2.3.96 Problems 9501 to 9600

Table 2.765: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

9501

12944

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

0.703

9502

18638

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

0.703

9503

22732

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

0.703

9504

24740

\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=15 \sqrt {1+{\mathrm e}^{-x}} \\ \end{align*}

0.703

9505

26422

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

0.703

9506

3235

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

0.704

9507

6223

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

0.704

9508

7769

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

0.704

9509

9703

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

0.704

9510

11827

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

0.704

9511

14747

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

Series expansion around \(x=0\).

0.704

9512

15222

\begin{align*} 4 y^{\prime \prime }-4 y^{\prime }+y&=t^{2} \\ y \left (0\right ) &= -12 \\ y^{\prime }\left (0\right ) &= 7 \\ \end{align*}

Using Laplace transform method.

0.704

9513

16175

\begin{align*} \left (6+x \right )^{{1}/{3}} y^{\prime }&=1 \\ y \left (2\right ) &= 10 \\ \end{align*}

0.704

9514

18819

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

0.704

9515

20134

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

0.704

9516

20871

\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=20 \,{\mathrm e}^{-2 x} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.704

9517

23514

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

0.704

9518

25983

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

0.704

9519

18863

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

0.705

9520

23668

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

Series expansion around \(x=0\).

0.705

9521

2035

\begin{align*} 4 x^{2} \left (x^{2}+4\right ) y^{\prime \prime }+3 x \left (3 x^{2}+8\right ) y^{\prime }+\left (-9 x^{2}+1\right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.706

9522

2040

\begin{align*} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (8 x^{2}+3\right ) y^{\prime }+\left (12 x^{2}+1\right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.706

9523

3433

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

0.706

9524

3748

\begin{align*} y^{\prime \prime }-4 y&=\frac {8}{{\mathrm e}^{2 x}+1} \\ \end{align*}

0.706

9525

4532

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

0.706

9526

9698

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

With initial conditions

\begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 2 \\ z \left (0\right ) &= 5 \\ \end{align*}

0.706

9527

10466

\begin{align*} 5 y^{\prime \prime }-2 x y^{\prime }+10 y&=0 \\ \end{align*}

0.706

9528

11822

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

0.706

9529

14791

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

0.706

9530

15220

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

Using Laplace transform method.

0.706

9531

19053

\begin{align*} x_{1}^{\prime }&=-7 x_{1}+9 x_{2}-6 x_{3} \\ x_{2}^{\prime }&=-8 x_{1}+11 x_{2}-7 x_{3} \\ x_{3}^{\prime }&=-2 x_{1}+3 x_{2}-x_{3} \\ \end{align*}

0.706

9532

21495

\begin{align*} y^{\prime \prime }-2 y^{\prime }+10 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}

0.706

9533

23748

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

Series expansion around \(x=0\).

0.706

9534

24558

\begin{align*} y^{\prime \prime }-y&=10 \sin \left (x \right )^{2} \\ \end{align*}

0.706

9535

2050

\begin{align*} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (9 x^{2}+1\right ) y^{\prime }+\left (25 x^{2}+1\right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.707

9536

2199

\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }-y^{\prime }-y&=4 \,{\mathrm e}^{-x} \left (1-6 x \right )-2 x \cos \left (x \right )+2 \left (x +1\right ) \sin \left (x \right ) \\ \end{align*}

0.707

9537

2805

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

0.707

9538

3688

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

0.707

9539

6930

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

0.707

9540

9508

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

Series expansion around \(x=0\).

0.707

9541

10361

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

0.707

9542

12402

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

0.707

9543

16807

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

Using Laplace transform method.

0.707

9544

18658

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

0.707

9545

19639

\begin{align*} x^{\prime }&=x+2 y+t -1 \\ y^{\prime }&=3 x+2 y-5 t -2 \\ \end{align*}

0.707

9546

20706

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

0.707

9547

20930

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

0.707

9548

21943

\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }-8 x y^{\prime }+20 y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.707

9549

24564

\begin{align*} 5 y+4 y^{\prime }+y^{\prime \prime }&=10 \,{\mathrm e}^{-3 x} \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.707

9550

24566

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

0.707

9551

338

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

0.708

9552

484

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

Series expansion around \(x=0\).

