y+3 z+{\mathrm e}^{5 t}-3 \,{\mathrm e}^{-2 t} \\ \end{align*}

49.460

24422

22341

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

49.518

24423

13417

\begin{align*} y^{\prime }&=y^{2}-\frac {\lambda ^{2}}{2}-\frac {3 \lambda ^{2} \tan \left (\lambda x \right )^{2}}{4}+a \cos \left (\lambda x \right )^{2} \sin \left (\lambda x \right )^{n} \\ \end{align*}

49.560

24424

7581

\begin{align*} y^{\prime \prime }+25 y&=\cos \left (\omega t \right ) \\ \end{align*}

49.654

24425

21579

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

49.659

24426

6111

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

49.671

24427

13382

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

49.682

24428

14646

\begin{align*} 16 y+8 y^{\prime }+y^{\prime \prime }&=8 \,{\mathrm e}^{-2 x} \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

49.718

24429

25763

\begin{align*} y^{\prime \prime }+2 y^{\prime }-3 y&=-12 x +8 \\ y \left (1\right ) &= -2 \\ y^{\prime }\left (1\right ) &= 4 \\ \end{align*}

49.718

24430

12616

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

49.726

24431

12652

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

49.761

24432

4390

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

49.765

24433

17766

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

49.801

24434

6142

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

49.943

24435

24270

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

49.956

24436

20510

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

49.981

24437

3186

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

50.004

24438

6083

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

50.031

24439

19860

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

50.074

24440

17435

\begin{align*} y^{\prime \prime }-4 y^{\prime }+13 y&=2 t \,{\mathrm e}^{-2 t} \sin \left (3 t \right ) \\ \end{align*}

50.189

24441

23875

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

50.206

24442

10119

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

50.333

24443

6106

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

50.379

24444

16098

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

50.402

24445

3649

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

50.497

24446

24359

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

50.562

24447

18309

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

50.815

24448

13533

\begin{align*} y y^{\prime }-y&=-\frac {6}{25} x -A \,x^{2} \\ \end{align*}

50.898

24449

17348

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

50.898

24450

12601

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

51.011

24451

2433

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

51.023

24452

17479

\begin{align*} x^{\prime \prime }+9 x&=\sin \left (3 t \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}

51.046

24453

22702

\begin{align*} 4 y+y^{\prime \prime }&=8 \cos \left (2 x \right )-4 x \\ \end{align*}

51.076

24454

16210

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

51.122

24455

13534

\begin{align*} y y^{\prime }-y&=\frac {6}{25} x -A \,x^{2} \\ \end{align*}

51.166

24456

24716

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

51.178

24457

3031

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

51.198

24458

11605

\begin{align*} \left (3 x^{3}+6 x^{2} y-3 x y^{2}+20 y^{3}\right ) y^{\prime }+4 x^{3}+9 x^{2} y+6 x y^{2}-y^{3}&=0 \\ \end{align*}

51.326

24459

18352

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

51.343

24460

2770

\begin{align*} x_{1}^{\prime }&=x_{1}+x_{2}-x_{3}+{\mathrm e}^{2 t} \\ x_{2}^{\prime }&=2 x_{1}+3 x_{2}-4 x_{3}+2 \,{\mathrm e}^{2 t} \\ x_{3}^{\prime }&=4 x_{1}+x_{2}-4 x_{3}+{\mathrm e}^{2 t} \\ \end{align*}

51.382

24461

12520

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

51.385

24462

15182

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

51.418

24463

5772

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

51.426

24464

18218

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

51.467

24465

7550

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

51.475

24466

3282

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

51.638

24467

12532

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

51.674

24468

20744

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

51.691

24469

13375

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

51.717

24470

12623

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

51.746

24471

8715

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

51.905

24472

14834

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

51.918

24473

17768

\begin{align*} y^{\prime \prime }+9 y&=\sin \left (3 t \right ) \\ y \left (0\right ) &= 6 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

51.922

24474

11787

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

51.924

24475

10432

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

51.960

24476

20066

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

52.001

24477

23188

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

52.081

24478

5802

\begin{align*} 16 y+8 y^{\prime }+y^{\prime \prime }&=4 \,{\mathrm e}^{x}-{\mathrm e}^{2 x} \\ \end{align*}

52.093

24479

8041

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

52.114

24480

7278

\begin{align*} y^{\prime \prime }-2 y^{\prime }-3 y&=24 \,{\mathrm e}^{-3 x} \\ \end{align*}

52.200

24481

24365

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

52.263

24482

5532

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

52.367

24483

6050

\begin{align*} y \left (\operatorname {a2} +\operatorname {b2} \,x^{k}+\operatorname {c2} \,x^{2 k}+\left (-1+\operatorname {a1} +\operatorname {b1} \,x^{k}\right ) f \left (x \right )+f \left (x \right )^{2}+f^{\prime }\left (x \right )\right )+x \left (\operatorname {a1} +\operatorname {b1} \,x^{k}+2 f \left (x \right )\right ) y^{\prime }+x^{2} y^{\prime \prime }&=0 \\ \end{align*}

52.428

24484

16265

\begin{align*} y^{\prime } x +\cos \left (x^{2}\right )&=827 y \\ \end{align*}

52.480

24485

17462

\begin{align*} y^{\prime \prime }+8 y^{\prime }+16 y&=4 \\ y \left (0\right ) &= {\frac {5}{4}} \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

52.517

24486

24166

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

52.522

24487

24896

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

52.544

24488

2436

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

52.568

24489

14620

\begin{align*} 5 y+2 y^{\prime }+y^{\prime \prime }&=6 \sin \left (2 x \right )+7 \cos \left (2 x \right ) \\ \end{align*}

52.582

24490

6583

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

52.602

24491

24044

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

52.607

24492

17909

\begin{align*} x^{2} y^{\prime }+\sin \left (2 y\right )&=1 \\ y \left (\infty \right ) &= \frac {11 \pi }{4} \\ \end{align*}

52.648

24493

13373

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

52.670

24494

22770

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

52.697

24495

17843

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

52.755

24496

4733

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

52.784

24497

17253

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

52.787

24498

12094

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

52.799

24499

14625

\begin{align*} y^{\prime \prime }+2 y^{\prime }+10 y&=5 \,{\mathrm e}^{-2 x} x \\ \end{align*}

52.815

24500

13847

\begin{align*} x^{3} y^{\prime \prime }+\left (a \,x^{2}+b x \right ) y^{\prime }+\left (c x +d \right ) y&=0 \\ \end{align*}

52.824