2.3.75 Problems 7401 to 7500

Table 2.699: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

7401

3110

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

0.552

7402

6251

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

0.552

7403

8075

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

0.552

7404

9066

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

0.552

7405

9249

\begin{align*} y^{\prime \prime }-y^{\prime }-6 y&=20 \,{\mathrm e}^{-2 x} \\ \end{align*}

0.552

7406

10069

\begin{align*} z^{\prime \prime }+3 z^{\prime }+2 z&=24 \,{\mathrm e}^{-3 t}-24 \,{\mathrm e}^{-4 t} \\ \end{align*}

0.552

7407

10949

\begin{align*} \left (3 x^{2}+x +1\right ) y^{\prime \prime }+\left (2+15 x \right ) y^{\prime }+12 y&=0 \\ \end{align*}

0.552

7408

17688

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

0.552

7409

19026

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

0.552

7410

19499

\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=14 \sin \left (2 x \right )-18 \cos \left (2 x \right ) \\ \end{align*}

0.552

7411

20368

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

0.552

7412

509

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

0.553

7413

3111

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

0.553

7414

3813

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

0.553

7415

5800

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

0.553

7416

7142

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

0.553

7417

7233

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

0.553

7418

9357

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

0.553

7419

14122

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

0.553

7420

17757

\begin{align*} y^{\prime \prime }+7 y^{\prime }+12 y&=3 t^{2} {\mathrm e}^{-4 t} \\ \end{align*}

0.553

7421

18129

\begin{align*} y^{\prime \prime }-4 y^{\prime }+3 y&=0 \\ y \left (0\right ) &= 6 \\ y^{\prime }\left (0\right ) &= 10 \\ \end{align*}

0.553

7422

18451

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

0.553

7423

19495

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

0.553

7424

22294

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

0.553

7425

23633

\begin{align*} y^{\prime }-3 y&=13 \cos \left (2 t \right ) \\ y \left (0\right ) &= -1 \\ \end{align*}
Using Laplace transform method.

0.553

7426

23795

\begin{align*} x^{\prime }&=5 x-6 y+1 \\ y^{\prime }&=6 x-7 y+1 \\ \end{align*}

0.553

7427

24756

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

0.553

7428

2559

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

0.554

7429

2624

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

0.554

7430

3124

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

0.554

7431

3195

\begin{align*} y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime }+9 y^{\prime \prime }&=\sin \left (3 x \right )+x \,{\mathrm e}^{x} \\ \end{align*}

0.554

7432

7583

\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=0 \\ \end{align*}

0.554

7433

9504

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

0.554

7434

9609

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

0.554

7435

15831

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

0.554

7436

16012

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

0.554

7437

16743

\begin{align*} y^{\prime \prime }-12 y^{\prime }+36 y&=3 x \,{\mathrm e}^{6 x}-2 \,{\mathrm e}^{6 x} \\ \end{align*}

0.554

7438

22327

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

0.554

7439

1908

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

0.555

7440

3817

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

0.555

7441

9246

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

0.555

7442

11670

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

0.555

7443

12960

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

0.555

7444

13162

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

N/A

N/A

N/A

0.555

7445

14138

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

0.555

7446

15752

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

0.555

7447

19497

\begin{align*} y^{\prime \prime }-2 y^{\prime }+5 y&=25 x^{2}+12 \\ \end{align*}

0.555

7448

20935

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

0.555

7449

21541

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

0.555

7450

24437

\begin{align*} y^{\prime \prime }+3 y^{\prime }-10 y&=0 \\ y \left (0\right ) &= 0 \\ y \left (2\right ) &= 1 \\ \end{align*}

0.555

7451

1359

\begin{align*} u^{\prime \prime }+\frac {u^{\prime }}{8}+4 u&=3 \cos \left (6 t \right ) \\ u \left (0\right ) &= 2 \\ u^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.556

7452

1404

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

0.556

7453

1904

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

0.556

7454

2161

\begin{align*} y^{\prime \prime \prime \prime }+8 y^{\prime \prime \prime }+24 y^{\prime \prime }+32 y^{\prime }&=-16 \,{\mathrm e}^{-2 x} \left (-x^{3}+x^{2}+x +1\right ) \\ \end{align*}

0.556

7455

3923

\begin{align*} x_{1}^{\prime }&=7 x_{1}-2 x_{2} \\ x_{2}^{\prime }&=x_{1}+4 x_{2} \\ \end{align*}

0.556

7456

8817

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

0.556

7457

8967

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

0.556

7458

14623

\begin{align*} -4 y-3 y^{\prime }+y^{\prime \prime }&=16 x -12 \,{\mathrm e}^{2 x} \\ \end{align*}

0.556

7459

16108

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

0.556

7460

16509

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

0.556

7461

17424

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

0.556

7462

17822

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

0.556

7463

19654

\begin{align*} x^{\prime }&=5 x+2 y \\ y^{\prime }&=-17 x-5 y \\ \end{align*}

0.556

7464

19878

\begin{align*} V^{\prime \prime }+\frac {2 V^{\prime }}{r}&=0 \\ \end{align*}

0.556

7465

22622

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

0.556

7466

23833

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

0.556

7467

24047

\begin{align*} y^{\prime \prime \prime }+y&={\mathrm e}^{x} \sin \left (x \right ) \\ \end{align*}
Using Laplace transform method.

0.556

7468

24104

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

0.556

7469

25295

\begin{align*} y^{\prime }+5 y&=\left \{\begin {array}{cc} -5 & 0\le t <1 \\ 5 & 1\le t \end {array}\right . \\ y \left (0\right ) &= 1 \\ \end{align*}
Using Laplace transform method.

0.556

7470

25385

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

0.556

7471

25546

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

0.556

7472

26012

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

0.556

7473

26578

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

0.556

7474

474

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

0.557

7475

481

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

0.557

7476

2593

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

0.557

7477

3188

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

0.557

7478

9664

\begin{align*} x^{\prime }&=3 x-4 y \\ y^{\prime }&=4 x-7 y \\ \end{align*}

0.557

7479

10027

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

0.557

7480

14107

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

0.557

7481

17449

\begin{align*} y^{\prime \prime }-y^{\prime }-20 y&=-2 \,{\mathrm e}^{t} \\ \end{align*}

0.557

7482

17829

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

0.557

7483

20148

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

0.557

7484

20181

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

0.557

7485

24646

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

0.557

7486

245

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

0.558

7487

3344

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

0.558

7488

3835

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

0.558

7489

4069

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

0.558

7490

5512

\begin{align*} x^{2} {y^{\prime }}^{2}-5 y y^{\prime } x +6 y^{2}&=0 \\ \end{align*}

0.558

7491

6289

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

0.558

7492

6366

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

0.558

7493

9262

\begin{align*} y^{\prime \prime }-2 y^{\prime }-3 y&=64 x \,{\mathrm e}^{-x} \\ \end{align*}

0.558

7494

9765

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

0.558

7495

10237

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

0.558

7496

16566

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

0.558

7497

24545

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

0.558

7498

2571

\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*}

0.559

7499

3741

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

0.559

7500

8340

\begin{align*} 1+{\mathrm e}^{3 x} y^{\prime }&=0 \\ \end{align*}

0.559