2.3.149 Problems 14801 to 14900

Table 2.871: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

14801

7264

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

1.675

14802

4582

\begin{align*} x_{1}^{\prime }&=x_{1}-x_{2}-x_{3}+4 \,{\mathrm e}^{t} \\ x_{2}^{\prime }&=x_{1}+x_{2} \\ x_{3}^{\prime }&=3 x_{1}+x_{3} \\ \end{align*}

1.676

14803

13496

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

1.676

14804

3558

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

1.677

14805

5590

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

1.677

14806

705

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

1.678

14807

3447

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

1.678

14808

5896

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

1.678

14809

18091

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

1.678

14810

23466

\begin{align*} 3 x^{2} y^{\prime \prime }-2 x y^{\prime }-8 y&=5+3 x \\ \end{align*}

1.678

14811

4527

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

Using Laplace transform method.

1.679

14812

20498

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

1.679

14813

8209

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

1.680

14814

9947

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

Series expansion around \(x=0\).

1.681

14815

14369

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

Using Laplace transform method.

1.681

14816

9399

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

Series expansion around \(x=0\).

1.682

14817

14308

\begin{align*} x^{\prime \prime }-x^{\prime }&=6+{\mathrm e}^{2 t} \\ \end{align*}

1.682

14818

15185

\begin{align*} y^{\prime \prime }+\left (5+2 x \right ) y^{\prime }+\left (8+4 x \right ) y&={\mathrm e}^{-2 x} \\ \end{align*}

1.682

14819

26670

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

1.682

14820

27345

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

1.683

14821

3221

\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }+16 y&=0 \\ \end{align*}

1.684

14822

7351

\begin{align*} y^{\prime \prime }-2 y^{\prime }+5 y&=5 x +4 \,{\mathrm e}^{x} \left (1+\sin \left (2 x \right )\right ) \\ \end{align*}

1.684

14823

7380

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

1.684

14824

18115

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

1.684

14825

1827

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

1.685

14826

5719

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

1.685

14827

7006

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

1.685

14828

12562

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

1.685

14829

17577

\begin{align*} \frac {31 y^{\prime \prime \prime }}{100}+\frac {56 y^{\prime \prime }}{5}-\frac {49 y^{\prime }}{5}+\frac {53 y}{10}&=0 \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= -1 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ \end{align*}

1.685

14830

19751

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

1.685

14831

20152

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

1.685

14832

9940

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

Series expansion around \(x=0\).

1.686

14833

10210

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

Series expansion around \(x=0\).

1.686

14834

9220

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

1.687

14835

9918

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

Series expansion around \(x=0\).

1.687

14836

18121

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

1.687

14837

822

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

1.688

14838

2087

\begin{align*} x^{2} \left (2 x +1\right ) y^{\prime \prime }-x \left (9+8 x \right ) y^{\prime }-12 y x&=0 \\ \end{align*}

Series expansion around \(x=0\).

1.688

14839

16520

\begin{align*} y^{\prime \prime }+16 y&=0 \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= 12 \\ \end{align*}

1.688

14840

20462

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

1.688

14841

6013

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

1.689

14842

7956

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

1.689

14843

6393

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

1.690

14844

14755

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

Series expansion around \(x=0\).

1.690

14845

1302

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

1.691

14846

3967

\begin{align*} y^{\prime \prime }+y^{\prime }-6 y&=30 \operatorname {Heaviside}\left (t -1\right ) {\mathrm e}^{1-t} \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= -4 \\ \end{align*}

Using Laplace transform method.

1.691

14847

6051

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

1.691

14848

20632

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

1.691

14849

12304

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

1.692

14850

25433

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

1.692

14851

6401

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

1.693

14852

11825

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

1.693

14853

16259

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

1.693

14854

8217

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

1.694

14855

9880

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

1.694

14856

9919

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

Series expansion around \(x=0\).

