2.3.57 Problems 5601 to 5700

Table 2.687: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

5601

24695

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

0.370

5602

660

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

0.371

5603

2462

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

Series expansion around \(t=0\).

0.371

5604

4136

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

0.371

5605

4162

\begin{align*} 25 y^{\prime \prime }-30 y^{\prime }+9 y&=0 \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= 2 \\ \end{align*}

0.371

5606

6684

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

0.371

5607

7075

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

0.371

5608

8034

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

0.371

5609

10930

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

0.371

5610

11097

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

0.371

5611

14134

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

0.371

5612

14581

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

0.371

5613

14924

\begin{align*} 2 z^{\prime \prime }+7 z^{\prime }-4 z&=0 \\ z \left (0\right ) &= 0 \\ z^{\prime }\left (0\right ) &= 9 \\ \end{align*}

0.371

5614

16712

\begin{align*} y^{\prime \prime }-9 y^{\prime }+14 y&=0 \\ \end{align*}

0.371

5615

17582

\begin{align*} y^{\prime \prime \prime \prime }+9 y^{\prime \prime }&=1 \\ \end{align*}

0.371

5616

19472

\begin{align*} 4 y^{\prime \prime }-8 y^{\prime }+7 y&=0 \\ \end{align*}

0.371

5617

21217

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

With initial conditions

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

0.371

5618

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.

0.371

5619

24748

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

0.371

5620

26184

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

0.371

5621

26414

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

0.371

5622

334

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

0.372

5623

625

\begin{align*} x_{1}^{\prime }&=6 x_{1}-7 x_{2} \\ x_{2}^{\prime }&=x_{1}-2 x_{2} \\ \end{align*}

0.372

5624

862

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

0.372

5625

863

\begin{align*} 3 x^{\prime \prime }+30 x^{\prime }+63 x&=0 \\ x \left (0\right ) &= 2 \\ x^{\prime }\left (0\right ) &= 2 \\ \end{align*}

0.372

5626

1362

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

Series expansion around \(x=0\).

0.372

5627

1766

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

0.372

5628

1767

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

0.372

5629

2832

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

0.372

5630

3335

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

Series expansion around \(x=0\).

0.372

5631

3422

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

0.372

5632

3690

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

0.372

5633

5617

\begin{align*} {y^{\prime }}^{3}-7 y^{\prime }+6&=0 \\ \end{align*}

0.372

5634

6085

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

0.372

5635

7221

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

0.372

5636

8013

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

0.372

5637

8906

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

0.372

5638

9319

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

0.372

5639

9321

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

0.372

5640

10389

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

0.372

5641

10788

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

0.372

5642

14309

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

0.372

5643

14771

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

0.372

5644

18036

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

0.372

5645

18683

\begin{align*} i^{\prime }&=\frac {i}{2}-\frac {v}{8} \\ v^{\prime }&=2 i-\frac {v}{2} \\ \end{align*}

0.372

5646

19462

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

0.372

5647

23031

\begin{align*} z^{\prime \prime }+8 z^{\prime }+16 z&=0 \\ \end{align*}

0.372

5648

24055

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

Using Laplace transform method.

0.372

5649

24881

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

0.372

5650

25537

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

0.372

5651

26001

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

Using Laplace transform method.

0.372

5652

26944

\begin{align*} y^{\prime \prime }-6 y^{\prime }+7 y&=0 \\ \end{align*}

0.372

5653

2825

\begin{align*} x_{1}^{\prime }&=-x_{2} \\ x_{2}^{\prime }&=8 x_{1}-6 x_{2} \\ \end{align*}

0.373

5654

3187

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

0.373

5655

3883

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

0.373

5656

7572

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

0.373

5657

9264

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

0.373

5658

11035

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

0.373

5659

11215

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

0.373

5660

16794

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

Using Laplace transform method.

0.373

5661

20837

\begin{align*} 20 y-9 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}

0.373

5662

26039

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

0.373

5663

2224

\begin{align*} 16 x^{4} y^{\prime \prime \prime \prime }+96 x^{3} y^{\prime \prime \prime }+72 x^{2} y^{\prime \prime }-24 y^{\prime } x +9 y&=96 x^{{5}/{2}} \\ \end{align*}

0.374

5664

3829

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

0.374

5665

4062

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

Series expansion around \(x=0\).

0.374

5666

7632

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

Series expansion around \(x=0\).

0.374

5667

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 \(x=0\).

0.374

5668

9501

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

Series expansion around \(x=0\).

0.374

5669

10081

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

0.374

5670

14146

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

0.374

5671

16772

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

Using Laplace transform method.

0.374

5672

17599

\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }-10 y^{\prime }-24 y&={\mathrm e}^{-3 t} \\ \end{align*}

0.374

5673

17600

\begin{align*} y^{\prime \prime \prime }-13 y^{\prime }+12 y&=\cos \left (t \right ) \\ \end{align*}

0.374

5674

18212

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

0.374

5675

21524

\begin{align*} 5 y+2 y^{\prime }+y^{\prime \prime }&=3 \sin \left (x +\frac {\pi }{4}\right ) \\ \end{align*}

0.374

5676

24642

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

0.374

5677

24707

\begin{align*} y^{\prime \prime }-4 y^{\prime }+13 y&=24 \,{\mathrm e}^{2 x} \cos \left (x \right ) \\ \end{align*}

0.374

5678

223

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

0.375

5679

1271

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

0.375

5680

1425

\begin{align*} x_{1}^{\prime }&=3 x_{1}+9 x_{2} \\ x_{2}^{\prime }&=-x_{1}-3 x_{2} \\ \end{align*}

With initial conditions

\begin{align*} x_{1} \left (0\right ) &= 2 \\ x_{2} \left (0\right ) &= 4 \\ \end{align*}

0.375

5681

1759

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

0.375

5682

3881

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

0.375

5683

4063

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

Series expansion around \(x=0\).

0.375

5684

6236

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

0.375

5685

6938

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

0.375

5686

8105

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

Series expansion around \(x=0\).

0.375

5687

8114

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

Series expansion around \(x=0\).

0.375

5688

8395

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

0.375

5689

9330

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

0.375

5690

9447

\begin{align*} L i^{\prime }+R i&=E_{0} \sin \left (\omega t \right ) \\ i \left (0\right ) &= 0 \\ \end{align*}

Using Laplace transform method.

0.375

5691

10482

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

0.375

5692

10505

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

0.375

5693

11323

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

0.375

5694

11685

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

0.375

5695

14656

\begin{align*} y^{\prime \prime \prime }-4 y^{\prime \prime }+y^{\prime }+6 y&=3 x \,{\mathrm e}^{x}+2 \,{\mathrm e}^{x}-\sin \left (x \right ) \\ y \left (0\right ) &= {\frac {33}{40}} \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ \end{align*}

0.375

5696

16795

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

Using Laplace transform method.

0.375

5697

17572

\begin{align*} y^{\left (6\right )}-3 y^{\prime \prime \prime \prime }+3 y^{\prime \prime }-y&=0 \\ y \left (0\right ) &= 16 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ y^{\prime \prime \prime }\left (0\right ) &= 0 \\ y^{\prime \prime \prime \prime }\left (0\right ) &= 0 \\ y^{\left (5\right )}\left (0\right ) &= 0 \\ \end{align*}

0.375

5698

18660

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

With initial conditions

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

0.375

5699

19021

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

0.375

5700

24677

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

0.375