2.3.128 Problems 12701 to 12800

Table 2.829: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

12701

12853

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

1.112

12702

16391

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

1.112

12703

19850

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

1.112

12704

21141

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

1.112

12705

25384

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

With initial conditions

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

1.112

12706

26619

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

1.112

12707

2663

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

Series expansion around \(t=0\).

1.113

12708

20167

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

1.113

12709

22833

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

Series expansion around \(x=0\).

1.113

12710

3975

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

Using Laplace transform method.

1.114

12711

14783

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

1.114

12712

4546

\begin{align*} 3 x^{\prime }+2 x+y^{\prime }-6 y&=5 \,{\mathrm e}^{t} \\ 4 x^{\prime }+2 x+y^{\prime }-8 y&=5 \,{\mathrm e}^{t}+2 t -3 \\ \end{align*}

1.115

12713

7629

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

Series expansion around \(x=0\).

1.115

12714

8519

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

Series expansion around \(x=0\).

1.115

12715

14318

\begin{align*} x^{\prime \prime }+\frac {x^{\prime }}{100}+4 x&=\cos \left (2 t \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}

1.115

12716

16876

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

Series expansion around \(x=0\).

1.115

12717

18415

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

1.115

12718

22692

\begin{align*} y^{\prime \prime }+16 y&=5 \sin \left (x \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

1.115

12719

23549

\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=\frac {{\mathrm e}^{2 x}}{\left (1+{\mathrm e}^{x}\right )^{2}} \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= {\frac {5}{2}} \\ \end{align*}

1.115

12720

26041

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

1.115

12721

1338

\begin{align*} y^{\prime \prime }+9 y&=9 \sec \left (3 t \right )^{2} \\ \end{align*}

1.116

12722

2362

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

1.116

12723

2661

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

Series expansion around \(t=0\).

1.116

12724

3973

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

Using Laplace transform method.

1.116

12725

7566

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

1.116

12726

8250

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

1.116

12727

14677

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

1.116

12728

16410

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

1.116

12729

19420

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

1.116

12730

20771

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

1.116

12731

20908

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

Series expansion around \(x=0\).

1.116

12732

26372

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

1.116

12733

2011

\begin{align*} 16 x^{2} y^{\prime \prime }+4 x \left (2 x^{2}+x +6\right ) y^{\prime }+\left (18 x^{2}+5 x +1\right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

1.117

12734

4456

\begin{align*} y^{\prime \prime }-8 y^{\prime }+17 y&={\mathrm e}^{4 x} \left (x^{2}-3 x \sin \left (x \right )\right ) \\ \end{align*}

1.117

12735

11782

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

1.117

12736

14655

\begin{align*} 4 y+y^{\prime \prime }&=8 \sin \left (2 x \right ) \\ y \left (0\right ) &= 6 \\ y^{\prime }\left (0\right ) &= 8 \\ \end{align*}

1.117

12737

15075

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

1.117

12738

15808

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

1.117

12739

22331

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

1.117

12740

248

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

1.118

12741

6374

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

1.118

12742

6438

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

1.118

12743

8999

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

Series expansion around \(x=0\).

1.118

12744

9396

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

Series expansion around \(x=0\).

1.118

12745

12885

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

1.118

12746

14117

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

1.118

12747

14687

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

1.118

12748

16498

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

1.118

12749

17531

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

1.118

12750

18097

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

1.118

12751

22216

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

Series expansion around \(x=0\).

1.118

12752

22419

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

1.118

12753

24804

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

1.118

12754

26563

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

1.118

12755

4067

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

Series expansion around \(x=0\).

1.119

12756

8558

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

Series expansion around \(x=0\).

1.119

12757

25681

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

1.119

12758

2654

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

Series expansion around \(t=0\).

1.120

12759

14306

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

1.120

12760

26187

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

1.120

12761

6178

\begin{align*} \left (4 x +3\right ) y+16 x^{2} y^{\prime \prime }&=0 \\ \end{align*}

1.121

12762

22214

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

Series expansion around \(x=0\).

1.121

12763

26645

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

1.121

12764

16815

\begin{align*} y^{\prime \prime }+4 y^{\prime }-12 y&=\delta \left (-3+t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

Using Laplace transform method.

1.122

12765

17793

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

Series expansion around \(x=0\).

1.122

12766

17794

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

Series expansion around \(x=0\).

1.122

12767

22904

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

With initial conditions

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

1.122

12768

27369

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

1.122

12769

4478

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

1.123

12770

19968

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

1.123

12771

2772

\begin{align*} x_{1}^{\prime }&=3 x_{1}+2 x_{2}+4 x_{3}+2 \,{\mathrm e}^{8 t} \\ x_{2}^{\prime }&=2 x_{1}+2 x_{3}+{\mathrm e}^{8 t} \\ x_{3}^{\prime }&=4 x_{1}+2 x_{2}+3 x_{3}+2 \,{\mathrm e}^{8 t} \\ \end{align*}

1.124

12772

12470

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

1.124

12773

14148

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

1.124

12774

14986

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

With initial conditions

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

1.124

12775

22919

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

With initial conditions

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

1.124

12776

2765

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

1.125

12777

6779

\begin{align*} \operatorname {A4} y+\operatorname {A3} x y^{\prime }+\operatorname {A2} \,x^{2} y^{\prime \prime }+\operatorname {A1} \,x^{3} y^{\prime \prime \prime }+x^{4} y^{\prime \prime \prime \prime }&=0 \\ \end{align*}

1.125

12778

9323

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

1.125

12779

11721

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

1.125

12780

11894

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

1.125

12781

15092

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

1.125

12782

20793

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

1.125

12783

21162

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

1.125

12784

2026

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

Series expansion around \(x=0\).

1.126

12785

8647

\begin{align*} y^{\prime \prime }+4 y&=\delta \left (t -\pi \right ) \\ y \left (0\right ) &= 8 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

Using Laplace transform method.

1.126

12786

17492

\begin{align*} y^{\prime \prime }+12 y^{\prime }+37 y&={\mathrm e}^{-6 t} \csc \left (t \right ) \\ \end{align*}

1.126

12787

17610

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

1.126

12788

18869

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

1.126

12789

14059

\begin{align*} {y^{\prime }}^{3}-4 x y y^{\prime }+8 y^{2}&=0 \\ \end{align*}

1.127

12790

14680

\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=\frac {{\mathrm e}^{-3 x}}{x^{3}} \\ \end{align*}

1.127

12791

18233

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

1.127

12792

25349

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

Series expansion around \(t=0\).

1.127

12793

95

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

1.128

12794

645

\begin{align*} x_{1}^{\prime }&=5 x_{1}+5 x_{2}+2 x_{3} \\ x_{2}^{\prime }&=-6 x_{1}-6 x_{2}-5 x_{3} \\ x_{3}^{\prime }&=6 x_{1}+6 x_{2}+5 x_{3} \\ \end{align*}

1.128

12795

6664

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

1.128

12796

7731

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

1.128

12797

16714

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

1.128

12798

21905

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

Series expansion around \(x=0\).

1.128

12799

3879

\begin{align*} x_{1}^{\prime }&=2 x_{1}-3 x_{2}+34 \sin \left (t \right ) \\ x_{2}^{\prime }&=-4 x_{1}-2 x_{2}+17 \cos \left (t \right ) \\ \end{align*}

1.129

12800

7036

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

1.129