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

6598

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

1.320

14802

17708

\begin{align*} \left (x^{2}-25\right )^{2} y^{\prime \prime }-\left (x +5\right ) y^{\prime }+10 y&=0 \\ \end{align*}

Series expansion around \(x=0\).

1.320

14803

26584

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

1.320

14804

2473

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

1.321

14805

9483

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

1.322

14806

13109

\begin{align*} x^{\prime }&=-3 x+48 y-28 z \\ y^{\prime }&=-4 x+40 y-22 z \\ z^{\prime }&=-6 x+57 y-31 z \\ \end{align*}

1.322

14807

1293

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

1.323

14808

6940

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

1.323

14809

9536

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

Series expansion around \(x=0\).

1.323

14810

14702

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

1.323

14811

26973

\begin{align*} y^{\prime \prime }-4 y^{\prime }&=8 x^{2}+2 \,{\mathrm e}^{3 x} \\ \end{align*}

1.323

14812

672

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

1.324

14813

1792

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

1.324

14814

9237

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

1.324

14815

14722

\begin{align*} x^{2} y^{\prime \prime }+2 y^{\prime } x -6 y&=10 x^{2} \\ y \left (1\right ) &= 1 \\ y^{\prime }\left (1\right ) &= -6 \\ \end{align*}

1.324

14816

5552

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

1.325

14817

6292

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

1.325

14818

12885

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

1.325

14819

26650

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

1.325

14820

8860

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

1.326

14821

20076

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

1.326

14822

20747

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

1.326

14823

26992

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

1.326

14824

16248

\begin{align*} y^{\prime }&=200 y-2 y^{2} \\ \end{align*}

1.327

14825

18566

\begin{align*} y^{\prime }+2 y&=\left \{\begin {array}{cc} 1 & 0\le t \le 1 \\ 0 & 1<t \end {array}\right . \\ y \left (0\right ) &= 0 \\ \end{align*}

1.327

14826

25305

\begin{align*} y^{\prime \prime }+2 y^{\prime }+y&=\left \{\begin {array}{cc} {\mathrm e}^{-t} & 0\le t <4 \\ 0 & 4\le t \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

Using Laplace transform method.

1.327

14827

7164

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

Series expansion around \(x=0\).

1.328

14828

2374

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

1.329

14829

8748

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

1.329

14830

9635

\begin{align*} y^{\prime \prime }+16 y&=\left \{\begin {array}{cc} \cos \left (4 t \right ) & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}

Using Laplace transform method.

1.329

14831

11787

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

1.329

14832

21446

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

1.329

14833

9951

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

Series expansion around \(x=0\).

1.330

14834

13000

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

1.330

14835

9

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

1.331

14836

26507

\begin{align*} 4 y^{\prime \prime }-3 y^{\prime }&=x \,{\mathrm e}^{\frac {3 x}{4}} \\ \end{align*}

1.331

14837

2758

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

1.332

14838

5982

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

1.332

14839

8888

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

1.332

14840

9771

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

1.332

14841

18109

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

1.332

14842

20905

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

Series expansion around \(x=0\).

1.332

14843

12475

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

1.333

14844

17710

\begin{align*} 5 y^{\prime \prime } x +8 y^{\prime }-y x&=0 \\ \end{align*}

Series expansion around \(x=0\).

1.333

14845

17518

\begin{align*} y^{\prime \prime }+9 y&=\sec \left (3 t \right ) \tan \left (3 t \right ) \\ \end{align*}

1.334

14846

17609

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

1.334

14847

20638

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

1.334

14848

23567

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

1.334

14849

25615

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

1.334

14850

2074

\begin{align*} 4 x^{2} \left (x +1\right ) y^{\prime \prime }+4 x \left (3+8 x \right ) y^{\prime }-\left (5-49 x \right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

1.335

14851

4010

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

Series expansion around \(x=0\).

1.335

14852

9915

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

Series expansion around \(x=1\).