0.708

9553

3734

\begin{align*} y+2 y^{\prime }+y^{\prime \prime }&=50 \sin \left (3 x \right ) \\ \end{align*}

0.708

9554

6961

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

0.708

9555

7304

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

0.708

9556

8000

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

0.708

9557

9273

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

0.708

9558

10447

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

0.708

9559

12589

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

0.708

9560

19609

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

Series expansion around \(x=0\).

0.708

9561

21546

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

0.708

9562

23228

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

0.708

9563

24559

\begin{align*} y^{\prime \prime }+y&=12 \cos \left (x \right )^{2} \\ \end{align*}

0.708

9564

24591

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

0.708

9565

25764

\begin{align*} y^{\prime \prime }+2 y^{\prime }-3 y&=-12 x +8 \\ y \left (-1\right ) &= 1 \\ y^{\prime }\left (-1\right ) &= 1 \\ \end{align*}

0.708

9566

1436

\begin{align*} x_{1}^{\prime }&=-\frac {5 x_{1}}{4}+\frac {3 x_{2}}{4}+2 t \\ x_{2}^{\prime }&=\frac {3 x_{1}}{4}-\frac {5 x_{2}}{4}+{\mathrm e}^{t} \\ \end{align*}

0.709

9567

2717

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

0.709

9568

14856

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

0.709

9569

22938

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

0.709

9570

23732

\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{16}\right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.709

9571

2013

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

Series expansion around \(x=0\).

0.710

9572

2398

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

0.710

9573

3240

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

0.710

9574

4177

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

Series expansion around \(x=0\).

0.710

9575

4479

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

0.710

9576

6709

\begin{align*} 6 y+18 x y^{\prime }+9 x^{2} y^{\prime \prime }+\left (x^{3}+1\right ) y^{\prime \prime \prime }&=0 \\ \end{align*}

0.710

9577

6848

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

0.710

9578

7766

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

0.710

9579

8478

\begin{align*} \left (x^{2}-2 x +10\right ) y^{\prime \prime }+x y^{\prime }-4 y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.710

9580

10036

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

0.710

9581

14394

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

With initial conditions

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

0.710

9582

14395

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

With initial conditions

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

0.710

9583

14628

\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }+3 y^{\prime }-5 y&=5 \sin \left (2 x \right )+10 x^{2}+3 x +7 \\ \end{align*}

0.710

9584

15081

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

Series expansion around \(x=0\).

0.710

9585

18158

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

0.710

9586

18908

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

Using Laplace transform method.

0.710

9587

21150

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

0.710

9588

22185

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

Series expansion around \(x=2\).

0.710

9589

23623

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

With initial conditions

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

0.710

9590

25569

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

0.710

9591

1434

\begin{align*} x_{1}^{\prime }&=x_{1}+x_{2}+2 \,{\mathrm e}^{t} \\ x_{2}^{\prime }&=4 x_{1}+x_{2}-{\mathrm e}^{t} \\ \end{align*}

0.711

9592

2188

\begin{align*} y^{\prime \prime \prime \prime }-5 y^{\prime \prime \prime }+13 y^{\prime \prime }-19 y^{\prime }+10 y&={\mathrm e}^{x} \left (\cos \left (2 x \right )+\sin \left (2 x \right )\right ) \\ \end{align*}

0.711

9593

2271

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

With initial conditions

\begin{align*} y_{1} \left (0\right ) &= -6 \\ y_{2} \left (0\right ) &= -2 \\ y_{3} \left (0\right ) &= 0 \\ \end{align*}

0.711

9594

2570

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

0.711

9595

3485

\begin{align*} f^{\prime \prime }+2 f^{\prime }+5 f&={\mathrm e}^{-t} \cos \left (3 t \right ) \\ f \left (0\right ) &= 0 \\ f^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.711

9596

4500

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

0.711

9597

8044

\begin{align*} x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (9 x^{2}+6\right ) y&=0 \\ \end{align*}

0.711

9598

9075

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

0.711

9599

10194

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

Series expansion around \(x=0\).

0.711

9600

18704

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

0.711