2.3.99 Problems 9801 to 9900

Table 2.771: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

9801

7835

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

Series expansion around \(x=0\).

0.730

9802

9424

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

Series expansion around \(x=0\).

0.730

9803

16869

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

Series expansion around \(x=0\).

0.730

9804

18375

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

Series expansion around \(x=0\).

0.730

9805

18399

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

0.730

9806

19262

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

0.730

9807

20637

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

0.730

9808

21793

\begin{align*} y^{\prime \prime }+y^{\prime }&=6 y+5 \,{\mathrm e}^{2 x} \\ \end{align*}

0.730

9809

23989

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

0.730

9810

25129

\begin{align*} y^{\prime \prime }+y&=10 \,{\mathrm e}^{2 t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.730

9811

26158

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

0.730

9812

2405

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

0.731

9813

2749

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

0.731

9814

8497

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

Series expansion around \(x=0\).

0.731

9815

9422

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

Series expansion around \(x=0\).

0.731

9816

9506

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

Series expansion around \(x=0\).

0.731

9817

10754

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

0.731

9818

12608

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

0.731

9819

13075

\begin{align*} 4 x^{\prime }+9 y^{\prime }+11 x+31 y&={\mathrm e}^{t} \\ 3 x^{\prime }+7 y^{\prime }+8 x+24 y&={\mathrm e}^{2 t} \\ \end{align*}

0.731

9820

13880

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

0.731

9821

14639

\begin{align*} 4 y+y^{\prime \prime }&=12 x^{2}-16 x \cos \left (2 x \right ) \\ \end{align*}

0.731

9822

18636

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

0.731

9823

18829

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

0.731

9824

21239

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

0.731

9825

26032

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

Series expansion around \(x=0\).

0.731

9826

2031

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

Series expansion around \(x=0\).

0.732

9827

4136

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

0.732

9828

7174

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

Series expansion around \(x=0\).

0.732

9829

10079

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

0.732

9830

11723

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

0.732

9831

18191

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

0.732

9832

19879

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

0.732

9833

19986

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

0.732

9834

20066

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

0.732

9835

22193

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

Series expansion around \(x=0\).

0.732

9836

22502

\begin{align*} y&=x y^{\prime }+1+4 {y^{\prime }}^{2} \\ \end{align*}

0.732

9837

25567

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

0.732

9838

27781

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

Series expansion around \(x=0\).

0.732

9839

1433

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

0.733

9840

4132

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

0.733

9841

9376

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

Series expansion around \(x=0\).

0.733

9842

10169

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

Series expansion around \(x=0\).

0.733

9843

14854

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

0.733

9844

17686

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

Series expansion around \(x=0\).

0.733

9845

23478

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

0.733

9846

23617

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

0.733

9847

25522

\begin{align*} y^{\prime \prime }+9 y&={\mathrm e}^{i \omega t} \\ \end{align*}

0.733

9848

25568

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

0.733

9849

3369

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

Series expansion around \(x=0\).

0.734

9850

3757

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

0.734

9851

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*}

0.734

9852

8487

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

Series expansion around \(x=0\).

0.734

9853

12700

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

0.734

9854

16889

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

Series expansion around \(x=2\).

0.734

9855

18727

\begin{align*} y^{\prime \prime }+y^{\prime }+16 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.734

9856

21232

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

With initial conditions

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

0.734

9857

22138

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

0.734

9858

24738

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

0.734

9859

25934

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

0.734

9860

25968

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

0.734

9861

26577

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

0.734

9862

483

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

Series expansion around \(x=0\).

0.735

9863

2061

\begin{align*} 9 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+3 x \left (13 x^{2}+7 x +1\right ) y^{\prime }+\left (25 x^{2}+4 x +1\right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.735

9864

4173

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

With initial conditions

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

0.735

9865

5386

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

0.735

9866

8509

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

Series expansion around \(x=0\).

0.735

9867

14176

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

0.735

9868

14332

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

0.735

9869

27527

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

0.735

9870

5391

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

0.736

9871

5550

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

0.736

9872

6152

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

0.736

9873

8854

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

With initial conditions

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

0.736

9874

9067

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

0.736

9875

10182

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

Series expansion around \(x=0\).

0.736

9876

12904

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

0.736

9877

17464

\begin{align*} y^{\prime \prime }+6 y^{\prime }+25 y&=-1 \\ y \left (0\right ) &= -{\frac {1}{25}} \\ y^{\prime }\left (0\right ) &= 7 \\ \end{align*}

0.736

9878

17504

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

0.736

9879

19513

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

0.736

9880

21474

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

0.736

9881

2015

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

Series expansion around \(x=0\).

0.737

9882

3141

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

0.737

9883

3248

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

0.737

9884

3368

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

Series expansion around \(x=0\).

0.737

9885

3904

\begin{align*} x_{1}^{\prime }&=-17 x_{1}-42 x_{3} \\ x_{2}^{\prime }&=-7 x_{1}+4 x_{2}-14 x_{3} \\ x_{3}^{\prime }&=7 x_{1}+18 x_{3} \\ \end{align*}

0.737

9886

6948

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

0.737

9887

7069

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

0.737

9888

9378

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

Series expansion around \(x=0\).

0.737

9889

9981

\begin{align*} y^{\prime \prime }-4 y^{\prime }+3 y&=9 x^{2}+4 \\ y \left (0\right ) &= 6 \\ y^{\prime }\left (0\right ) &= 8 \\ \end{align*}

0.737

9890

11334

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

0.737

9891

15214

\begin{align*} 4 y^{\prime \prime }+5 y^{\prime }+4 y&=3 \,{\mathrm e}^{-t} \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}

Using Laplace transform method.

0.737

9892

15310

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

Series expansion around \(x=0\).

0.737

9893

18049

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

0.737

9894

18194

\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&=8 \,{\mathrm e}^{-2 x} \\ \end{align*}

0.737

9895

21548

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

0.737

9896

21736

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

0.737

9897

22158

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

0.737

9898

26120

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

0.737

9899

26982

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

0.737

9900

1035

\begin{align*} x_{1}^{\prime }&=-15 x_{1}-7 x_{2}+4 x_{3} \\ x_{2}^{\prime }&=34 x_{1}+16 x_{2}-11 x_{3} \\ x_{3}^{\prime }&=17 x_{1}+7 x_{2}+5 x_{3} \\ \end{align*}

0.738