2.3.252 Problems 25101 to 25200

Table 2.1035: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

25101

21765

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

50.521

25102

24317

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

50.772

25103

1720

\begin{align*} 12 x^{3} y+24 y^{2} x^{2}+\left (9 x^{4}+32 x^{3} y+4 y\right ) y^{\prime }&=0 \\ \end{align*}

50.786

25104

5624

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

50.827

25105

19950

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

50.895

25106

24365

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

50.968

25107

13562

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

51.056

25108

5590

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

51.137

25109

13475

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

51.138

25110

25086

\begin{align*} y^{\prime \prime }-y y^{\prime }&=6 \\ \end{align*}

51.208

25111

13818

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

51.295

25112

25445

\begin{align*} z^{\prime }+4 z&={\mathrm e}^{8 i t} \\ \end{align*}

51.434

25113

25447

\begin{align*} z^{\prime }+4 i z&={\mathrm e}^{8 t} \\ \end{align*}

51.465

25114

13860

\begin{align*} \left (a \,x^{3}+b \,x^{2}+c x \right ) y^{\prime \prime }+\left (n \,x^{2}+m x +k \right ) y^{\prime }+\left (-2 \left (a +n \right ) x +1\right ) y&=0 \\ \end{align*}

51.512

25115

19936

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

51.539

25116

6235

\begin{align*} \left (\operatorname {b1} \,x^{2}+\operatorname {b0} \right ) y+\left (\operatorname {a2} \,x^{2}+\operatorname {a1} x +\operatorname {a0} \right ) y^{\prime }+4 \left (1-x \right ) x \left (-a x +1\right ) y^{\prime \prime }&=0 \\ \end{align*}

51.627

25117

11528

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

51.663

25118

13474

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

51.924

25119

5238

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

51.961

25120

5232

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

51.966

25121

20594

\begin{align*} y^{\prime \prime }&=\frac {1}{\sqrt {a y}} \\ \end{align*}

52.122

25122

13214

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

52.125

25123

8399

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

52.256

25124

14247

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

52.319

25125

10073

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

52.467

25126

9146

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

52.482

25127

20001

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

52.485

25128

12075

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

52.894

25129

13617

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

52.945

25130

24326

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

53.100

25131

20952

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

53.354

25132

21844

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

53.454

25133

19712

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

53.530

25134

20966

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

53.541

25135

24886

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

53.602

25136

23188

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

53.613

25137

13500

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

53.694

25138

14841

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

53.710

25139

20984

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

53.731

25140

13530

\begin{align*} y^{\prime } y-y&=-\frac {3 x}{16}+\frac {3 A}{x^{{1}/{3}}}-\frac {12 A^{2}}{x^{{5}/{3}}} \\ \end{align*}

53.769

25141

6083

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

53.771

25142

12106

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

53.776

25143

24348

\begin{align*} x -4 y-3-\left (x -6 y-5\right ) y^{\prime }&=0 \\ \end{align*}

53.835

25144

21761

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

53.965

25145

683

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

53.993

25146

11558

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

54.079

25147

13621

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

54.204

25148

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*}

54.226

25149

5038

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

54.310

25150

14065

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

54.400

25151

24221

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

54.400

25152

8715

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

54.496

25153

21375

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

54.510

25154

7125

\begin{align*} r^{\prime \prime }&=-\frac {k}{r^{2}} \\ \end{align*}

54.526

25155

784

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

54.609

25156

13352

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

54.706

25157

11998

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

54.805

25158

12509

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

54.852

25159

6234

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

54.930

25160

5181

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

54.938

25161

12508

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

54.962

25162

12169

\begin{align*} y^{\prime }&=-\frac {\left (-8-8 y^{3}+24 y^{{3}/{2}} {\mathrm e}^{x}-18 \,{\mathrm e}^{2 x}-8 y^{{9}/{2}}+36 y^{3} {\mathrm e}^{x}-54 \,{\mathrm e}^{2 x} y^{{3}/{2}}+27 \,{\mathrm e}^{3 x}\right ) {\mathrm e}^{x}}{8 \sqrt {y}} \\ \end{align*}

54.996

25163

13520

\begin{align*} y^{\prime } y-y&=-\frac {3 x}{16}+\frac {A}{x^{{5}/{3}}} \\ \end{align*}

55.118

25164

13384

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

55.142

25165

13324

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

55.186

25166

11946

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

55.231

25167

5665

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

55.273

25168

13547

\begin{align*} y^{\prime } y-y&=\frac {15 x}{4}+\frac {6 A}{x^{{1}/{3}}}-\frac {3 A^{2}}{x^{{5}/{3}}} \\ \end{align*}

55.285

25169

11935

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

55.426

25170

19897

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

55.483

25171

24305

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

55.501

25172

13396

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

55.569

25173

11650

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

55.602

25174

20511

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

56.003

25175

12006

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

56.379

25176

21043

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

56.438

25177

8156

\begin{align*} R^{\prime \prime }&=-\frac {k}{R^{2}} \\ \end{align*}

56.555

25178

13655

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

56.664

25179

17307

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

56.664

25180

6315

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

56.839

25181

14068

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

56.909

25182

10411

\begin{align*} y {y^{\prime \prime }}^{3}+y^{3} {y^{\prime }}^{5}&=0 \\ \end{align*}

56.931

25183

17322

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

56.944

25184

12078

\begin{align*} y^{\prime }&=\frac {y^{3} x \,{\mathrm e}^{3 x^{2}} {\mathrm e}^{-\frac {9 x^{2}}{2}}}{9 \,{\mathrm e}^{\frac {3 x^{2}}{2}}+3 \,{\mathrm e}^{\frac {3 x^{2}}{2}} y+9 y} \\ \end{align*}

56.960

25185

12002

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

56.966

25186

2521

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

57.204

25187

3004

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

57.204

25188

20961

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

57.283

25189

15357

\begin{align*} 3 y-7 x +7-\left (3 x -7 y-3\right ) y^{\prime }&=0 \\ \end{align*}

57.296

25190

13540

\begin{align*} y^{\prime } y-y&=-\frac {12 x}{49}+A \sqrt {x} \\ \end{align*}

57.339

25191

13846

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

57.417

25192

5345

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

57.491

25193

5165

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

57.535

25194

19373

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

57.563

25195

4851

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

57.595

25196

20129

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

57.627

25197

6267

\begin{align*} \left (\operatorname {c1} \,x^{4}+\operatorname {b1} \,x^{2}+\operatorname {a1} \right ) y+x \left (\operatorname {b0} \,x^{2}+\operatorname {a0} \right ) y^{\prime }+\left (a^{2}-x^{2}\right )^{2} \left (b^{2}-x^{2}\right ) y^{\prime \prime }&=0 \\ \end{align*}

57.648

25198

18043

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

57.711

25199

12004

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

57.727

25200

21368

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

57.768