2.3.212 Problems 21101 to 21200

Table 2.997: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

21101

17969

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

11.206

21102

12243

\begin{align*} y^{\prime }&=\frac {-4 \cos \left (x \right ) x +4 x^{2} \sin \left (x \right )+4 x +4+4 y^{2}+8 y \cos \left (x \right ) x -8 y x +2 x^{2} \cos \left (2 x \right )+6 x^{2}-8 x^{2} \cos \left (x \right )+4 y^{3}+12 y^{2} \cos \left (x \right ) x -12 x y^{2}+6 y x^{2} \cos \left (2 x \right )+18 x^{2} y-24 y \cos \left (x \right ) x^{2}+x^{3} \cos \left (3 x \right )+15 x^{3} \cos \left (x \right )-6 x^{3} \cos \left (2 x \right )-10 x^{3}}{4 x} \\ \end{align*}

11.207

21103

11386

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

11.213

21104

24201

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

11.213

21105

15511

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

11.217

21106

115

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

11.230

21107

22525

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

11.237

21108

11996

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

11.239

21109

26979

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

11.244

21110

16338

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

11.248

21111

27370

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

11.249

21112

24264

\begin{align*} L i^{\prime }+R i&=e \sin \left (w t \right ) \\ i \left (0\right ) &= 0 \\ \end{align*}

11.250

21113

11411

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

11.253

21114

12051

\begin{align*} y^{\prime }&=-\frac {i \left (16 i x^{2}+16 y^{4}+8 y^{2} x^{4}+x^{8}\right ) x}{32 y} \\ \end{align*}

11.253

21115

21432

\begin{align*} y^{\prime }+q \left (x \right ) y&=0 \\ y \left (\textit {x\_0} \right ) &= y_{0} \\ \end{align*}

11.253

21116

8458

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

11.254

21117

19249

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

11.260

21118

25201

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

11.260

21119

26701

\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+2 y^{\prime \prime }-2 y^{\prime }+y&=\cos \left (2 x \right ) \\ y \left (0\right ) &= {\frac {1}{25}} \\ y \left (\pi \right ) &= {\frac {1}{25}} \\ y^{\prime }\left (0\right ) &= {\frac {2}{15}} \\ y^{\prime }\left (\pi \right ) &= {\frac {2}{25}} \\ \end{align*}

11.260

21120

21337

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

11.262

21121

10437

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

11.264

21122

8374

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

11.270

21123

15961

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

11.271

21124

24471

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

11.273

21125

7748

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

11.276

21126

4317

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

11.278

21127

12041

\begin{align*} y^{\prime }&=-\frac {i \left (54 i x^{2}+81 y^{4}+18 y^{2} x^{4}+x^{8}\right ) x}{243 y} \\ \end{align*}

11.282

21128

12171

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

11.282

21129

12263

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

11.283

21130

16518

\begin{align*} y^{\prime \prime }+16 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

11.283

21131

15397

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

11.289

21132

23054

\begin{align*} s^{\prime \prime }&=-9 s \\ s \left (0\right ) &= 9 \\ s^{\prime }\left (0\right ) &= 0 \\ \end{align*}

11.289

21133

15499

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

11.292

21134

19097

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

11.292

21135

25202

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

11.292

21136

2956

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

11.294

21137

15554

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

11.298

21138

22538

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

11.300

21139

9520

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

Series expansion around \(x=1\).

11.301

21140

15522

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

11.302

21141

7535

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

11.309

21142

21986

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

11.314

21143

24880

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

11.315

21144

12234

\begin{align*} y^{\prime }&=\frac {150 x^{3}+125 \sqrt {x}+125+125 y^{2}-100 x^{3} y-500 \sqrt {x}\, y+20 x^{6}+200 x^{{7}/{2}}+500 x +125 y^{3}-150 x^{3} y^{2}-750 y^{2} \sqrt {x}+60 x^{6} y+600 x^{{7}/{2}} y+1500 y x -8 x^{9}-120 x^{{13}/{2}}-600 x^{4}-1000 x^{{3}/{2}}}{125 x} \\ \end{align*}

11.317

21145

20716

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

11.317

21146

10315

\begin{align*} {y^{\prime }}^{2}&=\frac {1}{x^{2} y^{3}} \\ \end{align*}

11.318

21147

18056

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

11.323

21148

24246

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

11.325

21149

20831

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

11.326

21150

4348

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

11.329

21151

11851

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

11.330

21152

15796

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

11.330

21153

7847

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

11.334

21154

9093

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

11.336

21155

26098

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

11.336

21156

5276

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

11.339

21157

11566

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

11.339

21158

25558

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

11.339

21159

25861

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

11.342

21160

10055

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

11.348

21161

10325

\begin{align*} y^{\prime }&=10+{\mathrm e}^{x +y} \\ \end{align*}

11.350

21162

24985

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

11.352

21163

13252

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

11.353

21164

8611

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

Series expansion around \(x=0\).

11.358

21165

14012

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

11.360

21166

22363

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

11.362

21167

22603

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

11.365

21168

25452

\begin{align*} y^{\prime }-a y&=A \cos \left (\omega t \right )+B \sin \left (\omega t \right ) \\ \end{align*}

11.368

21169

24306

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

11.373

21170

22042

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

11.375

21171

5025

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

11.376

21172

7480

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

11.382

21173

22964

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

11.383

21174

735

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

11.384

21175

10161

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

11.385

21176

10428

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

11.388

21177

15719

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

Using Laplace transform method.

11.391

21178

9923

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

Series expansion around \(x=0\).

11.392

21179

15803

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

11.394

21180

25203

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

11.396

21181

18878

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

11.400

21182

9207

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

11.401

21183

24134

\begin{align*} \theta ^{\prime }&=z \left (-z^{2}+1\right ) \sec \left (\theta \right )^{2} \\ \end{align*}

11.401

21184

732

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

11.402

21185

13453

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

11.402

21186

15548

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

11.406

21187

11911

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

11.411

21188

19412

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

11.411

21189

16207

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

11.417

21190

19852

\begin{align*} e y^{\prime \prime }&=P \left (-y+a \right ) \\ \end{align*}

11.418

21191

11923

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

11.419

21192

18059

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

11.419

21193

6594

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

11.420

21194

20466

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

11.421

21195

5065

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

11.422

21196

15347

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

11.424

21197

22285

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

11.427

21198

19738

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

11.428

21199

11918

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

11.430

21200

22598

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

11.432