2.3.197 Problems 19601 to 19700

Table 2.977: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

19601

26174

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{2} y^{\prime \prime }+\left (2 x^{4}-5 x \right ) y^{\prime }+\left (3 x^{2}+2\right ) y&=0 \end {array} \]

Series expansion around \(x=0\).

6.894

19602

126

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 y^{\prime \prime } x +2 y^{\prime }+y&=0 \end {array} \]

Series expansion around \(x=0\).

6.895

19603

12314

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y^{\prime \prime } x +\left (3-x \right ) y^{\prime }-y&=0 \end {array} \]

Series expansion around \(x=0\).

6.895

19604

14829

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y^{\prime \prime } x +\left (x +1\right ) y^{\prime }+3 y&=0 \end {array} \]

Series expansion around \(x=0\).

6.895

19605

21031

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} y^{\prime \prime }+y^{\prime } x -\left (x +1\right ) y&=0 \end {array} \]

Series expansion around \(x=0\).

6.895

19606

3517

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x +x^{2} y&=0 \end {array} \]

Series expansion around \(x=0\).

6.898

19607

8539

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+\frac {y^{\prime }}{x^{2}}-\frac {y}{x^{3}}&=0 \end {array} \]

Series expansion around \(x=0\).

6.898

19608

22804

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+\frac {n y^{\prime }}{x^{2}}+\frac {q y}{x^{3}}&=0 \end {array} \]

Series expansion around \(x=0\).

6.898

19609

2891

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-3 y^{\prime } x +\left (4 x +4\right ) y&=0 \end {array} \]

Series expansion around \(x=0\).

6.901

19610

14272

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{2} y^{\prime \prime }-8 x^{2} y^{\prime }+\left (4 x^{2}+1\right ) y&=0 \end {array} \]

Series expansion around \(x=0\).

6.902

19611

5066

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x +2 y^{\prime }+y x&=0 \end {array} \]

Series expansion around \(x=0\).

6.904

19612

4442

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-x^{2} y^{\prime }+\left (x^{2}-2\right ) y&=0 \end {array} \]

Series expansion around \(x=0\).

6.905

19613

17315

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x -y^{\prime }+4 x^{3} y&=0 \end {array} \]

Series expansion around \(x=0\).

6.909

19614

11430

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-1\right ) y&=0 \end {array} \]

Series expansion around \(x=0\).

6.911

19615

6255

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=0 \end {array} \]

Series expansion around \(x=0\).

6.912

19616

780

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (1-x \right ) x y^{\prime \prime }+\left (\frac {3}{2}-2 x \right ) y^{\prime }+2 y&=0 \end {array} \]

Series expansion around \(x=0\).

6.914

19617

5522

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (2 x^{2}+2 x \right ) y^{\prime \prime }+\left (5 x +1\right ) y^{\prime }+y&=0 \end {array} \]

Series expansion around \(x=0\).

6.914

19618

12001

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}-1\right ) y^{\prime \prime }+\left (5 x +4\right ) y^{\prime }+4 y&=0 \end {array} \]

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

6.914

19619

22550

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}-x -6\right ) y^{\prime \prime }+\left (3 x +5\right ) y^{\prime }+y&=0 \end {array} \]

Series expansion around \(x=3\).

6.917

19620

26208

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (1-x \right ) x y^{\prime \prime }+\left (1-3 x \right ) y^{\prime }-y&=0 \end {array} \]

Series expansion around \(x=0\).

6.918

19621

1128

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} n \left (n +1\right ) y-2 y^{\prime } x +\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \end {array} \]

Series expansion around \(x=\infty \).

6.919

19622

19086

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x +\left (-n^{2}+x^{2}\right ) y&=0 \end {array} \]

Series expansion around \(x=\infty \).

6.921

19623

24392

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+y&=3 \,{\mathrm e}^{2 x}\\ y \left (0\right )&=0\\ \end {array} \]

Using Laplace transform method.

6.921

19624

785

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-4 y^{\prime }+4 y&=0\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=3\\ \end {array} \]

Using Laplace transform method.

