2.3.148 Problems 14701 to 14800

Table 2.827: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

14701

13669

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

1.097

14702

20173

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

1.097

14703

21676

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

1.097

14704

20037

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

1.098

14705

21742

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

1.098

14706

22226

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

1.098

14707

1265

\begin{align*} y^{\prime \prime }-y&=0 \\ y \left (0\right ) &= {\frac {5}{4}} \\ y^{\prime }\left (0\right ) &= -{\frac {3}{4}} \\ \end{align*}

1.099

14708

2635

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

1.099

14709

9915

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

1.099

14710

15412

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

1.099

14711

15814

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

1.099

14712

18733

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

1.099

14713

650

\begin{align*} x_{1}^{\prime }&=4 x_{1}+x_{2}+x_{3}+7 x_{4} \\ x_{2}^{\prime }&=x_{1}+4 x_{2}+10 x_{3}+x_{4} \\ x_{3}^{\prime }&=x_{1}+10 x_{2}+4 x_{3}+x_{4} \\ x_{4}^{\prime }&=7 x_{1}+x_{2}+x_{3}+4 x_{4} \\ \end{align*}
With initial conditions
\begin{align*} x_{1} \left (0\right ) &= 3 \\ x_{2} \left (0\right ) &= 1 \\ x_{3} \left (0\right ) &= 1 \\ x_{4} \left (0\right ) &= 3 \\ \end{align*}

1.100

14714

10046

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

1.100

14715

3564

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

1.101

14716

14696

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

1.101

14717

19605

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

1.101

14718

21152

\begin{align*} x^{\prime \prime }+9 x&=\sin \left (t \right )+\sin \left (3 t \right ) \\ \end{align*}

1.101

14719

2272

\begin{align*} y_{1}^{\prime }&=-7 y_{1}-4 y_{2}+4 y_{3} \\ y_{2}^{\prime }&=y_{1}+y_{3} \\ y_{3}^{\prime }&=-9 y_{1}-5 y_{2}+6 y_{3} \\ \end{align*}
With initial conditions
\begin{align*} y_{1} \left (0\right ) &= -6 \\ y_{2} \left (0\right ) &= 9 \\ y_{3} \left (0\right ) &= -1 \\ \end{align*}

1.102

14720

5715

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

1.102

14721

25202

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

1.102

14722

7982

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

1.103

14723

14938

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

1.103

14724

24979

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

1.103

14725

1534

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

1.104

14726

2410

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

1.104

14727

9242

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

1.104

14728

20461

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

1.104

14729

21289

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

1.104

14730

21955

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

1.104

14731

22106

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

1.104

14732

22490

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

1.104

14733

22589

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

1.104

14734

6182

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

1.105

14735

6247

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

1.105

14736

7373

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

1.105

14737

17306

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

1.105

14738

21621

\begin{align*} \theta ^{\prime \prime }+4 \theta &=15 \cos \left (3 t \right ) \\ \theta \left (0\right ) &= 0 \\ \theta ^{\prime }\left (0\right ) &= 0 \\ \end{align*}

1.105

14739

21677

\begin{align*} 18 x^{2} y^{\prime \prime }+3 x \left (x +5\right ) y^{\prime }-\left (10 x +1\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

1.105

14740

24393

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

1.105

14741

9869

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

1.106

14742

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 \(x=0\).

1.106

14743

20569

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

1.106

14744

22481

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

1.106

14745

5677

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

1.107

14746

9325

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

1.107

14747

15399

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

1.107

14748

2544

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

1.108

14749

2608

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

1.108

14750

2835

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

1.108

14751

7319

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

1.108

14752

17386

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

1.108

14753

17852

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

1.108

14754

25200

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

1.108

14755

15757

\begin{align*} y_{1}^{\prime }&=5 y_{1}-5 y_{2}-5 y_{3} \\ y_{2}^{\prime }&=-y_{1}+4 y_{2}+2 y_{3} \\ y_{3}^{\prime }&=3 y_{1}-5 y_{2}-3 y_{3} \\ \end{align*}

1.109

14756

15844

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

1.109

14757

21674

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

1.109

14758

22564

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

1.109

14759

23598

\begin{align*} x^{\prime }&=a \left (b -x\right )-c f y \\ y^{\prime }&=d \left (x-y\right )-c f y-a y \\ \end{align*}
With initial conditions
\begin{align*} x \left (0\right ) &= b \\ y \left (0\right ) &= \frac {d b}{a +d} \\ \end{align*}

1.109

14760

16947

\begin{align*} x^{\prime }&=4 x+3 y+5 \operatorname {Heaviside}\left (t -2\right ) \\ y^{\prime }&=x+6 y+17 \operatorname {Heaviside}\left (t -2\right ) \\ \end{align*}
With initial conditions
\begin{align*} x \left (0\right ) &= 0 \\ y \left (0\right ) &= 0 \\ \end{align*}

1.110

14761

17321

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

1.110

14762

2757

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

1.111

14763

11357

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

1.111

14764

16361

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

1.111

14765

808

\begin{align*} y^{\prime \prime }-9 y&=0 \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 15 \\ \end{align*}

1.112

14766

7150

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

1.112

14767

8145

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

1.112

14768

8444

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

1.112

14769

10545

\begin{align*} x^{2} \left (10 x^{2}+x +5\right ) y^{\prime \prime }+x \left (48 x^{2}+3 x +4\right ) y^{\prime }+\left (36 x^{2}+x \right ) y&=0 \\ \end{align*}

1.112

14770

13074

\begin{align*} 4 x^{\prime }+9 y^{\prime }+2 x+31 y&={\mathrm e}^{t} \\ 3 x^{\prime }+7 y^{\prime }+x+24 y&=3 \\ \end{align*}

1.112

14771

16520

\begin{align*} y^{\prime \prime }+16 y&=0 \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= 12 \\ \end{align*}

1.112

14772

20648

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

1.112

14773

22477

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

1.112

14774

22588

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

1.112

14775

9236

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

1.113

14776

18643

\begin{align*} x^{\prime }&=-\frac {x}{4}-\frac {3 y}{4}+8 \\ y^{\prime }&=\frac {x}{2}+y-\frac {23}{2} \\ \end{align*}

1.113

14777

16470

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

1.114

14778

19610

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

1.114

14779

20793

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

1.114

14780

2592

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

1.115

14781

10033

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

1.115

14782

12578

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

1.115

14783

21124

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

1.115

14784

23370

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

1.115

14785

25002

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

1.115

14786

3306

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

1.116

14787

15296

\begin{align*} x^{\prime }&=9 x-3 y-6 t \\ y^{\prime }&=-x+11 y+10 t \\ \end{align*}

1.116

14788

7036

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

1.117

14789

8002

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

1.117

14790

13011

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

1.117

14791

20566

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

1.117

14792

22504

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

1.117

14793

3275

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

1.118

14794

3594

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

1.118

14795

4531

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

1.118

14796

6708

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

1.118

14797

12306

\begin{align*} y^{\prime \prime }-\left (n \left (n +1\right ) k^{2} \operatorname {JacobiSN}\left (x , k\right )^{2}+b \right ) y&=0 \\ \end{align*}

1.118

14798

13954

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

1.118

14799

18292

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

1.118

14800

20860

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

1.118