2.3.76 Problems 7501 to 7600

Table 2.725: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

7501

21945

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

Using Laplace transform method.

0.558

7502

24598

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

0.558

7503

25329

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

Series expansion around \(t=0\).

0.558

7504

977

\begin{align*} x_{1}^{\prime }&=5 x_{1}-9 x_{2} \\ x_{2}^{\prime }&=2 x_{1}-x_{2} \\ \end{align*}

0.559

7505

1812

\begin{align*} 4 x^{2} y^{\prime \prime }+\left (-8 x^{2}+4 x \right ) y^{\prime }+\left (4 x^{2}-4 x -1\right ) y&=4 \sqrt {x}\, {\mathrm e}^{x} \\ \end{align*}

0.559

7506

2370

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

0.559

7507

3994

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

Series expansion around \(x=0\).

0.559

7508

4476

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

0.559

7509

4590

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

Series expansion around \(x=0\).

0.559

7510

7667

\begin{align*} x^{\prime \prime }+42 x^{\prime }+x&=0 \\ x \left (0\right ) &= 1 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.559

7511

8192

\begin{align*} y^{\prime \prime }+4 y^{\prime }+6 y&=10 \\ \end{align*}

0.559

7512

8272

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

0.559

7513

8329

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

0.559

7514

8963

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

Series expansion around \(x=0\).

0.559

7515

9171

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

0.559

7516

9357

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

Series expansion around \(x=0\).

0.559

7517

9501

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

Series expansion around \(x=0\).

0.559

7518

9741

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

0.559

7519

14116

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

0.559

7520

16176

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

0.559

7521

16635

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

0.559

7522

16990

\begin{align*} y^{\prime }&=\frac {1}{x^{2}-16} \\ \end{align*}

0.559

7523

17424

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

0.559

7524

18686

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

0.559

7525

18692

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

With initial conditions

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

0.559

7526

18794

\begin{align*} y^{\prime \prime }+y^{\prime }+\frac {5 y}{4}&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}

0.559

7527

22668

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

0.559

7528

23751

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

Series expansion around \(x=0\).

0.559

7529

25041

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

0.559

7530

26510

\begin{align*} y^{\prime \prime }+25 y&=\cos \left (5 x \right ) \\ \end{align*}

0.559

7531

1797

\begin{align*} 36 y^{\prime }+36 y^{2}-12 y+1&=0 \\ \end{align*}

0.560

7532

7094

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

0.560

7533

7179

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

Series expansion around \(x=0\).

0.560

7534

8847

\begin{align*} x_{1}^{\prime }&=3 x_{1}-x_{2} \\ x_{2}^{\prime }&=16 x_{1}-5 x_{2} \\ \end{align*}

With initial conditions

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

0.560

7535

9173

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

0.560

7536

13161

\(\left [\begin {array}{cccc} 1 & 0 & 4 & 0 \\ 0 & 1 & 4 & 0 \\ 0 & 0 & 3 & 0 \\ 0 & 0 & 0 & 3 \end {array}\right ]\)

N/A

N/A

N/A

0.560

7537

14358

\begin{align*} x^{\prime \prime }+9 x&=\sin \left (3 t \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}

Using Laplace transform method.

0.560

7538

17829

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

0.560

7539

18113

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

0.560

7540

18684

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

0.560

7541

21208

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

0.560

7542

21211

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

With initial conditions

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

0.560

7543

21628

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

Series expansion around \(x=0\).

0.560

7544

27543

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

0.560

7545

1907

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

Series expansion around \(x=1\).

0.561

7546

2401

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

0.561

7547

7113

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

0.561

7548

12662

\begin{align*} y^{\prime \prime }&=\frac {\left (1+3 x \right ) y^{\prime }}{\left (x -1\right ) \left (x +1\right )}-\frac {36 \left (x +1\right )^{2} y}{\left (x -1\right )^{2} \left (5+3 x \right )^{2}} \\ \end{align*}

0.561

7549

12943

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

0.561

7550

16606

\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&=27 \,{\mathrm e}^{6 x} \\ \end{align*}

0.561

7551

19110

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

0.561

7552

19192

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

0.561

7553

19843

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

0.561

7554

23611

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

0.561

7555

25372

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

With initial conditions

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

0.561

7556

26389

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

0.561

7557

26513

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

0.561

7558

27100

\(\left [\begin {array}{ccc} 1 & -2 & 0 \\ 0 & 0 & 0 \\ -5 & 0 & 7 \end {array}\right ]\)

N/A

N/A

N/A

0.561

7559

7768

\begin{align*} y^{\prime \prime }-y^{\prime }+10 y&=20-{\mathrm e}^{2 x} \\ \end{align*}

0.562

7560

10251

\begin{align*} y^{\prime \prime }+2 y^{\prime }-24 y&=16-\left (x +2\right ) {\mathrm e}^{4 x} \\ \end{align*}

0.562

7561

17443

\begin{align*} y^{\prime \prime }-6 y^{\prime }+8 y&=-256 t^{3} \\ \end{align*}

0.562

7562

19260

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

0.562

7563

19659

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

0.562

7564

20009

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

0.562

7565

20521

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

0.562

7566

22108

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

0.562

7567

22238

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

Using Laplace transform method.

0.562

7568

22684

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

0.562

7569

25603

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

0.562

7570

26049

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

0.562

7571

1931

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

Series expansion around \(x=0\).

0.563

7572

2625

\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 \(t=0\).

0.563

7573

3489

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

0.563

7574

7657

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

Series expansion around \(x=0\).

0.563

7575

7794

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

0.563

7576

8490

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

Series expansion around \(x=0\).

0.563

7577

8901

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

0.563

7578

9607

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

Using Laplace transform method.

0.563

7579

12668

\begin{align*} y^{\prime \prime }&=\frac {\left (2 x^{2}+1\right ) y^{\prime }}{x^{3}}-\frac {\left (a \,x^{4}+10 x^{2}+1\right ) y}{4 x^{6}} \\ \end{align*}

0.563

7580

16617

\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&=18 x^{2}+3 x +4 \\ \end{align*}

0.563

7581

17405

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

0.563

7582

19515

\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=\frac {1}{1+{\mathrm e}^{-x}} \\ \end{align*}

0.563

7583

19755

\begin{align*} v^{\prime \prime }-6 v^{\prime }+13 v&={\mathrm e}^{-2 u} \\ \end{align*}

0.563

7584

20581

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

0.563

7585

21103

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

With initial conditions

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

0.563

7586

21657

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

Series expansion around \(x=0\).

0.563

7587

21920

\begin{align*} y^{\prime \prime }+4 y&=t \sin \left (t \right ) \\ y \left (0\right ) &= {\frac {7}{9}} \\ y^{\prime }\left (0\right ) &= -{\frac {5}{2}} \\ \end{align*}

Using Laplace transform method.

0.563

7588

23080

\begin{align*} x^{\prime \prime }-3 x^{\prime }+2 x&=5 \cos \left (t \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.563

7589

26113

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

0.563

7590

26727

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

0.563

7591

151

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

0.564

7592

7600

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

0.564

7593

8938

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

0.564

7594

16105

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

0.564

7595

19052

\begin{align*} x_{1}^{\prime }&=5 x_{1}-3 x_{2}-2 x_{3} \\ x_{2}^{\prime }&=8 x_{1}-5 x_{2}-4 x_{3} \\ x_{3}^{\prime }&=-4 x_{1}+3 x_{2}+3 x_{3} \\ \end{align*}

0.564

7596

19495

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

0.564

7597

20062

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

0.564

7598

20926

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

0.564

7599

22130

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

0.564

7600

24806

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

0.564