2.3.145 Problems 14401 to 14500

Table 2.863: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

14401

20017

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

1.540

14402

13929

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

1.541

14403

1223

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

1.542

14404

5834

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

1.542

14405

15937

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

1.542

14406

9897

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

Series expansion around \(x=0\).

1.543

14407

18237

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

1.543

14408

18251

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

1.543

14409

18841

\begin{align*} y^{\prime \prime }+4 y&=t^{2} \sin \left (2 t \right )+\left (6 t +7\right ) \cos \left (2 t \right ) \\ \end{align*}

1.543

14410

26979

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

1.543

14411

13724

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

1.544

14412

15860

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

1.544

14413

5277

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

1.545

14414

9866

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

Series expansion around \(x=0\).

1.545

14415

20289

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

1.545

14416

22828

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

Series expansion around \(x=2\).

1.545

14417

2767

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

1.546

14418

6200

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

1.546

14419

7367

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

1.546

14420

9706

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

1.546

14421

11321

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

1.546

14422

14159

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

1.546

14423

23383

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

1.546

14424

25357

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

Series expansion around \(t=0\).

1.546

14425

1794

\begin{align*} y^{\prime }+y^{2}+8 y+7&=0 \\ \end{align*}

1.547

14426

7602

\begin{align*} 3 y^{\prime }-7 y&=0 \\ \end{align*}

1.547

14427

8331

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

1.547

14428

9208

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

1.547

14429

13297

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

1.547

14430

13755

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

1.547

14431

15903

\begin{align*} y^{\prime }&=3 y-4 \,{\mathrm e}^{3 t} \\ \end{align*}

1.547

14432

23120

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

1.547

14433

6853

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

1.548

14434

17760

\begin{align*} y^{\prime \prime \prime \prime }+6 y^{\prime \prime \prime }+18 y^{\prime \prime }+30 y^{\prime }+25 y&={\mathrm e}^{-t} \cos \left (2 t \right )+{\mathrm e}^{-2 t} \sin \left (t \right ) \\ \end{align*}

1.548

14435

1300

\begin{align*} t^{2} y^{\prime \prime }+7 t y^{\prime }+10 y&=0 \\ \end{align*}

1.549

14436

6022

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

1.549

14437

6542

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

1.549

14438

18229

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

1.549

14439

27303

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

1.549

14440

11378

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

1.550

14441

14777

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

1.550

14442

27357

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

1.551

14443

9937

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

Series expansion around \(x=0\).

1.552

14444

11831

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

1.552

14445

2487

\begin{align*} y+y^{\prime }&=\left \{\begin {array}{cc} 2 & 0\le t \le 1 \\ 0 & 1<t \end {array}\right . \\ y \left (0\right ) &= 0 \\ \end{align*}

1.553

14446

20804

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

1.554

14447

25454

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

1.554

14448

18293

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

1.555

14449

15720

\begin{align*} 4 y+y^{\prime \prime }&=\left \{\begin {array}{cc} 0 & 0\le x <\pi \\ -\sin \left (3 x \right ) & \pi \le x \end {array}\right . \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}

Using Laplace transform method.

1.556

14450

19991

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

1.556

14451

23329

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

1.556

14452

1574

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

1.557

14453

9558

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

Series expansion around \(x=0\).

1.557

14454

23183

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

1.557

14455

14416

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

1.558

14456

14673

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

1.558

14457

16499

\begin{align*} y^{\prime \prime }-9 y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= -3 \\ \end{align*}

1.558

14458

17847

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

1.558

14459

2592

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

1.559

14460

11863

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

1.559

14461

16482

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

1.559

14462

22910

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

With initial conditions

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

1.559

14463

6036

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

1.560

14464

6551

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

1.560

14465

10149

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

1.560

14466

16392

\begin{align*} x y^{\prime \prime }-{y^{\prime }}^{2}&=6 x^{5} \\ \end{align*}

1.560

14467

20860

\begin{align*} x^{2} y^{\prime \prime }+5 x y^{\prime }+4 y&=0 \\ \end{align*}

1.560

14468

12446

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

1.561

14469

4507

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

1.562

14470

9498

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

1.562

14471

23331

\begin{align*} y^{\prime \prime }+25 y&=0 \\ \end{align*}

1.562

14472

25218

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

1.562

14473

25434

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

1.562

14474

10111

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

1.563

14475

18681

\begin{align*} x^{\prime }&=a x+10 y \\ y^{\prime }&=-x-4 y \\ \end{align*}

1.563

14476

22868

\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{9}\right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

1.563

14477

12603

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

1.564

14478

16563

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

1.564

14479

1234

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

1.565

14480

7369

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

1.565

14481

16732

\begin{align*} 9 x^{2} y^{\prime \prime }+3 x y^{\prime }+y&=0 \\ \end{align*}

1.565

14482

24816

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

1.565

14483

1

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

1.566

14484

2443

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

Series expansion around \(t=0\).

1.566

14485

6079

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

1.566

14486

18032

\begin{align*} 8 {y^{\prime }}^{3}-12 {y^{\prime }}^{2}&=-27 x +27 y \\ \end{align*}

1.567

14487

26586

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

1.567

14488

9812

\begin{align*} 5 {y^{\prime }}^{2}+6 x y^{\prime }-2 y&=0 \\ \end{align*}

1.568

14489

14661

\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&={\mathrm e}^{x} x^{4}+x^{3} {\mathrm e}^{2 x}+x^{2} {\mathrm e}^{3 x} \\ \end{align*}

1.569

14490

23502

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

1.569

14491

6517

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

1.570

14492

9590

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

Series expansion around \(x=0\).

1.570

14493

14190

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

1.570

14494

21613

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

1.570

14495

4086

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

1.571

14496

16433

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

1.571

14497

2632

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

1.572

14498

4522

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

Using Laplace transform method.

1.572

14499

6237

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

1.572

14500

8193

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

1.572