2.3.158 Problems 15701 to 15800

Table 2.847: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

15701

1237

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

1.374

15702

2474

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

1.374

15703

7697

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

1.374

15704

11327

\begin{align*} y^{\prime }+a y^{2}-b \,x^{2 \nu }-c \,x^{\nu -1}&=0 \\ \end{align*}

1.374

15705

18567

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

1.374

15706

20278

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

1.374

15707

24999

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

1.374

15708

17785

\begin{align*} x^{2} y^{\prime \prime }-7 y^{\prime } x +25 y&=0 \\ \end{align*}

1.375

15709

18353

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

1.375

15710

6837

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

1.377

15711

21017

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

1.377

15712

2865

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

1.378

15713

12937

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

1.378

15714

19430

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

1.378

15715

19619

\begin{align*} \left (x^{2}-x -6\right ) y^{\prime \prime }+\left (3 x +5\right ) y^{\prime }+y&=0 \\ \end{align*}
Series expansion around \(x=3\).

1.378

15716

25424

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

1.378

15717

1226

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

1.381

15718

2390

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

1.381

15719

10438

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

1.381

15720

19162

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

1.381

15721

3634

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

1.382

15722

14098

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

1.382

15723

9184

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

1.383

15724

10435

\begin{align*} y^{\prime \prime } x -y^{\prime }+4 x^{3} y&=x^{5} \\ \end{align*}

1.383

15725

17357

\begin{align*} t^{2} y^{\prime \prime }+7 t y^{\prime }-7 y&=0 \\ y \left (1\right ) &= 2 \\ y^{\prime }\left (1\right ) &= -22 \\ \end{align*}

1.383

15726

17806

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

1.383

15727

7692

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

1.384

15728

16694

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

1.384

15729

22060

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

1.384

15730

25191

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

1.384

15731

226

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

1.385

15732

791

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

1.385

15733

17525

\begin{align*} y^{\prime \prime }+9 y&=\csc \left (3 t \right ) \\ y \left (\frac {\pi }{12}\right ) &= 0 \\ y^{\prime }\left (\frac {\pi }{12}\right ) &= 1 \\ \end{align*}

1.385

15734

18242

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

1.385

15735

23622

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

1.385

15736

1039

\begin{align*} x_{1}^{\prime }&=11 x_{1}-x_{2}+26 x_{3}+6 x_{4}-3 x_{5} \\ x_{2}^{\prime }&=3 x_{2} \\ x_{3}^{\prime }&=-9 x_{1}-24 x_{3}-6 x_{4}+3 x_{5} \\ x_{4}^{\prime }&=3 x_{1}+9 x_{3}+5 x_{4}-x_{5} \\ x_{5}^{\prime }&=-48 x_{1}-3 x_{2}-138 x_{3}-30 x_{4}+18 x_{5} \\ \end{align*}

1.386

15737

3447

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

1.386

15738

7643

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

1.386

15739

8984

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

1.386

15740

15410

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

1.386

15741

20628

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

1.386

15742

21026

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

1.386

15743

9755

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

1.387

15744

2491

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

1.388

15745

9232

\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 5 \\ \end{align*}

1.388

15746

14100

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

1.388

15747

17457

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

1.388

15748

19526

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

1.388

15749

20113

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

1.388

15750

15521

\begin{align*} x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=0 \\ y^{\prime }\left (1\right ) &= 3 \\ y^{\prime }\left (2\right ) &= 0 \\ \end{align*}

1.389

15751

15719

\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=\left \{\begin {array}{cc} 0 & 0\le x <1 \\ x^{2}-2 x +3 & 1\le x \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}
Using Laplace transform method.

1.389

15752

24108

\begin{align*} x^{2} y^{\prime \prime }+5 y^{\prime } x +\left (4+2 x \right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

1.389

15753

22960

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

1.390

15754

25425

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

1.390

15755

14662

\begin{align*} y^{\prime \prime }+6 y^{\prime }+13 y&=x \,{\mathrm e}^{-3 x} \sin \left (2 x \right )+x^{2} {\mathrm e}^{-2 x} \sin \left (3 x \right ) \\ \end{align*}

1.391

15756

15135

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

1.391

15757

20514

\begin{align*} \left (5+2 x \right )^{2} y^{\prime \prime }-6 \left (5+2 x \right ) y^{\prime }+8 y&=0 \\ \end{align*}

1.391

15758

2352

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

1.392

15759

13877

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

1.392

15760

15520

\begin{align*} x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=0 \\ y \left (1\right ) &= 1 \\ y^{\prime }\left (2\right ) &= -12 \\ \end{align*}

1.392

15761

21924

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

1.392

15762

24019

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

1.392

15763

23672

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

1.393

15764

23720

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

1.393

15765

24109

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

1.393

15766

2164

\begin{align*} y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+6 y^{\prime \prime }-4 y^{\prime }+2 y&={\mathrm e}^{2 x} \left (x^{4}+x +24\right ) \\ \end{align*}

1.394

15767

2354

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

1.394

15768

5086

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

1.394

15769

206

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

1.395

15770

5974

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

1.395

15771

8324

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

1.395

15772

9797

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

1.395

15773

10090

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

1.395

15774

18056

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

1.396

15775

22036

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

1.396

15776

2473

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

1.397

15777

9209

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

1.397

15778

21018

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

1.397

15779

22994

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

1.397

15780

6018

\begin{align*} \operatorname {a2} y+\operatorname {a1} x y^{\prime }+x^{2} y^{\prime \prime }&=0 \\ \end{align*}

1.398

15781

6291

\begin{align*} \left (-a^{2}+4 b \right ) y+12 x^{5} y^{\prime }+4 x^{6} y^{\prime \prime }&=0 \\ \end{align*}

1.398

15782

6483

\begin{align*} 2 y y^{\prime \prime }&=y^{2} \left (1-3 y^{2}\right )+6 {y^{\prime }}^{2} \\ \end{align*}

1.398

15783

12367

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

1.398

15784

21106

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

1.398

15785

1821

\begin{align*} y^{\prime \prime } x -y^{\prime }-4 x^{3} y&=8 x^{5} \\ \end{align*}

1.399

15786

25426

\begin{align*} -2 y+y^{\prime }&={\mathrm e}^{\frac {201 t}{100}} \\ y \left (0\right ) &= 1 \\ \end{align*}

1.400

15787

377

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

1.401

15788

4057

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

1.401

15789

5432

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

1.401

15790

13057

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

1.401

15791

24075

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

1.401

15792

7406

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

1.402

15793

10415

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

1.402

15794

19363

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

1.402

15795

19506

\begin{align*} 4 y+y^{\prime \prime }&=4 \cos \left (2 x \right )+6 \cos \left (x \right )+8 x^{2}-4 x \\ \end{align*}

1.402

15796

17196

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

1.403

15797

25697

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

1.403

15798

4219

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

1.404

15799

4741

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

1.404

15800

6960

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

1.404