2.3.38 Problems 3701 to 3800

Table 2.649: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

3701

7457

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

0.302

3702

7977

\begin{align*} y^{\prime \prime }+2 y^{\prime }-15 y&=0 \\ \end{align*}

0.302

3703

9113

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

0.302

3704

10941

\begin{align*} \left (x^{2}-8 x +14\right ) y^{\prime \prime }-8 \left (x -4\right ) y^{\prime }+20 y&=0 \\ \end{align*}

0.302

3705

20915

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

Using Laplace transform method.

0.302

3706

2200

\begin{align*} y^{\prime \prime \prime \prime }-5 y^{\prime \prime }+4 y&=-12 \,{\mathrm e}^{x}+6 \,{\mathrm e}^{-x}+10 \cos \left (x \right ) \\ \end{align*}

0.303

3707

3065

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

0.303

3708

3696

\begin{align*} y^{\prime \prime }+7 y^{\prime }+10 y&=0 \\ \end{align*}

0.303

3709

7821

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

Using Laplace transform method.

0.303

3710

7843

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

Series expansion around \(x=0\).

0.303

3711

13178

\(\left [\begin {array}{cc} 6 & -10 \\ 2 & -3 \end {array}\right ]\)

N/A

N/A

N/A

0.303

3712

15989

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

0.303

3713

19272

\begin{align*} 6 y-5 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}

0.303

3714

19732

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

0.303

3715

23049

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

0.303

3716

23807

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

0.303

3717

3788

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

0.304

3718

10654

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

0.304

3719

10706

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

0.304

3720

13146

\(\left [\begin {array}{cc} 8 & -10 \\ 2 & -1 \end {array}\right ]\)

N/A

N/A

N/A

0.304

3721

13148

\(\left [\begin {array}{cc} 19 & -10 \\ 21 & -10 \end {array}\right ]\)

N/A

N/A

N/A

0.304

3722

15104

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

0.304

3723

23319

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

0.304

3724

25514

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

0.304

3725

26124

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

0.304

3726

27642

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

0.304

3727

27766

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

Series expansion around \(x=0\).

0.304

3728

274

\begin{align*} 2 y^{\prime \prime }-7 y^{\prime }+3 y&=0 \\ \end{align*}

0.305

3729

7819

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

Using Laplace transform method.

0.305

3730

10572

\begin{align*} 4 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+4 x \left (6 x^{2}+1\right ) y^{\prime }-\left (-25 x^{2}+1\right ) y&=0 \\ \end{align*}

0.305

3731

11008

\begin{align*} x^{2} \left (2 x +1\right ) y^{\prime \prime }+x \left (3 x^{2}+14 x +5\right ) y^{\prime }+\left (12 x^{2}+18 x +4\right ) y&=0 \\ \end{align*}

0.305

3732

11295

\begin{align*} y^{\prime \prime }&=\left (-\frac {3}{16 x^{2}}-\frac {2}{9 \left (x -1\right )^{2}}+\frac {3}{16 \left (x -1\right ) x}\right ) y \\ \end{align*}

0.305

3733

13149

\(\left [\begin {array}{cc} 13 & -15 \\ 6 & -6 \end {array}\right ]\)

N/A

N/A

N/A

0.305

3734

14273

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

0.305

3735

14844

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

0.305

3736

16053

\(\left [\begin {array}{cc} 0 & 1 \\ 2 & 0 \end {array}\right ]\)

N/A

N/A

N/A

0.305

3737

23024

\begin{align*} z^{\prime \prime }-7 z^{\prime }-13 z&=0 \\ \end{align*}

0.305

3738

27145

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

0.305

3739

27197

\begin{align*} x_{1}^{\prime }&=-6 x_{1}-7 x_{2} \\ x_{2}^{\prime }&=7 x_{1}-20 x_{2} \\ \end{align*}

0.305

3740

27641

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

0.305

3741

1055

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

Series expansion around \(x=0\).