6.922

19625

5925

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 y^{\prime }+2 y&=2\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]

Using Laplace transform method.

6.922

19626

1177

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y^{\prime }&=3 x^{2}\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]

Using Laplace transform method.

6.924

19627

11333

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 5 y+2 y^{\prime }+y^{\prime \prime }&=3 \,{\mathrm e}^{-x} \sin \left (x \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=3\\ \end {array} \]

Using Laplace transform method.

6.924

19628

1821

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-2 a y^{\prime }+a^{2} y&=0\\ y \left (0\right )&=y_{0}\\ y^{\prime }\left (0\right )&=\operatorname {yd}_{0}\\ \end {array} \]

Using Laplace transform method.

6.929

19629

21318

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x +\left (3 x -1\right ) y^{\prime }-\left (9+4 x \right ) y&=0\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]

Using Laplace transform method.

6.929

19630

5362

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x +\left (2 x +3\right ) y^{\prime }+\left (x +3\right ) y&=3 \,{\mathrm e}^{-x}\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]

Using Laplace transform method.

6.930

19631

12091

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+x^{2} y&=0\\ y \left (0\right )&=y_{0}\\ y^{\prime }\left (0\right )&=\operatorname {yd}_{0}\\ \end {array} \]

Using Laplace transform method.

6.930

19632

1239

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+a^{2} y&=f \left (x \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]

Using Laplace transform method.

6.932

19633

19945

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+5 y^{\prime }+6 y&=4 \,{\mathrm e}^{3 t}\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]

Using Laplace transform method.

6.933

19634

22516

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y^{\prime }-6 y&=t\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]

Using Laplace transform method.

6.934

19635

18539

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y^{\prime }&=t^{2}\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]

Using Laplace transform method.

6.939

19636

748

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+3 y^{\prime }+2 y&=f \left (t \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]

Using Laplace transform method.

6.940

19637

21456

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x \left (t \right )&=x \left (t \right )+3 y \left (t \right )\\ \frac {d}{d t}y \left (t \right )&=3 x \left (t \right )+y \left (t \right )\\ \end {array} \]

6.940

19638

5040

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x \left (t \right )&=x \left (t \right )+2 y \left (t \right )\\ \frac {d}{d t}y \left (t \right )&=3 x \left (t \right )+2 y \left (t \right )\\ \end {array} \]

6.941

19639

8318

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x \left (t \right )&=x \left (t \right )+2 y \left (t \right )+t -1\\ \frac {d}{d t}y \left (t \right )&=3 x \left (t \right )+2 y \left (t \right )-5 t -2\\ \end {array} \]

6.941

19640

18515

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }\left (t \right )&=x \left (t \right )+y\\ y^{\prime }&=y\\ \end {array} \]

6.943

19641

22039

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x \left (t \right )&=x \left (t \right )\\ \frac {d}{d t}y \left (t \right )&=y \left (t \right )\\ \end {array} \]

6.943

19642

7743

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x \left (t \right )&=-3 x \left (t \right )+4 y \left (t \right )\\ \frac {d}{d t}y \left (t \right )&=-2 x \left (t \right )+3 y \left (t \right )\\ \end {array} \]

6.944

19643

26468

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x \left (t \right )&=4 x \left (t \right )-2 y \left (t \right )\\ \frac {d}{d t}y \left (t \right )&=5 x \left (t \right )+2 y \left (t \right )\\ \end {array} \]

6.944

19644

12683

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x \left (t \right )&=5 x \left (t \right )+4 y \left (t \right )\\ \frac {d}{d t}y \left (t \right )&=-x \left (t \right )+y \left (t \right )\\ \end {array} \]

6.947

19645

12220

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x \left (t \right )&=4 x \left (t \right )-3 y \left (t \right )\\ \frac {d}{d t}y \left (t \right )&=8 x \left (t \right )-6 y \left (t \right )\\ \end {array} \]

6.948

19646

17242

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }\left (t \right )&=2 x \left (t \right )\\ y^{\prime }&=3 y\\ \end {array} \]

