2.3.249 Problems 24801 to 24900

Table 2.1071: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

24801

12689

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

15.809

24802

4260

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

15.815

24803

20788

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

15.822

24804

20323

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

15.824

24805

5064

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

15.826

24806

17048

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

15.845

24807

16353

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

15.858

24808

6431

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

15.859

24809

19674

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

15.867

24810

13631

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

15.868

24811

20470

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

15.877

24812

24294

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

15.902

24813

2505

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

15.905

24814

7558

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

15.933

24815

20836

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

15.933

24816

5586

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

15.934

24817

27476

\begin{align*} 2 x^{2} y+2 \sqrt {1+y^{2} x^{4}}+x^{3} y^{\prime }&=0 \\ \end{align*}

15.959

24818

13758

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

15.963

24819

11370

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

15.978

24820

8839

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

15.993

24821

18074

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

16.020

24822

24168

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

16.031

24823

5705

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

16.049

24824

3034

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

16.056

24825

15625

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

16.067

24826

14883

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

16.070

24827

22535

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

16.080

24828

11526

\begin{align*} \left (12 y-5 x -8\right ) y^{\prime }-5 y+2 x +3&=0 \\ \end{align*}

16.082

24829

24295

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

16.082

24830

19069

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

16.089

24831

13284

\begin{align*} y^{\prime }&=\sigma y^{2}+a y+b \,{\mathrm e}^{x}+c \\ \end{align*}

16.092

24832

13909

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

16.100

24833

2900

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

16.102

24834

12159

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

16.106

24835

5040

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

16.115

24836

3666

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

16.118

24837

25883

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

16.125

24838

5140

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

16.127

24839

15027

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

16.130

24840

15940

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

16.146

24841

8370

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

16.156

24842

4779

\begin{align*} x y^{\prime }&=k +a \,x^{n}+b y+c y^{2} \\ \end{align*}

16.161

24843

9158

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

16.161

24844

25034

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

16.161

24845

22332

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

16.164

24846

5598

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

16.180

24847

15377

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

16.195

24848

7488

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

16.207

24849

21973

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

16.209

24850

11533

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

16.214

24851

19942

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

16.220

24852

8042

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

16.222

24853

20799

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

16.227

24854

9148

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

16.238

24855

2892

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

16.249

24856

13656

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

16.252

24857

26207

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

16.259

24858

12108

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

16.263

24859

2899

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

16.269

24860

22966

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

16.274

24861

13916

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

16.275

24862

7548

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

16.276

24863

12146

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

16.278

24864

24175

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

16.284

24865

26307

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

16.284

24866

12559

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

16.287

24867

13352

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

16.290

24868

22963

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

16.299

24869

15650

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

16.325

24870

27513

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

16.329

24871

13468

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

16.354

24872

8717

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

16.356

24873

19960

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

16.359

24874

27026

\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }+4 y^{\prime }-4 y&=\left \{\begin {array}{cc} 1 & 0\le t <5 \\ 2 & 5\le t \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 1 \\ \end{align*}

Using Laplace transform method.

16.367

24875

10313

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

16.381

24876

13637

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

16.392

24877

20688

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

16.408

24878

26319

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

16.411

24879

22527

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

16.425

24880

25030

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

16.439

24881

19315

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

16.442

24882

6341

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

16.451

24883

21596

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

16.455

24884

17958

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

16.462

24885

14467

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

16.479

24886

24344

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

16.492

24887

19339

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

16.494

24888

22593

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

16.502

24889

5850

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

16.513

24890

11570

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

16.541

24891

18058

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

16.543

24892

27237

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

16.550

24893

1247

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

16.555

24894

5074

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

16.557

24895

13734

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

16.563

24896

26256

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

16.563

24897

3024

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

16.566

24898

5504

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

16.568

24899

15622

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

16.570

24900

23122

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

16.576