2.3.77 Problems 7601 to 7700

Table 2.685: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

7601

13413

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

0.678

7602

15087

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

0.678

7603

16140

\begin{align*} y^{\prime \prime }+3 y&=5 \delta \left (-2+t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

0.678

7604

17303

\begin{align*} y&=-y^{\prime } t +\frac {{y^{\prime }}^{5}}{5} \\ \end{align*}

0.678

7605

21278

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

0.678

7606

1917

\begin{align*} \left (2 x^{2}+3 x +1\right ) y^{\prime \prime }+\left (6+8 x \right ) y^{\prime }+4 y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.679

7607

2277

\begin{align*} y_{1}^{\prime }&=y_{1}+10 y_{2}-12 y_{3} \\ y_{2}^{\prime }&=2 y_{1}+2 y_{2}+3 y_{3} \\ y_{3}^{\prime }&=2 y_{1}-y_{2}+6 y_{3} \\ \end{align*}

0.679

7608

10951

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

0.679

7609

11718

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

0.679

7610

9704

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

0.680

7611

9838

\begin{align*} \left (x^{2}+4\right ) y^{\prime \prime }+2 y^{\prime } x -12 y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.680

7612

10708

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

0.680

7613

17900

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

0.680

7614

18113

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

0.680

7615

1548

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

0.681

7616

2643

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

0.681

7617

8113

\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}+\frac {9}{4}\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.681

7618

8541

\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (36 x^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.681

7619

9595

\begin{align*} y^{\prime \prime }+y^{\prime } x +y&=0 \\ y \left (1\right ) &= -6 \\ y^{\prime }\left (1\right ) &= 3 \\ \end{align*}
Series expansion around \(x=1\).

0.681

7620

10633

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

0.681

7621

15274

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

0.681

7622

16178

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

0.681

7623

18442

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

0.681

7624

20420

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

0.681

7625

21273

\begin{align*} t^{2} x^{\prime \prime }-3 t x^{\prime }+\left (4-t \right ) x&=0 \\ \end{align*}
Series expansion around \(t=0\).

0.681

7626

22237

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

0.681

7627

25377

\begin{align*} y_{1}^{\prime }&=2 y_{1}-y_{2}+{\mathrm e}^{t} \\ y_{2}^{\prime }&=3 y_{1}-2 y_{2}+{\mathrm e}^{t} \\ \end{align*}
With initial conditions
\begin{align*} y_{1} \left (0\right ) &= 1 \\ y_{2} \left (0\right ) &= 3 \\ \end{align*}

0.681

7628

2550

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

0.682

7629

5630

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

0.682

7630

10248

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

0.682

7631

10897

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

0.682

7632

5401

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

0.683

7633

6512

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

0.683

7634

8536

\begin{align*} 4 x^{2} y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}-25\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.683

7635

18612

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

0.683

7636

22

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

0.684

7637

2026

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

0.684

7638

2650

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

0.684

7639

2653

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

0.684

7640

5631

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

0.684

7641

8393

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

0.684

7642

10693

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

0.684

7643

13294

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

0.684

7644

14103

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

0.684

7645

20210

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

0.684

7646

21871

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

0.684

7647

22268

\begin{align*} x^{\prime }&=y \\ y^{\prime }&=8 x-2 y+{\mathrm e}^{t} \\ \end{align*}
With initial conditions
\begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= -4 \\ \end{align*}

0.684

7648

23618

\begin{align*} x^{\prime }&=7 x+4 y-4 z \\ y^{\prime }&=4 x-8 y-z \\ z^{\prime }&=-4 x-y-8 z \\ \end{align*}

0.684

7649

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*}

0.684

7650

2706

\begin{align*} x^{\prime }&=3 x-4 y+{\mathrm e}^{t} \\ y^{\prime }&=x-y+{\mathrm e}^{t} \\ \end{align*}
With initial conditions
\begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 1 \\ \end{align*}

0.685

7651

9371

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

0.685

7652

10294

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

0.685

7653

10354

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

0.685

7654

11730

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

0.685

7655

12933

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

0.685

7656

21225

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

0.685

7657

21492

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

0.685

7658

22274

\begin{align*} x_{1}^{\prime }&=x_{2} \\ x_{2}^{\prime }&=6 x_{1}+4 \\ \end{align*}
With initial conditions
\begin{align*} x_{1} \left (0\right ) &= 0 \\ x_{2} \left (0\right ) &= 0 \\ \end{align*}

0.685

7659

23568

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

0.685

7660

291

\begin{align*} y^{\prime \prime }-4 y^{\prime }+3 y&=0 \\ y \left (0\right ) &= 7 \\ y^{\prime }\left (0\right ) &= 11 \\ \end{align*}

0.686

7661

2251

\begin{align*} y_{1}^{\prime }&=3 y_{1}+2 y_{2}-2 y_{3} \\ y_{2}^{\prime }&=-2 y_{1}+7 y_{2}-2 y_{3} \\ y_{3}^{\prime }&=-10 y_{1}+10 y_{2}-5 y_{3} \\ \end{align*}

0.686

7662

9849

\begin{align*} y^{\prime \prime }+3 y^{\prime } x +7 y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.686

7663

10478

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

0.686

7664

13668

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

0.686

7665

17688

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

0.686

7666

20425

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

0.686

7667

20463

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

0.686

7668

22939

\begin{align*} x^{\prime }&=-12 x-7 y \\ y^{\prime }&=19 x+11 y \\ \end{align*}

0.686

7669

1921

\begin{align*} \left (3 x^{2}+8 x +4\right ) y^{\prime \prime }+\left (16+12 x \right ) y^{\prime }+6 y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.687

7670

6440

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

0.687

7671

7176

\begin{align*} x^{2} y^{\prime \prime }+\left (x^{2}+x \right ) y^{\prime }+\left (x -9\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.687

7672

7649

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

0.687

7673

19616

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

0.687

7674

511

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

0.688

7675

4041

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

0.688

7676

9851

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

0.688

7677

19060

\begin{align*} x_{1}^{\prime }&=x_{1}+x_{2} \\ x_{2}^{\prime }&=-14 x_{1}-5 x_{2}+x_{3} \\ x_{3}^{\prime }&=15 x_{1}+5 x_{2}-2 x_{3} \\ \end{align*}
With initial conditions
\begin{align*} x_{1} \left (0\right ) &= 5 \\ x_{2} \left (0\right ) &= 5 \\ x_{3} \left (0\right ) &= -4 \\ \end{align*}

0.688

7678

22727

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

0.688

7679

3859

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

0.689

7680

5575

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

0.689

7681

15975

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

0.689

7682

17337

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

0.689

7683

20946

\begin{align*} x^{\prime }&=5 x+3 y+1 \\ y^{\prime }&=-6 x-4 y+{\mathrm e}^{t} \\ \end{align*}
With initial conditions
\begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 0 \\ \end{align*}

0.689

7684

25349

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

0.689

7685

2735

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

0.690

7686

10703

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

0.690

7687

14368

\begin{align*} x^{\prime \prime }-x&=\delta \left (t -5\right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

0.690

7688

18447

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

0.690

7689

1420

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

0.691

7690

1435

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

0.691

7691

3239

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

0.691

7692

10562

\begin{align*} 4 x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }+x \left (-19 x^{2}+7\right ) y^{\prime }-\left (14 x^{2}+1\right ) y&=0 \\ \end{align*}

0.691

7693

11672

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

0.691

7694

11717

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

0.691

7695

20073

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

0.691

7696

20896

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

0.691

7697

20909

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

0.691

7698

23726

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

0.691

7699

25583

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

0.691

7700

3910

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

0.692