2.3.202 Problems 20101 to 20200

Table 2.947: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

20101

16928

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

5.317

20102

7187

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

5.318

20103

14903

\begin{align*} y^{\prime }+2 \cot \left (x \right ) y&=5 \\ y \left (\frac {\pi }{2}\right ) &= 1 \\ \end{align*}

5.318

20104

15959

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

5.319

20105

4765

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

5.320

20106

2509

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

5.322

20107

4632

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

5.322

20108

17477

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

5.322

20109

19090

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

5.325

20110

13323

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

5.331

20111

6324

\begin{align*} y^{\prime \prime }&=\operatorname {f3} \left (x \right )+\operatorname {f2} \left (x \right ) y^{2}+\left (\operatorname {f1} \left (x \right )-2 y\right ) y^{\prime } \\ \end{align*}

5.339

20112

12266

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

5.339

20113

13709

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

5.339

20114

14229

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

5.339

20115

5584

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

5.342

20116

5538

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

5.344

20117

17962

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

5.345

20118

22325

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

5.345

20119

4915

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

5.348

20120

17221

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

5.348

20121

1708

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

5.350

20122

4617

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

5.351

20123

4102

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

5.352

20124

14509

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

5.352

20125

20285

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

5.353

20126

22439

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

5.354

20127

13303

\begin{align*} y^{\prime }&=a \,{\mathrm e}^{\lambda x} y^{2}+b n \,x^{n -1}-a \,b^{2} {\mathrm e}^{\lambda x} x^{2 n} \\ \end{align*}

5.355

20128

5747

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

5.356

20129

17908

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

5.357

20130

17937

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

5.358

20131

4914

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

5.359

20132

4760

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

5.360

20133

16366

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

5.361

20134

26205

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

5.361

20135

10030

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

5.362

20136

10250

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

5.362

20137

10454

\begin{align*} x^{2} y^{\prime \prime }-x \left (6+x \right ) y^{\prime }+10 y&=0 \\ \end{align*}
Series expansion around \(x=0\).

5.362

20138

12244

\begin{align*} y^{\prime }&=-\frac {8 x \left (-1+a \right ) \left (1+a \right )}{8+2 x^{4}+x^{6}-8 y-8 y^{2} a^{2} x^{2}-2 y^{4} a^{2}+y^{6}+4 a^{4} y^{2} x^{2}+2 y^{4}+3 x^{2} y^{4}-9 y^{2} a^{2} x^{4}+a^{8} x^{6}-4 a^{6} x^{6}+6 a^{4} x^{6}-8 a^{2}+3 y^{2} x^{4}+4 y^{2} x^{2}-6 a^{2} x^{4}-6 y^{4} a^{2} x^{2}-2 a^{6} x^{4}+6 a^{4} x^{4}-4 a^{2} x^{6}-y^{6} a^{2}+3 a^{4} y^{4} x^{2}-3 a^{6} y^{2} x^{4}+9 y^{2} a^{4} x^{4}} \\ \end{align*}

5.362

20139

5744

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

5.365

20140

17082

\begin{align*} y^{\prime }&={\mathrm e}^{2 y+10 t} \\ \end{align*}

5.367

20141

24222

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

5.367

20142

12028

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

5.368

20143

23972

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

5.371

20144

8251

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

5.372

20145

2344

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

5.374

20146

22451

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

5.375

20147

21048

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

5.376

20148

22531

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

5.377

20149

2862

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

5.378

20150

7465

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

5.379

20151

8266

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

5.380

20152

17170

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

5.380

20153

12162

\begin{align*} y^{\prime }&=-\frac {\left (-108 x^{{3}/{2}}-216-216 y^{2}+72 x^{3} y-6 x^{6}-216 y^{3}+108 x^{3} y^{2}-18 x^{6} y+x^{9}\right ) \sqrt {x}}{216} \\ \end{align*}

5.381

20154

1733

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

5.382

20155

19740

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

5.390

20156

7409

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

5.391

20157

12052

\begin{align*} y^{\prime }&=\frac {2 y^{6}}{y^{3}+2+16 x y^{2}+32 x^{2} y^{4}} \\ \end{align*}

5.391

20158

19414

\begin{align*} \frac {\cos \left (y\right )}{x +3}-\left (\sin \left (y\right ) \ln \left (5 x +15\right )-\frac {1}{y}\right ) y^{\prime }&=0 \\ \end{align*}

5.392

20159

12932

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

5.393

20160

16906

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

5.393

20161

18355

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

5.393

20162

7397

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

5.396

20163

20825

\begin{align*} 2 x y^{2}-3 y^{3}+\left (7-3 x y^{2}\right ) y^{\prime }&=0 \\ \end{align*}

5.400

20164

7484

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

5.401

20165

13239

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

5.401

20166

20751

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

5.401

20167

10163

\begin{align*} v v^{\prime }&=\frac {2 v^{2}}{r^{3}}+\frac {\lambda r}{3} \\ \end{align*}

5.405

20168

2843

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

5.406

20169

22091

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

5.408

20170

7563

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

5.409

20171

25736

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

5.413

20172

12057

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

5.414

20173

14351

\begin{align*} x^{\prime }+5 x&=\operatorname {Heaviside}\left (-2+t \right ) \\ x \left (0\right ) &= 1 \\ \end{align*}
Using Laplace transform method.

5.414

20174

2845

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

5.415

20175

22544

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

5.416

20176

11988

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

5.420

20177

22445

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

5.421

20178

7183

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

5.423

20179

13885

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

5.428

20180

15647

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

5.429

20181

12296

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

5.431

20182

22440

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

5.432

20183

16919

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

5.434

20184

11595

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

5.435

20185

5044

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

5.436

20186

207

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

5.437

20187

7549

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

5.440

20188

903

\begin{align*} x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=x^{3} \\ \end{align*}

5.441

20189

15961

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

5.444

20190

18490

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

5.444

20191

25789

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

5.445

20192

24914

\begin{align*} y^{\prime }&=\frac {y^{2}-4 t y+6 t^{2}}{t^{2}} \\ \end{align*}

5.446

20193

714

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

5.447

20194

1243

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

5.450

20195

22599

\begin{align*} y^{\prime }&={\mathrm e}^{x +3 y}+1 \\ \end{align*}

5.450

20196

22575

\begin{align*} i^{\prime }&=\frac {i t^{2}}{t^{3}-i^{3}} \\ \end{align*}

5.454

20197

10431

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

5.455

20198

20544

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

5.457

20199

3778

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

5.459

20200

1566

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

5.460