2.3.265 Problems 26401 to 26500

Table 2.1103: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

26401

9117

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

35.426

26402

5192

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

35.431

26403

5198

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

35.504

26404

27052

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

Using Laplace transform method.

35.572

26405

25528

\begin{align*} m y^{\prime \prime }+k y&=1 \\ \end{align*}

35.619

26406

7519

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

35.677

26407

26271

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

35.742

26408

24166

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

35.780

26409

3682

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

35.815

26410

20127

\begin{align*} y^{\prime \prime }&=\frac {1}{\sqrt {a y}} \\ \end{align*}

35.830

26411

13905

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

35.841

26412

9975

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

35.855

26413

17052

\begin{align*} y^{\prime }&=\sqrt {25-y^{2}} \\ y \left (4\right ) &= -5 \\ \end{align*}

35.866

26414

21593

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

35.876

26415

13403

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

35.888

26416

12612

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

35.891

26417

19351

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

35.928

26418

10407

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

35.996

26419

13372

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

36.024

26420

13267

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

36.042

26421

12054

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

36.052

26422

12651

\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 )-a^{2} x \right ) y}{4 x^{2} \left (x -1\right )^{2}} \\ \end{align*}

36.257

26423

12596

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

36.348

26424

13484

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

36.355

26425

13795

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

36.408

26426

10322

\begin{align*} y^{\prime }&=\left (\pi +x +7 y\right )^{{7}/{2}} \\ \end{align*}

36.411

26427

3556

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

36.477

26428

2943

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

36.516

26429

12560

\begin{align*} \operatorname {a2} \,x^{2} y^{\prime \prime }+\left (\operatorname {a1} \,x^{2}+\operatorname {b1} x \right ) y^{\prime }+\left (\operatorname {a0} \,x^{2}+\operatorname {b0} x +\operatorname {c0} \right ) y&=0 \\ \end{align*}

36.546

26430

26390

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

36.595

26431

13635

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

36.628

26432

27520

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

36.635

26433

11794

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

36.658

26434

13247

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

36.667

26435

27467

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

36.697

26436

5205

\begin{align*} x^{7} y y^{\prime }&=2 x^{2}+2+5 x^{3} y \\ \end{align*}

36.709

26437

24572

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

36.736

26438

7008

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

36.837

26439

22408

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

36.844

26440

5238

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

36.847

26441

8730

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

37.015

26442

26681

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

37.021

26443

27201

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

37.148

26444

2934

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

37.180

26445

17307

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

37.207

26446

13024

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

37.214

26447

18611

\begin{align*} 3 y^{\prime } t +9 y&=2 t y^{{5}/{3}} \\ \end{align*}

37.230

26448

13714

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

37.271

26449

27248

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

37.319

26450

6090

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

37.379

26451

3653

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

37.386

26452

4331

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

37.401

26453

17276

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

37.408

26454

24179

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

37.415

26455

27452

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

37.430

26456

13486

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

37.463

26457

12125

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

37.484

26458

5301

\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*}

37.523

26459

11643

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

37.535

26460

5691

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

37.586

26461

6338

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

37.591

26462

27260

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

37.594

26463

16315

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

37.616

26464

25760

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

37.675

26465

12118

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

37.709

26466

7713

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

37.742

26467

20470

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

37.757

26468

7498

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

37.803

26469

5135

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

37.917

26470

25516

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

37.971

26471

25523

\begin{align*} y^{\prime \prime }+100 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 10 \\ \end{align*}

37.980

26472

23893

\begin{align*} 20 y-20 x y^{2}+\left (5 x -8 x^{2} y\right ) y^{\prime }&=0 \\ \end{align*}

38.072

26473

7029

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

38.076

26474

12106

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

38.269

26475

22458

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

38.432

26476

20237

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

38.473

26477

27323

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

38.474

26478

27334

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

38.487

26479

5092

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

38.509

26480

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*}

38.513

26481

21275

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

38.700

26482

21922

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

38.701

26483

25734

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

38.733

26484

19922

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

38.785

26485

2514

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

38.793

26486

12093

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

38.816

26487

20400

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

38.829

26488

5166

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

38.971

26489

12044

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

39.086

26490

21044

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

39.113

26491

11912

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

39.138

26492

13214

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

39.159

26493

2903

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

39.207

26494

9125

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

39.212

26495

17319

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

39.307

26496

16362

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

39.310

26497

11741

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

39.323

26498

23864

\begin{align*} x \left (6 x^{2}+14 y^{2}\right )+y \left (13 x^{2}+30 y^{2}\right ) y^{\prime }&=0 \\ \end{align*}

39.339

26499

5077

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

39.395

26500

11478

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

39.402