2.3.77 Problems 7601 to 7700

Table 2.727: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

7601

27558

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

0.564

7602

1399

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

Series expansion around \(x=0\).

0.565

7603

2832

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

0.565

7604

3215

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

0.565

7605

4174

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

0.565

7606

4528

\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }+4 y^{\prime }-4 y&=10 \,{\mathrm e}^{-t} \\ y \left (0\right ) &= 5 \\ y^{\prime }\left (0\right ) &= -2 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ \end{align*}

Using Laplace transform method.

0.565

7607

5882

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

0.565

7608

14412

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

0.565

7609

16102

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

0.565

7610

16631

\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&=10 \,{\mathrm e}^{3 x} \\ \end{align*}

0.565

7611

18796

\begin{align*} y^{\prime \prime }+8 y^{\prime }-9 y&=0 \\ y \left (1\right ) &= 1 \\ y^{\prime }\left (1\right ) &= 0 \\ \end{align*}

0.565

7612

19392

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

0.565

7613

19696

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

0.565

7614

20937

\begin{align*} x^{\prime }&=12 x-15 y \\ y^{\prime }&=4 x-4 y \\ \end{align*}

With initial conditions

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

0.565

7615

21315

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

0.565

7616

22247

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

Using Laplace transform method.

0.565

7617

24627

\begin{align*} y^{\prime \prime }-9 y&=18 x -162 x \,{\mathrm e}^{2 x} \\ \end{align*}

0.565

7618

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*}

0.566

7619

8909

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

0.566

7620

15761

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

0.566

7621

16655

\begin{align*} y^{\prime \prime }-4 y^{\prime }+20 y&={\mathrm e}^{4 x} \sin \left (2 x \right ) \\ \end{align*}

0.566

7622

17433

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

0.566

7623

18240

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

0.566

7624

18691

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

With initial conditions

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

0.566

7625

20653

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

0.566

7626

21146

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

0.566

7627

22292

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

0.566

7628

24726

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

0.566

7629

26551

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

0.566

7630

27099

\(\left [\begin {array}{ccc} 3 & 0 & 0 \\ 1 & -2 & -8 \\ 0 & -5 & 1 \end {array}\right ]\)

N/A

N/A

N/A

0.566

7631

27192

\begin{align*} x_{1}^{\prime }&=7 x_{1}-17 x_{2} \\ x_{2}^{\prime }&=2 x_{1}+x_{2} \\ \end{align*}

0.566

7632

27396

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

0.566

7633

4151

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

0.567

7634

9463

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

0.567

7635

10448

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

0.567

7636

16125

\begin{align*} y^{\prime \prime }+4 y^{\prime }+20 y&=3+2 \cos \left (2 t \right ) \\ \end{align*}

0.567

7637

16634

\begin{align*} y^{\prime \prime }-10 y^{\prime }+25 y&=6 \,{\mathrm e}^{5 x} \\ \end{align*}

0.567

7638

16741

\begin{align*} y^{\prime \prime }-12 y^{\prime }+36 y&=81 \,{\mathrm e}^{3 x} \\ \end{align*}

0.567

7639

21130

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

0.567

7640

21496

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

0.567

7641

21541

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

0.567

7642

22763

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

0.567

7643

24467

\begin{align*} y^{\prime \prime \prime }+5 y^{\prime \prime }+3 y^{\prime }-9 y&=0 \\ y \left (0\right ) &= -1 \\ y \left (1\right ) &= 0 \\ y \left (\infty \right ) &= 0 \\ \end{align*}

0.567

7644

24581

\begin{align*} y^{\prime \prime }+9 y&=18 x -3+20 \,{\mathrm e}^{x} \\ \end{align*}

0.567

7645

24748

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

0.567

7646

27565

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

0.567

7647

2562

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

0.568

7648

4562

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

0.568

7649

9245

\begin{align*} y^{\prime \prime }+3 y^{\prime }-10 y&=6 \,{\mathrm e}^{4 x} \\ \end{align*}