1.335

14853

20947

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

With initial conditions

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

1.335

14854

23783

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

1.335

14855

26345

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

1.335

14856

6124

\begin{align*} 6 y-4 \left (x +1\right ) y^{\prime }+\left (x +1\right )^{2} y^{\prime \prime }&=0 \\ \end{align*}

1.336

14857

2070

\begin{align*} 2 x^{2} \left (3 x +2\right ) y^{\prime \prime }+x \left (4+21 x \right ) y^{\prime }-\left (1-9 x \right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

1.337

14858

22723

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

1.337

14859

24912

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

1.337

14860

8651

\begin{align*} 4 y^{\prime \prime }+24 y^{\prime }+37 y&=17 \,{\mathrm e}^{-t}+\delta \left (t -\frac {1}{2}\right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}

Using Laplace transform method.

1.339

14861

17682

\begin{align*} \left (x^{2}-4\right ) y^{\prime \prime }+16 \left (2+x \right ) y^{\prime }-y&=0 \\ \end{align*}

Series expansion around \(x=1\).

1.339

14862

20852

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

1.339

14863

1348

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

1.340

14864

7207

\begin{align*} y^{\prime \prime }+n^{2} y&=\frac {6 y}{x^{2}} \\ \end{align*}

1.340

14865

17719

\begin{align*} x^{2} y^{\prime \prime }+7 y^{\prime } x -7 y&=0 \\ \end{align*}

Series expansion around \(x=0\).

1.340

14866

22639

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

1.340

14867

24948

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

1.340

14868

25789

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

1.341

14869

924

\begin{align*} x^{\prime }&=2 x+4 y+3 \,{\mathrm e}^{t} \\ y^{\prime }&=5 x-y-t^{2} \\ \end{align*}

1.342

14870

2474

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

1.342

14871

15271

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

1.342

14872

16384

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

1.342

14873

19761

\begin{align*} t^{4} x^{\prime \prime \prime \prime }-2 t^{3} x^{\prime \prime \prime }-20 t^{2} x^{\prime \prime }+12 t x^{\prime }+16 x&=\cos \left (3 \ln \left (t \right )\right ) \\ \end{align*}

1.342

14874

21374

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

1.342

14875

22282

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

1.342

14876

25211

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

1.342

14877

25526

\begin{align*} m y^{\prime \prime }+k y&=\delta \left (-t +T \right ) \\ \end{align*}

1.342

14878

5871

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

1.343

14879

24433

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

1.343

14880

3224

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

1.345

14881

6510

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

1.345

14882

2355

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

1.346

14883

1796

\begin{align*} 6 y^{\prime }+6 y^{2}-y-1&=0 \\ \end{align*}

1.347

14884

9776

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

1.347

14885

10076

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

1.348

14886

10542

\begin{align*} 2 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+x \left (11 x^{2}+11 x +9\right ) y^{\prime }+\left (7 x^{2}+10 x +6\right ) y&=0 \\ \end{align*}

1.348

14887

231

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

1.349

14888

603

\begin{align*} x^{\prime }&=2 x+4 y+3 \,{\mathrm e}^{t} \\ y^{\prime }&=5 x-y-t^{2} \\ \end{align*}

1.349

14889

7946

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

1.349

14890

9415

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

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

1.349

14891

10230

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

1.351

14892

12399

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

1.351

14893

17606

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

1.351

14894

24981

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

1.351

14895

1184

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

1.352

14896

6351

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

1.352

14897

14072

\begin{align*} 3 x {y^{\prime }}^{2}-6 y y^{\prime }+x +2 y&=0 \\ \end{align*}

1.352

14898

15176

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

1.352

14899

15726

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

Using Laplace transform method.

1.352

14900

16049

\begin{align*} x^{\prime }&=-4 x+3 y \\ y^{\prime }&=z-y \\ z^{\prime }&=5 x-5 y \\ \end{align*}

1.352