2.3.108 Problems 10701 to 10800

Table 2.747: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

10701

15411

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

1.443

10702

565

\begin{align*} x^{\prime \prime }+4 x&=\delta \left (t \right )+\delta \left (t -\pi \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

1.444

10703

7025

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

1.444

10704

9917

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

1.444

10705

19437

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

1.444

10706

24846

\begin{align*} 9 {y^{\prime }}^{2}+3 x y^{4} y^{\prime }+y^{5}&=0 \\ \end{align*}

1.444

10707

7120

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

1.445

10708

9642

\begin{align*} y^{\prime \prime }+y&=\delta \left (t -2 \pi \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}
Using Laplace transform method.

1.446

10709

12300

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

1.446

10710

22006

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

1.446

10711

15659

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

1.447

10712

8422

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

1.448

10713

13018

\begin{align*} \left (4 y^{3}-a y-b \right ) \left (y^{\prime \prime }+f y^{\prime }\right )-\left (6 y^{2}-\frac {a}{2}\right ) {y^{\prime }}^{2}&=0 \\ \end{align*}

1.448

10714

15666

\begin{align*} y^{\prime \prime }-4 y&=31 \\ y \left (0\right ) &= -9 \\ y^{\prime }\left (0\right ) &= 6 \\ \end{align*}

1.448

10715

8837

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

1.449

10716

15717

\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=\left \{\begin {array}{cc} 1 & 2\le x <4 \\ 0 & \operatorname {otherwise} \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}
Using Laplace transform method.

1.449

10717

16172

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

1.449

10718

20037

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

1.450

10719

20444

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

1.450

10720

5937

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

1.451

10721

12958

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

1.451

10722

13212

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

1.451

10723

15925

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

1.451

10724

21868

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

1.451

10725

24982

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

1.451

10726

130

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

1.452

10727

5742

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

1.452

10728

5814

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

1.452

10729

14389

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

1.452

10730

25312

\begin{align*} y^{\prime \prime }+4 y^{\prime }+3 y&=2 \delta \left (-2+t \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*}
Using Laplace transform method.

1.453

10731

5158

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

1.454

10732

15759

\begin{align*} y_{1}^{\prime }&=y_{1}+2 y_{2}-3 y_{3} \\ y_{2}^{\prime }&=-3 y_{1}+4 y_{2}-2 y_{3} \\ y_{3}^{\prime }&=2 y_{1}+y_{3} \\ \end{align*}

1.454

10733

21319

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

1.454

10734

2071

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

1.455

10735

5491

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

1.455

10736

9752

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

1.455

10737

19773

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

1.455

10738

24996

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

1.455

10739

25710

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

1.455

10740

1108

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

1.456

10741

1235

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

1.456

10742

6006

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

1.456

10743

1268

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

1.457

10744

3865

\begin{align*} x_{1}^{\prime }&=-x_{2} \\ x_{2}^{\prime }&=x_{1} \\ x_{3}^{\prime }&=x_{1}+2 x_{3}+x_{4} \\ x_{4}^{\prime }&=x_{2}+2 x_{4} \\ \end{align*}

1.457

10745

12703

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

1.457

10746

20168

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

1.457

10747

20622

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

1.457

10748

22310

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

1.457

10749

25803

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

1.457

10750

836

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

1.458

10751

12823

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

1.458

10752

9326

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

1.459

10753

10009

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

1.460

10754

14245

\begin{align*} 7 t^{2} x^{\prime }&=3 x-2 t \\ \end{align*}

1.460

10755

49

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

1.461

10756

8856

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

1.461

10757

11835

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

1.461

10758

7424

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

1.462

10759

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.

1.462

10760

22456

\begin{align*} i^{\prime }+2 i&=10 \,{\mathrm e}^{-2 t} \\ i \left (0\right ) &= 0 \\ \end{align*}

1.462

10761

23287

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

1.462

10762

20772

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

1.463

10763

840

\begin{align*} y^{\prime \prime }-2 y^{\prime }-3 y&=6 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 11 \\ \end{align*}

1.464

10764

4127

\begin{align*} y^{\prime \prime }-6 y^{\prime }+5 y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 7 \\ \end{align*}

1.464

10765

7311

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

1.464

10766

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*}

1.465

10767

16361

\begin{align*} y^{\prime }-3 y&=12 \,{\mathrm e}^{2 x} \\ \end{align*}

1.465

10768

21333

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

1.465

10769

9944

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

1.466

10770

23347

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

1.466

10771

18

\begin{align*} x^{\prime \prime }&=50 \sin \left (5 t \right ) \\ x \left (0\right ) &= 8 \\ x^{\prime }\left (0\right ) &= -10 \\ \end{align*}

1.467

10772

7149

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

1.467

10773

8883

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

1.467

10774

10366

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

1.467

10775

12991

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

1.467

10776

22349

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

1.467

10777

25026

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

1.467

10778

2076

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

1.468

10779

5208

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

1.469

10780

13010

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

1.469

10781

15070

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

1.470

10782

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*}

1.471

10783

16216

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

1.471

10784

8164

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

1.472

10785

17728

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

1.472

10786

22342

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

1.472

10787

11365

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

1.473

10788

11745

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

1.473

10789

15812

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

1.473

10790

22022

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

1.473

10791

5507

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

1.474

10792

9968

\begin{align*} x \left (1-2 x \right ) y^{\prime \prime }-2 \left (2+x \right ) y^{\prime }+18 y&=0 \\ \end{align*}
Series expansion around \(x=0\).

1.474

10793

23267

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

1.474

10794

24931

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

1.474

10795

26

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

1.475

10796

5220

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

1.475

10797

15863

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

1.475

10798

16378

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

1.475

10799

11602

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

1.476

10800

15109

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

1.476