0.568

7650

16082

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

0.568

7651

20061

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

0.568

7652

24539

\begin{align*} 4 y+y^{\prime \prime }&=15 \,{\mathrm e}^{x}-8 x \\ \end{align*}

0.568

7653

26434

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

0.568

7654

26557

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

0.568

7655

1024

\begin{align*} x_{1}^{\prime }&=x_{1} \\ x_{2}^{\prime }&=18 x_{1}+7 x_{2}+4 x_{3} \\ x_{3}^{\prime }&=-27 x_{1}-9 x_{2}-5 x_{3} \\ \end{align*}

0.569

7656

2391

\begin{align*} 9 y^{\prime \prime }-12 y^{\prime }+4 y&=0 \\ y \left (\pi \right ) &= 0 \\ y^{\prime }\left (\pi \right ) &= 2 \\ \end{align*}

0.569

7657

5412

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

0.569

7658

6768

\begin{align*} 12 y^{\prime \prime }+8 x y^{\prime \prime \prime }+x^{2} y^{\prime \prime \prime \prime }&=0 \\ \end{align*}

0.569

7659

7210

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

0.569

7660

7215

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

0.569

7661

7785

\begin{align*} y^{\prime \prime }-6 y^{\prime }+25 y&=2 \sin \left (\frac {t}{2}\right )-\cos \left (\frac {t}{2}\right ) \\ \end{align*}

0.569

7662

8813

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

0.569

7663

9442

\begin{align*} y^{\prime \prime }+5 y^{\prime }+6 y&=5 \,{\mathrm e}^{3 t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

Using Laplace transform method.

0.569

7664

9831

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

Series expansion around \(x=0\).

0.569

7665

12890

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

0.569

7666

14206

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

0.569

7667

15667

\begin{align*} y^{\prime \prime }+9 y&=27 x +18 \\ y \left (0\right ) &= 23 \\ y^{\prime }\left (0\right ) &= 21 \\ \end{align*}

0.569

7668

16104

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

0.569

7669

22031

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

0.569

7670

23496

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

0.569

7671

24600

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

0.569

7672

26452

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

0.569

7673

659

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

0.570

7674

2428

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

Series expansion around \(t=0\).

0.570

7675

16983

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

0.570

7676

17404

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

0.570

7677

19839

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

0.570

7678

20708

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

0.570

7679

20765

\begin{align*} 2 x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (3+7 x \right ) y^{\prime }-3 y&=x^{2} \\ \end{align*}

0.570

7680

24671

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

0.570

7681

24695

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

0.570

7682

25181

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

0.570

7683

25997

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

Using Laplace transform method.

0.570

7684

27555

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

0.570

7685

2288

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

0.571

7686

2748

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

0.571

7687

4122

\begin{align*} y^{\prime \prime }-4 y^{\prime }+13 y&=0 \\ \end{align*}

0.571

7688

9381

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

Series expansion around \(x=0\).

0.571

7689

10057

\begin{align*} x^{\prime }&=9 x+4 y \\ y^{\prime }&=-6 x-y \\ z^{\prime }&=6 x+4 y+3 z \\ \end{align*}

0.571

7690

10505

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

0.571

7691

14390

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

0.571

7692

14406

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

With initial conditions

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

0.571

7693

23088

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

0.571

7694

24548

\begin{align*} 5 y+4 y^{\prime }+y^{\prime \prime }&=50 x +13 \,{\mathrm e}^{3 x} \\ \end{align*}

0.571

7695

24722

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

0.571

7696

26682

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

0.571

7697

27125

\(\left [\begin {array}{ccc} 0 & 1 & 1 \\ 1 & 2 & 0 \\ 0 & 0 & 3 \end {array}\right ]\)

N/A

N/A

N/A

0.571

7698

1448

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

0.572

7699

1840

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

Series expansion around \(x=0\).

0.572

7700

1871

\begin{align*} \left (3 x^{2}+6 x +5\right ) y^{\prime \prime }+9 \left (x +1\right ) y^{\prime }+3 y&=0 \\ \end{align*}

Series expansion around \(x=-1\).

0.572