1.694

14857

13018

\begin{align*} \left (4 y^{3}-a y-b \right ) \left (y^{\prime \prime }+f y^{\prime }\right )-\left (6 y^{2}-\frac {a}{2}\right ) {y^{\prime }}^{2}&=0 \\ \end{align*}

1.694

14858

14881

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

1.694

14859

11604

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

1.695

14860

15890

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

1.695

14861

16572

\begin{align*} x^{2} y^{\prime \prime }-11 x y^{\prime }+36 y&=0 \\ y \left (1\right ) &= {\frac {1}{2}} \\ y^{\prime }\left (1\right ) &= 2 \\ \end{align*}

1.695

14862

9413

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

Series expansion around \(x=0\).

1.697

14863

21259

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

1.697

14864

14725

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

1.698

14865

26468

\begin{align*} 3 y^{\prime \prime }&=\frac {1}{y^{{5}/{3}}} \\ \end{align*}

1.698

14866

17031

\begin{align*} x^{2} y^{\prime \prime }+5 x y^{\prime }+4 y&=0 \\ y \left (1\right ) &= 1 \\ y^{\prime }\left (1\right ) &= 0 \\ \end{align*}

1.699

14867

1041

\begin{align*} x_{1}^{\prime }&=2 x_{1}-8 x_{3}-3 x_{4} \\ x_{2}^{\prime }&=-18 x_{1}-x_{2} \\ x_{3}^{\prime }&=-9 x_{1}-3 x_{2}-25 x_{3}-9 x_{4} \\ x_{4}^{\prime }&=33 x_{1}+10 x_{2}+90 x_{3}+32 x_{4} \\ \end{align*}

1.700

14868

16137

\begin{align*} y^{\prime \prime }+3 y&=\operatorname {Heaviside}\left (-4+t \right ) \cos \left (-20+5 t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= -2 \\ \end{align*}

Using Laplace transform method.

1.700

14869

23280

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

1.700

14870

2439

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

1.701

14871

5410

\begin{align*} {y^{\prime }}^{2}+4 x^{5} y^{\prime }-12 x^{4} y&=0 \\ \end{align*}

1.701

14872

9809

\begin{align*} 9 {y^{\prime }}^{2}+3 x y^{4} y^{\prime }+y^{5}&=0 \\ \end{align*}

1.701

14873

14276

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

1.701

14874

21848

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

1.701

14875

2693

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

Using Laplace transform method.

1.702

14876

20802

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

1.702

14877

22719

\begin{align*} q^{\prime \prime }+q&=t \sin \left (t \right )+\cos \left (t \right ) \\ \end{align*}

1.702

14878

1184

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

1.703

14879

23375

\begin{align*} x^{2} y^{\prime \prime }+3 x y^{\prime }+5 y&=0 \\ \end{align*}

1.703

14880

15578

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

1.704

14881

18871

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

1.704

14882

271

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

1.705

14883

810

\begin{align*} y^{\prime \prime }+25 y&=0 \\ y \left (0\right ) &= 10 \\ y^{\prime }\left (0\right ) &= -10 \\ \end{align*}

1.705

14884

9557

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

Series expansion around \(x=0\).

1.705

14885

19997

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

1.705

14886

1715

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

1.706

14887

15108

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

1.706

14888

215

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

1.707

14889

6204

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

1.707

14890

26217

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

1.707

14891

24247

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

1.708

14892

26150

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

1.708

14893

11826

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

1.709

14894

13376

\begin{align*} \left (\sin \left (\lambda x \right ) a +b \right ) y^{\prime }&=y^{2}+c \sin \left (\mu x \right ) y-d^{2}+c d \sin \left (\mu x \right ) \\ \end{align*}

1.709

14895

23014

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

1.709

14896

9922

\begin{align*} x^{2} \left (4 x -1\right ) y^{\prime \prime }+x \left (1+5 x \right ) y^{\prime }+3 y&=0 \\ \end{align*}

Series expansion around \(x=0\).

1.710

14897

9969

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

Series expansion around \(x=0\).

1.710

14898

12615

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

1.710

14899

13387

\begin{align*} \left (\cos \left (\lambda x \right ) a +b \right ) y^{\prime }&=y^{2}+c \cos \left (\mu x \right ) y-d^{2}+c d \cos \left (\mu x \right ) \\ \end{align*}

1.710

14900

20670

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

1.710