2.3.175 Problems 17401 to 17500

Table 2.923: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

17401

24937

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

2.796

17402

14145

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

2.797

17403

15803

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

2.797

17404

18805

\begin{align*} x^{2} y^{\prime \prime }-5 x y^{\prime }+9 y&=0 \\ \end{align*}

2.797

17405

15559

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

2.798

17406

24912

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

2.798

17407

25287

\begin{align*} -y+y^{\prime }&=\left \{\begin {array}{cc} 1 & 0\le t <2 \\ -1 & 2\le t <4 \\ 0 & 4\le t <\infty \end {array}\right . \\ y \left (0\right ) &= 0 \\ \end{align*}

Using Laplace transform method.

2.798

17408

16389

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

2.799

17409

7564

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

2.800

17410

12354

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

2.800

17411

26302

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

2.800

17412

4385

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

2.801

17413

14968

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

2.801

17414

18376

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

Series expansion around \(x=\pi \).

2.801

17415

2363

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

2.802

17416

8149

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

Series expansion around \(x=0\).

2.802

17417

8718

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

2.802

17418

10327

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

2.802

17419

14851

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

2.802

17420

20759

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

2.802

17421

21382

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

2.802

17422

27213

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

2.802

17423

3633

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

2.803

17424

6513

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

2.803

17425

25462

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

2.804

17426

27222

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

2.804

17427

7520

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

2.805

17428

7429

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

2.806

17429

24264

\begin{align*} L i^{\prime }+R i&=e \sin \left (w t \right ) \\ i \left (0\right ) &= 0 \\ \end{align*}

2.806

17430

25435

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

2.806

17431

12400

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

2.807

17432

16750

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

2.807

17433

21869

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

2.807

17434

7494

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

2.808

17435

3905

\begin{align*} x_{1}^{\prime }&=-16 x_{1}+30 x_{2}-18 x_{3} \\ x_{2}^{\prime }&=-8 x_{1}+8 x_{2}+16 x_{3} \\ x_{3}^{\prime }&=8 x_{1}-15 x_{2}+9 x_{3} \\ \end{align*}

2.809

17436

4191

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

2.809

17437

16693

\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }-9 y&=12 x^{3} \\ \end{align*}

2.809

17438

17457

\begin{align*} y^{\prime \prime }+3 y^{\prime }&=18 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*}

2.809

17439

19507

\begin{align*} y^{\prime \prime }+9 y&=2 \sin \left (3 x \right )+4 \sin \left (x \right )-26 \,{\mathrm e}^{-2 x}+27 x^{3} \\ \end{align*}

2.809

17440

22074

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

2.809

17441

4296

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

2.810

17442

16255

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

2.810

17443

11800

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

2.811

17444

18927

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

Using Laplace transform method.

2.811

17445

90

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

2.812

17446

5816

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

2.813

17447

6116

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

2.813

17448

6184

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

2.814

17449

8470

\begin{align*} x y^{\prime }-4 y&=x^{6} {\mathrm e}^{x} \\ y \left (0\right ) &= 0 \\ \end{align*}

2.816

17450

16269

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

2.818

17451

5817

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

2.819

17452

23914

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

2.819

17453

25289

\begin{align*} -y+y^{\prime }&=\left \{\begin {array}{cc} 0 & 0\le t <1 \\ t -1 & 1\le t <2 \\ 3-t & 2\le t <3 \\ 0 & 3\le t <\infty \end {array}\right . \\ y \left (0\right ) &= 0 \\ \end{align*}

Using Laplace transform method.

2.819

17454

17057

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

2.821

17455

21431

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

2.821

17456

23158

\begin{align*} x y^{\prime }+6 y&=1+3 x \\ \end{align*}

2.821

17457

14701

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

2.822

17458

14835

\begin{align*} t^{2} x^{\prime \prime }+\left (2 t^{3}+7 t \right ) x^{\prime }+\left (8 t^{2}+8\right ) x&=0 \\ \end{align*}

2.822

17459

18833

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

2.822

17460

14351

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

Using Laplace transform method.

2.823

17461

17419

\begin{align*} y^{\prime \prime }-16 y&=0 \\ \end{align*}

2.823

17462

19869

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

2.823

17463

12299

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

2.824

17464

22590

\begin{align*} u^{\prime \prime }+\frac {u^{\prime }}{r}&=4-4 r \\ u \left (1\right ) &= 15 \\ u^{\prime }\left (1\right ) &= 0 \\ \end{align*}

2.824

17465

3531

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

2.825

17466

4792

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

2.826

17467

15795

\begin{align*} x^{\prime }&=-x t \\ x \left (0\right ) &= \frac {1}{\sqrt {\pi }} \\ \end{align*}

2.826

17468

134

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

2.827

17469

6006

\begin{align*} -5 y-3 x y^{\prime }+x^{2} y^{\prime \prime }&=0 \\ \end{align*}

2.827

17470

12441

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

2.828

17471

3634

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

2.829

17472

4099

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

2.829

17473

15817

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

2.829

17474

4941

\begin{align*} \left (x -2\right ) \left (x -3\right ) y^{\prime }+x^{2}-8 y+3 y x&=0 \\ \end{align*}

2.830

17475

12968

\begin{align*} 4 y y^{\prime \prime }-3 {y^{\prime }}^{2}+a y^{3}+b y^{2}+c y&=0 \\ \end{align*}

2.831

17476

12076

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

2.832

17477

19341

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

2.832

17478

20755

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

2.832

17479

20687

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

2.834

17480

22574

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

2.834

17481

1712

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

2.835

17482

2491

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

2.835

17483

19388

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

2.835

17484

1613

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

2.836

17485

3023

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

2.836

17486

17619

\begin{align*} 2 x^{2} y^{\prime \prime }-2 x y^{\prime }+20 y&=0 \\ \end{align*}

2.836

17487

1140

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

2.837

17488

18526

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

2.837

17489

7549

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

2.838

17490

18357

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

2.838

17491

21446

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

2.838

17492

1541

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

2.839

17493

2563

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

2.839

17494

4245

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

2.839

17495

4608

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

2.839

17496

8313

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

2.840

17497

25775

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

2.841

17498

21093

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

2.842

17499

8318

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

2.843

17500

23900

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

2.843