2.3.188 Problems 18701 to 18800

Table 2.949: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

18701

14252

\begin{align*} \theta ^{\prime }&=-a \theta +{\mathrm e}^{b t} \\ \end{align*}

6.426

18702

15933

\begin{align*} y^{\prime }&=a t y+4 \,{\mathrm e}^{-t^{2}} \\ \end{align*}

6.428

18703

22818

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

Using Laplace transform method.

6.428

18704

15229

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

Using Laplace transform method.

6.430

18705

5004

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

6.431

18706

7921

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

6.432

18707

11383

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

6.432

18708

18063

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

6.432

18709

14970

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

6.434

18710

22369

\begin{align*} i^{\prime }+5 i&=10 \\ i \left (0\right ) &= 0 \\ \end{align*}

6.434

18711

4763

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

6.438

18712

20977

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

6.440

18713

16573

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

6.441

18714

17980

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

6.441

18715

25571

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

6.442

18716

12340

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

6.444

18717

2875

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

6.445

18718

4962

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

6.447

18719

11497

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

6.451

18720

11640

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

6.451

18721

22145

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

6.451

18722

21047

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

6.457

18723

23453

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

Series expansion around \(x=0\).

6.458

18724

14969

\begin{align*} 4 t^{2} x^{\prime \prime }+8 t x^{\prime }+5 x&=0 \\ x \left (1\right ) &= 2 \\ x^{\prime }\left (1\right ) &= 0 \\ \end{align*}

6.459

18725

18932

\begin{align*} y^{\prime \prime \prime \prime }-y&=\operatorname {Heaviside}\left (t -1\right )-\operatorname {Heaviside}\left (-2+t \right ) \\ y \left (0\right ) &= 12 \\ y^{\prime }\left (0\right ) &= 7 \\ y^{\prime \prime }\left (0\right ) &= 2 \\ y^{\prime \prime \prime }\left (0\right ) &= -9 \\ \end{align*}

Using Laplace transform method.

6.461

18726

12365

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

6.463

18727

7434

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

6.467

18728

16405

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

6.467

18729

12181

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

6.469

18730

12374

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

6.469

18731

19162

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

6.469

18732

22653

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

6.469

18733

14364

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

Using Laplace transform method.

6.470

18734

26627

\begin{align*} \left (2 x +1\right ) y^{\prime \prime }+\left (4 x -2\right ) y^{\prime }-8 y&=0 \\ \end{align*}

6.470

18735

12216

\begin{align*} y^{\prime }&=-\frac {x}{4}+1+y^{2}+\frac {7 x^{2} y}{16}-\frac {y x}{2}+\frac {5 x^{4}}{128}-\frac {5 x^{3}}{64}+\frac {x^{2}}{16}+y^{3}+\frac {3 y^{2} x^{2}}{8}-\frac {3 x y^{2}}{4}+\frac {3 x^{4} y}{64}-\frac {3 x^{3} y}{16}+\frac {x^{6}}{512}-\frac {3 x^{5}}{256} \\ \end{align*}

6.471

18736

18495

\begin{align*} y^{\prime }&=\frac {-{\mathrm e}^{x}+3 x^{2}}{2 y-11} \\ y \left (0\right ) &= 11 \\ \end{align*}

6.473

18737

27050

\begin{align*} x^{\prime }-x+2 y^{\prime }&=0 \\ 4 x^{\prime }+3 y^{\prime }+y&=-6 \\ \end{align*}

With initial conditions

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

6.474

18738

27543

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

6.474

18739

20547

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

6.476

18740

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*}

6.477

18741

17903

\begin{align*} x^{2} y^{\prime }+\cos \left (2 y\right )&=1 \\ y \left (\infty \right ) &= \frac {10 \pi }{3} \\ \end{align*}

6.477

18742

23379

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

6.477

18743

4729

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

6.484

18744

17953

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

6.487

18745

25949

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

6.489

18746

25219

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

6.490

18747

17262

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

6.491

18748

8745

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

6.492

18749

22180

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

Series expansion around \(x=0\).

6.492

18750

23138

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

6.493

18751

15590

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

6.495

18752

11979

\begin{align*} y^{\prime }&=\frac {y \ln \left (-1+x \right )+{\mathrm e}^{x +1} x^{3}+7 \,{\mathrm e}^{x +1} x y^{2}}{\ln \left (-1+x \right ) x} \\ \end{align*}

6.496

18753

17088

\begin{align*} y^{\prime }&=\frac {t^{3}}{y \sqrt {\left (1-y^{2}\right ) \left (t^{4}+9\right )}} \\ \end{align*}

6.497

18754

25407

\begin{align*} y^{\prime }-4 y&=-8 \\ \end{align*}

6.497

18755

5008

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

6.500

18756

14963

\begin{align*} x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=0 \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= 1 \\ \end{align*}

6.501

18757

8218

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

6.504

18758

5190

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

6.506

18759

10308

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

6.507

18760

19323

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

6.508

18761

12269

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

6.510

18762

15897

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

6.512

18763

4902

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

6.516

18764

16243

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

6.516

18765

117

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

6.519

18766

14460

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

6.521

18767

12142

\begin{align*} y^{\prime }&=-\frac {\left (-\frac {y \,{\mathrm e}^{\frac {1}{x}}}{x}-\textit {\_F1} \left (y \,{\mathrm e}^{\frac {1}{x}}\right )\right ) {\mathrm e}^{-\frac {1}{x}}}{x} \\ \end{align*}

6.522

18768

8761

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

6.523

18769

25408

\begin{align*} y^{\prime }+4 y&=8 \\ \end{align*}

6.524

18770

18504

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

6.525

18771

4995

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

6.526

18772

12092

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

6.527

18773

1691

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

6.529

18774

20275

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

6.530

18775

26519

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

6.531

18776

8446

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

6.532

18777

15231

\begin{align*} y^{\prime \prime }+5 y^{\prime }+6 y&=36 t \left (\operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (t -1\right )\right ) \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= -2 \\ \end{align*}

Using Laplace transform method.

6.532

18778

1688

\begin{align*} 3 x^{2}+2 y x +4 y^{2}+\left (x^{2}+8 y x +18 y\right ) y^{\prime }&=0 \\ \end{align*}

6.533

18779

13824

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

6.533

18780

15944

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

6.535

18781

5027

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

6.536

18782

14328

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

6.536

18783

14501

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

6.537

18784

16955

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

6.539

18785

1576

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

6.542

18786

4883

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

6.542

18787

7340

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

6.543

18788

25211

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

6.544

18789

14062

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

6.546

18790

5313

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

6.548

18791

7423

\begin{align*} 3 r&=r^{\prime }-\theta ^{3} \\ \end{align*}

6.549

18792

20293

\begin{align*} \left (20 x^{2}+8 y x +4 y^{2}+3 y^{3}\right ) y+4 \left (x^{2}+y x +y^{2}+y^{3}\right ) x y^{\prime }&=0 \\ \end{align*}

6.549

18793

24797

\begin{align*} {y^{\prime }}^{2}+4 x^{5} y^{\prime }-12 x^{4} y&=0 \\ \end{align*}

6.549

18794

19680

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

6.552

18795

3457

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

6.553

18796

18007

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

6.555

18797

7446

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

6.556

18798

17888

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

6.560

18799

20223

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

6.560

18800

12330

\begin{align*} y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+\left (\operatorname {a1} \,x^{2}+\operatorname {b1} x +\operatorname {c1} \right ) y&=0 \\ \end{align*}

6.561