6.948

19647

19726

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }\left (t \right )&=-4 x \left (t \right )-y \left (t \right )\\ y^{\prime }\left (t \right )&=x \left (t \right )-2 y \left (t \right )\\ \end {array} \]

6.950

19648

6361

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x \left (t \right )&=7 x \left (t \right )+6 y \left (t \right )\\ \frac {d}{d t}y \left (t \right )&=2 x \left (t \right )+6 y \left (t \right )\\ \end {array} \]

6.951

19649

27921

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }\left (t \right )&=x \left (t \right )-2 y \left (t \right )\\ y^{\prime }\left (t \right )&=4 x \left (t \right )+5 y \left (t \right )\\ \end {array} \]

6.952

19650

23126

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x \left (t \right )&=x \left (t \right )+y \left (t \right )-5 t +2\\ \frac {d}{d t}y \left (t \right )&=4 x \left (t \right )-2 y \left (t \right )-8 t -8\\ \end {array} \]

6.953

19651

8313

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x \left (t \right )&=2 x \left (t \right )\\ \frac {d}{d t}y \left (t \right )&=3 y \left (t \right )\\ \end {array} \]

6.954

19652

11480

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x \left (t \right )&=-x \left (t \right )-2 y \left (t \right )\\ \frac {d}{d t}y \left (t \right )&=4 x \left (t \right )-5 y \left (t \right )\\ \end {array} \]

6.954

19653

1169

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }\left (t \right )&=-3 x \left (t \right )+4 y\\ y^{\prime }&=-2 x \left (t \right )+3 y\\ \end {array} \]

6.960

19654

5189

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x \left (t \right )&=5 x \left (t \right )+2 y \left (t \right )\\ \frac {d}{d t}y \left (t \right )&=-17 x \left (t \right )-5 y \left (t \right )\\ \end {array} \]

6.960

19655

25202

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }\left (t \right )&=-4 x \left (t \right )-y\\ y^{\prime }&=x \left (t \right )-2 y\\ \end {array} \]

6.961

19656

24306

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x \left (t \right )&=4 x \left (t \right )-3 y \left (t \right )\\ \frac {d}{d t}y \left (t \right )&=8 x \left (t \right )-6 y \left (t \right )\\ \end {array} \]

6.964

19657

22577

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }\left (t \right )&=4 x \left (t \right )-2 y \left (t \right )\\ y^{\prime }\left (t \right )&=5 x \left (t \right )+2 y \left (t \right )\\ \end {array} \]

6.967

19658

12142

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+\left (5 x^{4}-9 x^{2}\right ) x^{\prime }+x^{5}&=0 \end {array} \]

6.971

19659

26918

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=3 t^{2}+4 t\\ x \left (1\right )&=0\\ \end {array} \]

6.973

19660

25849

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=b \,{\mathrm e}^{t}\\ x \left (1\right )&=0\\ \end {array} \]

6.975

19661

18513

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=\frac {1}{t^{2}+1}\\ x \left (1\right )&=0\\ \end {array} \]

6.977

19662

13244

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=\frac {1}{\sqrt {t^{2}+1}}\\ x \left (1\right )&=0\\ \end {array} \]

6.978

19663

27463

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=\cos \left (t \right )\\ x \left (1\right )&=0\\ \end {array} \]

6.978

19664

19302

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=\frac {\cos \left (t \right )}{\sin \left (t \right )}\\ x \left (1\right )&=0\\ \end {array} \]

6.983

19665

22190

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x^{2}-3 x+2\\ x \left (0\right )&=1\\ \end {array} \]

6.987

19666

19682

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=b \,{\mathrm e}^{x}\\ x \left (0\right )&=1\\ \end {array} \]

6.988

19667

14235

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=\left (x-1\right )^{2}\\ x \left (0\right )&=1\\ \end {array} \]

6.989

19668

12698

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=\sqrt {x^{2}-1}\\ x \left (0\right )&=1\\ \end {array} \]

6.991

19669

27938

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 \sqrt {x}\\ x \left (0\right )&=1\\ \end {array} \]

6.991

19670

13495

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=\tan \left (x\right )\\ x \left (0\right )&=1\\ \end {array} \]

