2.3.139 Problems 13801 to 13900

Table 2.851: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

13801

9895

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

Series expansion around \(x=0\).

1.357

13802

13774

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

1.357

13803

21702

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

Series expansion around \(x=0\).

1.357

13804

10274

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

1.358

13805

25737

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

1.358

13806

18996

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

With initial conditions

\begin{align*} x_{1} \left (0\right ) &= 2 \\ x_{2} \left (0\right ) &= -1 \\ x_{3} \left (0\right ) &= -2 \\ \end{align*}

1.359

13807

21288

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

Using Laplace transform method.

1.359

13808

8254

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

1.360

13809

17882

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

1.360

13810

22209

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

Series expansion around \(x=0\).

1.360

13811

25261

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

1.361

13812

26146

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

1.361

13813

9432

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

Series expansion around \(x=0\).

1.362

13814

9642

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

Using Laplace transform method.

1.362

13815

19364

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

1.362

13816

21634

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

Series expansion around \(x=1\).

1.362

13817

22902

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

With initial conditions

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

1.362

13818

25278

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

1.362

13819

9905

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

Series expansion around \(x=0\).

1.363

13820

14668

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

1.363

13821

25933

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

1.363

13822

175

\begin{align*} x^{\prime }&=3 x \left (5-x\right ) \\ x \left (0\right ) &= 8 \\ \end{align*}

1.364

13823

5723

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

1.364

13824

11397

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

1.364

13825

22323

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

1.364

13826

8415

\begin{align*} y^{\prime }&=-\frac {8 x +5}{3 y^{2}+1} \\ y \left (-1\right ) &= 4 \\ \end{align*}

1.365

13827

24042

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

1.365

13828

9943

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

Series expansion around \(x=2\).

1.366

13829

17455

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

1.366

13830

25342

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

Series expansion around \(t=0\).

1.366

13831

5784

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

1.367

13832

18391

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

1.367

13833

9767

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

1.368

13834

12315

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

1.368

13835

12902

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

1.368

13836

12908

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

1.368

13837

13943

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

1.368

13838

3432

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

1.369

13839

6503

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

1.369

13840

14959

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

1.369

13841

27268

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

1.369

13842

8987

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

Series expansion around \(x=1\).

1.370

13843

9559

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

Series expansion around \(t=0\).

1.370

13844

14742

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

Series expansion around \(x=1\).

1.370

13845

21677

\begin{align*} 18 x^{2} y^{\prime \prime }+3 x \left (5+x \right ) y^{\prime }-\left (10 x +1\right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

1.370

13846

2103

\begin{align*} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (2 x^{2}+5\right ) y^{\prime }-21 y&=0 \\ \end{align*}

Series expansion around \(x=0\).

1.371

13847

8827

\begin{align*} \left (\phi ^{\prime }-\frac {\phi ^{2}}{2}\right ) \sin \left (\theta \right )^{2}-\phi \sin \left (\theta \right ) \cos \left (\theta \right )&=\frac {\cos \left (2 \theta \right )}{2}+1 \\ \end{align*}

1.371

13848

18000

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

1.371

13849

1037

\begin{align*} x_{1}^{\prime }&=2 x_{1}+x_{2}-2 x_{3}+x_{4} \\ x_{2}^{\prime }&=3 x_{2}-5 x_{3}+3 x_{4} \\ x_{3}^{\prime }&=-13 x_{2}+22 x_{3}-12 x_{4} \\ x_{4}^{\prime }&=-27 x_{2}+45 x_{3}-25 x_{4} \\ \end{align*}

1.372

13850

9993

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

1.372

13851

14651

\begin{align*} y^{\prime \prime }-y^{\prime }-6 y&=8 \,{\mathrm e}^{2 x}-5 \,{\mathrm e}^{3 x} \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 5 \\ \end{align*}

1.372

13852

21940

\begin{align*} y^{\prime }-3 z&=5 \\ y-z^{\prime }-x&=3-2 t \\ z+x^{\prime }&=-1 \\ \end{align*}

1.372

13853

23273

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

1.372

13854

5790

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

1.374

13855

9906

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

Series expansion around \(x=0\).

1.374

13856

25755

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

1.374

13857

27168

\begin{align*} x_{1}^{\prime }&=x_{1} \\ x_{2}^{\prime }&=4 x_{1}+3 x_{2}-2 \,{\mathrm e}^{t} \\ x_{3}^{\prime }&=3 x_{3} \\ x_{4}^{\prime }&=-x_{1}+2 x_{2}+9 x_{3}+x_{4}+{\mathrm e}^{t} \\ \end{align*}

1.374

13858

74

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

1.375

13859

6102

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

1.375

13860

14125

\begin{align*} y+3 x y^{\prime }+9 x^{2} y^{\prime \prime }+6 x^{3} y^{\prime \prime \prime }+x^{4} y^{\prime \prime \prime \prime }&=\left (1+\ln \left (x \right )\right )^{2} \\ \end{align*}

1.375

13861

16416

\begin{align*} x y^{\prime \prime }+4 y^{\prime }&=18 x^{2} \\ y \left (1\right ) &= 8 \\ y^{\prime }\left (1\right ) &= -3 \\ \end{align*}

1.375

13862

18037

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

1.375

13863

25954

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

1.375

13864

6276

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

1.376

13865

9039

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

1.376

13866

24739

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

1.376

13867

3917

\begin{align*} x_{1}^{\prime }&=2 x_{1}-4 x_{2}+3 x_{3}+{\mathrm e}^{6 t} \\ x_{2}^{\prime }&=-9 x_{1}-3 x_{2}-9 x_{3}+1 \\ x_{3}^{\prime }&=4 x_{1}+4 x_{2}+3 x_{3} \\ \end{align*}

1.377

13868

22707

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

1.377

13869

3224

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

1.378

13870

7042

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

1.378

13871

8161

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

1.378

13872

9427

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

Series expansion around \(x=0\).

1.378

13873

9649

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

Using Laplace transform method.

1.378

13874

15226

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

Using Laplace transform method.

1.378

13875

17997

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

1.378

13876

19484

\begin{align*} 2 x^{2} y^{\prime \prime }+10 x y^{\prime }+8 y&=0 \\ \end{align*}

1.378

13877

21974

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

1.378

13878

18150

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

1.379

13879

18837

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

1.379

13880

21258

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

1.379

13881

22866

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

Series expansion around \(x=0\).

1.379

13882

27265

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

1.379

13883

1831

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

1.381

13884

9546

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

Series expansion around \(x=0\).

1.381

13885

20556

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

1.381

13886

22878

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

Series expansion around \(x=0\).

1.381

13887

6372

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

1.382

13888

6565

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

1.382

13889

8808

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

1.382

13890

16737

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

1.382

13891

21924

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

With initial conditions

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

1.382

13892

21934

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

1.382

13893

22731

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

1.382

13894

22927

\begin{align*} 2 x^{\prime }-x-y^{\prime }+y&=4 t \,{\mathrm e}^{-t}-3 \,{\mathrm e}^{-t} \\ x^{\prime }+4 x-2 y^{\prime }-4 y&=2 t \,{\mathrm e}^{-t}-6 \,{\mathrm e}^{-t} \\ \end{align*}

1.382

13895

7688

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

1.383

13896

13798

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

1.384

13897

17869

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

1.384

13898

5904

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

1.385

13899

6677

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

1.385

13900

8897

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

1.385