2.3.145 Problems 14401 to 14500

Table 2.821: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

14401

8053

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

2.879

14402

8961

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

2.880

14403

16250

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

2.880

14404

25756

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

2.880

14405

24067

\begin{align*} y^{\prime \prime }+3 y^{\prime }-4 y&=12 \,{\mathrm e}^{2 x} \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 4 \\ \end{align*}

2.881

14406

25201

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

2.881

14407

22054

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

2.882

14408

20326

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

2.884

14409

3520

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

2.885

14410

4753

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

2.885

14411

6828

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

2.885

14412

8680

\begin{align*} z^{\prime }&=10^{x +z} \\ \end{align*}

2.885

14413

8984

\begin{align*} 3 x^{2} y^{\prime \prime }+x^{6} y^{\prime }+2 y x&=0 \\ \end{align*}
Series expansion around \(x=0\).

2.885

14414

23257

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

2.885

14415

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*}

2.886

14416

9183

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

2.887

14417

13235

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

2.887

14418

20694

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

2.887

14419

7510

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

2.888

14420

8306

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

2.888

14421

9189

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

2.888

14422

15548

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

2.889

14423

22544

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

2.889

14424

4408

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

2.890

14425

4907

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

2.890

14426

4925

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

2.890

14427

22361

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

2.890

14428

22656

\begin{align*} 4 y^{\prime \prime }+9 y&=0 \\ \end{align*}

2.890

14429

24880

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

2.890

14430

3738

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

2.891

14431

8167

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

2.891

14432

15063

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

2.891

14433

58

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

2.892

14434

2983

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

2.892

14435

8945

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

2.892

14436

19382

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

2.892

14437

21832

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

2.893

14438

7108

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

2.894

14439

3006

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

2.895

14440

4213

\begin{align*} y^{\prime }&=6 x y^{2} \\ \end{align*}

2.895

14441

8510

\begin{align*} y^{\prime \prime } x +\left (x +3\right ) y^{\prime }+7 x^{2} y&=0 \\ \end{align*}
Series expansion around \(x=0\).

2.895

14442

15293

\begin{align*} x^{\prime }&=-3 x+3 y+z+5 \sin \left (2 t \right ) \\ y^{\prime }&=x-5 y-3 z+5 \cos \left (2 t \right ) \\ z^{\prime }&=-3 x+7 y+3 z+23 \,{\mathrm e}^{t} \\ \end{align*}
With initial conditions
\begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 2 \\ z \left (0\right ) &= 3 \\ \end{align*}

2.895

14443

18356

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

2.896

14444

5868

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

2.897

14445

64

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

2.898

14446

2656

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

2.898

14447

3519

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

2.898

14448

13780

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

2.898

14449

19808

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

2.898

14450

21355

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

2.898

14451

4871

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

2.899

14452

9186

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

2.899

14453

11428

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

2.900

14454

21279

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

2.900

14455

13251

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

2.902

14456

1176

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

2.903

14457

5823

\begin{align*} -8 y+2 y^{\prime } x +y^{\prime \prime }&=0 \\ \end{align*}

2.903

14458

20677

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

2.903

14459

22145

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

2.903

14460

15554

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

2.904

14461

20317

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

2.904

14462

14258

\begin{align*} \cos \left (\theta \right ) v^{\prime }+v&=3 \\ \end{align*}

2.905

14463

2500

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

2.906

14464

3408

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

2.906

14465

9980

\begin{align*} y^{\prime \prime }+16 y&=4 \cos \left (x \right ) \\ \end{align*}

2.906

14466

18126

\begin{align*} 3 y^{\prime \prime }-2 y^{\prime }-8 y&=0 \\ \end{align*}

2.906

14467

13282

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

2.908

14468

1155

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

2.909

14469

4281

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

2.909

14470

4436

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

2.909

14471

5824

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

2.909

14472

23000

\begin{align*} y^{\prime \prime }-5 y^{\prime }+4 y&=0 \\ \end{align*}

2.909

14473

8368

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

2.910

14474

14448

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

2.910

14475

18230

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

2.910

14476

2948

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

2.911

14477

10325

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

2.911

14478

11785

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

2.911

14479

18511

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

2.911

14480

19806

\begin{align*} x^{3}-3 x^{2} y+5 x y^{2}-7 y^{3}+\left (y^{4}+2 y^{2}-x^{3}+5 x^{2} y-21 x y^{2}\right ) y^{\prime }&=0 \\ \end{align*}

2.912

14481

3535

\begin{align*} y^{\prime }+\frac {y}{x \ln \left (x \right )}&=9 x^{2} \\ \end{align*}

2.913

14482

7091

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

2.913

14483

14483

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

2.913

14484

5746

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

2.914

14485

16394

\begin{align*} y^{\prime \prime }&=2 y^{\prime }-6 \\ \end{align*}

2.914

14486

18070

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

2.915

14487

25739

\begin{align*} y^{\prime \prime }+9 y&=18 \\ \end{align*}

2.915

14488

3957

\begin{align*} -y+y^{\prime }&=4 \operatorname {Heaviside}\left (t -\frac {\pi }{4}\right ) \sin \left (t +\frac {\pi }{4}\right ) \\ y \left (0\right ) &= 1 \\ \end{align*}
Using Laplace transform method.

2.916

14489

11894

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

2.916

14490

7801

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

2.917

14491

8979

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

2.918

14492

22654

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

2.918

14493

15848

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

2.919

14494

18136

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

2.919

14495

9133

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

2.920

14496

21480

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

2.920

14497

23382

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

2.920

14498

2655

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

2.921

14499

3455

\begin{align*} y^{\prime }&=-\cot \left (t \right ) y+6 \cos \left (t \right )^{2} \\ y \left (\frac {\pi }{4}\right ) &= 3 \\ \end{align*}

2.921

14500

5483

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

2.921