0.306

3742

3063

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

0.306

3743

3790

\begin{align*} x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y&=8 x^{4} \\ \end{align*}

0.306

3744

7052

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

0.306

3745

10549

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

0.306

3746

10736

\begin{align*} u^{\prime \prime }+\frac {4 u^{\prime }}{x}+a^{2} u&=0 \\ \end{align*}

0.306

3747

11268

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

0.306

3748

16054

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

0.306

3749

16785

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

Using Laplace transform method.

0.306

3750

18745

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

0.306

3751

19580

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

Series expansion around \(x=0\).

0.306

3752

20916

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

Using Laplace transform method.

0.306

3753

23277

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

0.306

3754

23614

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

0.306

3755

23766

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

0.306

3756

1255

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

0.307

3757

7055

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

0.307

3758

10561

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

0.307

3759

10656

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

0.307

3760

10722

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

0.307

3761

10805

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

0.307

3762

11161

\begin{align*} u^{\prime \prime }+\frac {4 u^{\prime }}{x}+a^{2} u&=0 \\ \end{align*}

0.307

3763

12641

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

0.307

3764

7061

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

0.308

3765

10026

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

0.308

3766

14956

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

0.308

3767

16493

\begin{align*} 3 y^{\prime \prime }+7 y^{\prime }-6 y&=0 \\ \end{align*}

0.308

3768

16762

\begin{align*} y^{\prime \prime }+4 y&=20 \,{\mathrm e}^{4 t} \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 12 \\ \end{align*}

Using Laplace transform method.

0.308

3769

23520

\begin{align*} e i u^{\prime \prime \prime \prime }&=\sinh \left (x \right ) \\ \end{align*}

0.308

3770

23593

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

0.308

3771

24412

\begin{align*} y^{\prime \prime }-y^{\prime }-6 y&=0 \\ \end{align*}

0.308

3772

27526

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

0.308

3773

27764

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

Series expansion around \(x=0\).

0.308

3774

1311

\begin{align*} 25 y^{\prime \prime }-20 y^{\prime }+4 y&=0 \\ \end{align*}

0.309

3775

8184

\begin{align*} 2 y^{\prime \prime }+7 y^{\prime }-4 y&=0 \\ \end{align*}

0.309

3776

11025

\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*}

0.309

3777

14629

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

0.309

3778

16036

\begin{align*} y^{\prime \prime }-y^{\prime }-12 y&=0 \\ \end{align*}

0.309

3779

16421

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

0.309

3780

17777

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

0.309

3781

20030

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

0.309

3782

21713

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

Using Laplace transform method.

0.309

3783

21952

\begin{align*} 5 {b^{\prime \prime \prime \prime }}^{5}+7 {b^{\prime }}^{10}+b^{7}-b^{5}&=p \\ \end{align*}

0.309

3784

23717

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

Series expansion around \(x=0\).

0.309

3785

24052

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

Using Laplace transform method.

0.309

3786

26005

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

Series expansion around \(x=0\).

0.309

3787

26020

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

Series expansion around \(x=0\).

0.309

3788

26099

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

0.309

3789

26940

\begin{align*} y^{\prime \prime }+6 y^{\prime }-40 y&=0 \\ \end{align*}

0.309

3790

27742

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

0.309

3791

852

\begin{align*} y^{\prime \prime }-6 y^{\prime }+13 y&=0 \\ \end{align*}

0.310

3792

1281

\begin{align*} y^{\prime \prime }+y^{\prime }+\frac {5 y}{4}&=0 \\ \end{align*}

0.310

3793

5018

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

0.310

3794

10480

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

0.310

3795

10581

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

0.310

3796

10908

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

0.310

3797

12294

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

0.310

3798

13145

\(\left [\begin {array}{cc} 7 & -6 \\ 12 & -10 \end {array}\right ]\)

N/A

N/A

N/A

0.310

3799

14424

\begin{align*} x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-10 x y^{\prime }-8 y&=0 \\ \end{align*}

0.310

3800

16789

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

Using Laplace transform method.

0.310