6.992

19671

9329

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 t^{2} x-t x+\left (3 t^{3} x^{2}+t^{3} x^{4}\right ) x^{\prime }&=0 \end {array} \]

6.993

19672

17084

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 1+2 x+\left (-t^{2}+4\right ) x^{\prime }&=0 \end {array} \]

6.994

19673

21046

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=\cos \left (\frac {x}{t}\right ) \end {array} \]

6.994

19674

21058

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (t^{2}-x^{2}\right ) x^{\prime }&=t x \end {array} \]

6.995

19675

4794

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime } {\mathrm e}^{3 t}+3 x \,{\mathrm e}^{3 t}&=2 t \end {array} \]

6.996

19676

14038

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 t +3 x+\left (3 t -x\right ) x^{\prime }&=t^{2} \end {array} \]

6.999

19677

14222

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+2 x&={\mathrm e}^{t} \end {array} \]

6.999

19678

13653

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+x \tan \left (t \right )&=0 \end {array} \]

7.002

19679

11806

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }-x \tan \left (t \right )&=4 \sin \left (t \right ) \end {array} \]

7.004

19680

22585

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{3} x^{\prime }+\left (-3 t^{2}+2\right ) x&=t^{3} \end {array} \]

7.004

19681

3603

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+2 t x+t x^{4}&=0 \end {array} \]

7.006

19682

12466

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t x^{\prime }+x \ln \left (t \right )&=t^{2} \end {array} \]

7.007

19683

20381

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t x^{\prime }+x g \left (t \right )&=h \left (t \right ) \end {array} \]

7.007

19684

1606

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} x^{\prime \prime }-6 t x^{\prime }+12 x&=0 \end {array} \]

7.008

19685

6129

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-\lambda x \end {array} \]

7.010

19686

17330

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }\left (t \right )&=x \left (t \right )\\ y^{\prime }&=x \left (t \right )+2 y\\ \end {array} \]

7.010

19687

14889

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} x^{\prime \prime }-2 t x^{\prime }+2 x&=0 \end {array} \]

7.012

19688

9369

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }-5 x^{\prime }+6 x&=0 \end {array} \]

7.013

19689

18519

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }-4 x^{\prime }+4 x&=0 \end {array} \]

7.013

19690

18633

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }-4 x^{\prime }+5 x&=0 \end {array} \]

7.013

19691

21734

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+3 x^{\prime }&=0 \end {array} \]

7.013

19692

24197

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }-3 x^{\prime }+2 x&=0\\ x \left (0\right )&=0\\ x^{\prime }\left (0\right )&=1\\ \end {array} \]

7.013

19693

20269

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+x&=0\\ x \left (0\right )&=0\\ x^{\prime }\left (0\right )&=1\\ \end {array} \]

7.015

19694

25517

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+2 x^{\prime }+x&=0\\ x \left (0\right )&=0\\ x^{\prime }\left (0\right )&=1\\ \end {array} \]

7.018

19695

8540

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }-2 x^{\prime }+2 x&=0\\ x \left (0\right )&=0\\ x^{\prime }\left (0\right )&=1\\ \end {array} \]

7.019

19696

15311

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }-x&=t^{2}\\ x \left (0\right )&=0\\ x^{\prime }\left (0\right )&=1\\ \end {array} \]

7.019

19697

19403

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }-x&={\mathrm e}^{t}\\ x \left (0\right )&=0\\ x^{\prime }\left (0\right )&=1\\ \end {array} \]

7.019

19698

11400

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+2 x^{\prime }+4 x&={\mathrm e}^{t} \cos \left (2 t \right )\\ x \left (0\right )&=0\\ x^{\prime }\left (0\right )&=1\\ \end {array} \]

7.020

19699

12179

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }-x^{\prime }+x&=\sin \left (2 t \right )\\ x \left (0\right )&=0\\ x^{\prime }\left (0\right )&=1\\ \end {array} \]

7.020

19700

14420

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+4 x^{\prime }+3 x&=t \sin \left (t \right )\\ x \left (0\right )&=0\\ x^{\prime }\left (0\right )&=1\\ \end {array} \]

7.020