2.3.129 Problems 12801 to 12900

Table 2.789: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

12801

14521

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

2.225

12802

21607

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

2.225

12803

3590

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

2.226

12804

7369

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

2.226

12805

22985

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

2.226

12806

34

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

2.227

12807

6452

\begin{align*} y y^{\prime \prime }&=\operatorname {a0} +\operatorname {a1} y+\operatorname {a2} y^{2}+\operatorname {a3} y^{2}+\operatorname {a3} y^{3}+\operatorname {a4} y^{4}+a {y^{\prime }}^{2} \\ \end{align*}

2.227

12808

13279

\begin{align*} \left (a \,x^{n}+b \,x^{m}+c \right ) y^{\prime }&=\alpha \,x^{k} y^{2}+\beta \,x^{s} y-\alpha \,\lambda ^{2} x^{k}+\beta \lambda \,x^{s} \\ \end{align*}

2.227

12809

18945

\begin{align*} y^{\prime \prime }+y&=\operatorname {Heaviside}\left (t -\frac {\pi }{2}\right )+3 \delta \left (t -\frac {3 \pi }{2}\right )-\operatorname {Heaviside}\left (t -2 \pi \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

2.227

12810

6999

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

2.228

12811

13881

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

2.228

12812

18118

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

2.228

12813

21474

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

2.228

12814

22368

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

2.228

12815

4197

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

2.230

12816

4699

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

2.230

12817

10162

\begin{align*} 4 x^{2} y^{\prime \prime }+y&=8 \sqrt {x}\, \left (1+\ln \left (x \right )\right ) \\ \end{align*}

2.230

12818

15601

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

2.230

12819

2480

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

2.231

12820

18513

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

2.231

12821

21420

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

2.232

12822

22608

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

2.232

12823

1242

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

2.233

12824

22210

\begin{align*} x^{2} y^{\prime \prime }+{\mathrm e}^{x} y^{\prime } x +\left (x^{3}-1\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

2.233

12825

21371

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

2.234

12826

23053

\begin{align*} s^{\prime \prime }&=5 t^{2}-7 t \\ s \left (0\right ) &= 0 \\ s \left (1\right ) &= {\frac {1}{4}} \\ \end{align*}

2.234

12827

5350

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

2.235

12828

8218

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

2.235

12829

9319

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

2.235

12830

15916

\begin{align*} y^{\prime }&=\frac {3 y}{t}+t^{5} \\ \end{align*}

2.235

12831

22611

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

2.235

12832

17164

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

2.236

12833

4735

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

2.237

12834

5283

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

2.238

12835

5297

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

2.238

12836

6817

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

2.239

12837

22751

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

2.239

12838

4095

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

2.240

12839

5200

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

2.240

12840

8373

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

2.240

12841

14284

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

2.240

12842

17394

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

2.240

12843

25467

\begin{align*} y^{\prime }&=\frac {y}{1+t}+10 \\ \end{align*}

2.240

12844

6963

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

2.241

12845

8436

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

2.241

12846

8440

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

2.241

12847

15567

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

2.241

12848

12174

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

2.242

12849

12279

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

2.242

12850

18060

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

2.242

12851

23226

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

2.242

12852

1000

\begin{align*} x_{1}^{\prime }&=23 x_{1}-18 x_{2}-16 x_{3} \\ x_{2}^{\prime }&=-8 x_{1}+6 x_{2}+7 x_{3}+9 x_{4} \\ x_{3}^{\prime }&=34 x_{1}-27 x_{2}-26 x_{3}-9 x_{4} \\ x_{4}^{\prime }&=-26 x_{1}+21 x_{2}+25 x_{3}+12 x_{4} \\ \end{align*}

2.243

12853

4643

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

2.243

12854

10422

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

2.243

12855

18091

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

2.243

12856

2633

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

2.244

12857

5374

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

2.244

12858

20820

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

2.244

12859

22285

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

2.244

12860

9180

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

2.245

12861

13880

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

2.246

12862

15603

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

2.246

12863

5964

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

2.247

12864

13068

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

2.247

12865

14334

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

2.247

12866

9272

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

2.248

12867

15917

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

2.248

12868

22443

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

2.248

12869

24731

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

2.248

12870

25491

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

2.248

12871

18595

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

2.249

12872

8620

\begin{align*} y^{\prime \prime }+\frac {y}{4 x}&=0 \\ \end{align*}
Series expansion around \(x=0\).

2.250

12873

25451

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

2.250

12874

23049

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

2.251

12875

16237

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

2.252

12876

23298

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

2.252

12877

1531

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

2.253

12878

4644

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

2.253

12879

10425

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

2.253

12880

21345

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

2.253

12881

51

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

2.254

12882

15776

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

2.254

12883

6016

\begin{align*} 16 y-7 y^{\prime } x +x^{2} y^{\prime \prime }&=0 \\ \end{align*}

2.255

12884

7951

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

2.255

12885

8283

\begin{align*} y^{\prime \prime }+9 y&=5 \\ \end{align*}

2.255

12886

21325

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

2.255

12887

21352

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

2.256

12888

8031

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

2.257

12889

7404

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

2.258

12890

19929

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

2.258

12891

4613

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

2.259

12892

7749

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

2.260

12893

14704

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

2.260

12894

7468

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

2.262

12895

16491

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

2.262

12896

4290

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

2.264

12897

5443

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

2.264

12898

18502

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

2.264

12899

22333

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

2.264

12900

12417

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

2.265