2.3.193 Problems 19201 to 19300

Table 2.917: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

19201

24275

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

2.632

19202

128

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

2.633

19203

4349

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

2.633

19204

4852

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

2.633

19205

17850

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

2.634

19206

18495

\begin{align*} y^{\prime }&=\frac {-{\mathrm e}^{x}+3 x^{2}}{2 y-11} \\ y \left (0\right ) &= 11 \\ \end{align*}

2.634

19207

712

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

2.635

19208

13678

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

2.635

19209

5130

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

2.636

19210

23852

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

2.636

19211

11854

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

2.637

19212

21170

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

2.637

19213

12323

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

2.638

19214

14497

\begin{align*} y^{\prime }+\left (4 y-\frac {8}{y^{3}}\right ) x&=0 \\ \end{align*}

2.638

19215

1178

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

2.639

19216

1653

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

2.639

19217

11781

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

2.639

19218

4226

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

2.641

19219

4327

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

2.641

19220

12350

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

2.641

19221

16222

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

2.642

19222

1241

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

2.643

19223

17861

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

2.644

19224

3659

\begin{align*} y^{\prime }+\frac {2 y}{x}&=6 \sqrt {x^{2}+1}\, \sqrt {y} \\ \end{align*}

2.645

19225

9759

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

2.646

19226

21448

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

2.646

19227

656

\begin{align*} y^{\prime }&=x \sqrt {x^{2}+9} \\ y \left (-4\right ) &= 0 \\ \end{align*}

2.647

19228

18480

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

2.647

19229

3599

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

2.648

19230

24217

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

2.648

19231

4714

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

2.649

19232

16978

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

2.649

19233

4712

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

2.650

19234

4787

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

2.650

19235

7430

\begin{align*} y x^{\prime }+2 x&=5 y^{3} \\ \end{align*}

2.650

19236

6790

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

2.651

19237

7665

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

2.651

19238

7745

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

2.651

19239

4264

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

2.652

19240

5949

\begin{align*} \left (b x +a \right ) y+8 y^{\prime }+16 y^{\prime \prime } x&=0 \\ \end{align*}

2.652

19241

13810

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

2.652

19242

19461

\begin{align*} y^{\prime \prime }+8 y&=0 \\ \end{align*}

2.653

19243

2964

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

2.654

19244

5613

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

2.654

19245

7420

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

2.655

19246

11720

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

2.655

19247

12967

\begin{align*} 4 y y^{\prime \prime }-3 {y^{\prime }}^{2}-12 y^{3}&=0 \\ \end{align*}

2.655

19248

21319

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

2.655

19249

21602

\begin{align*} x^{2} u^{\prime \prime }-3 x u^{\prime }+13 u&=0 \\ u \left (1\right ) &= -1 \\ u^{\prime }\left (1\right ) &= 1 \\ \end{align*}

2.656

19250

9139

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

2.657

19251

9093

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

2.658

19252

9928

\begin{align*} y^{\prime \prime } x +\left (2 x +3\right ) y^{\prime }+8 y&=0 \\ \end{align*}
Series expansion around \(x=0\).

2.658

19253

14982

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

2.658

19254

17908

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

2.658

19255

15052

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

2.659

19256

16226

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

2.660

19257

1181

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

2.661

19258

17123

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

2.661

19259

11333

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

2.663

19260

1133

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

2.664

19261

3390

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

2.665

19262

4637

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

2.666

19263

12448

\begin{align*} x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y-5 x&=0 \\ \end{align*}

2.667

19264

25783

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

2.667

19265

7356

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

2.668

19266

7702

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

2.668

19267

11757

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

2.669

19268

19338

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

2.669

19269

1580

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

2.670

19270

2952

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

2.670

19271

7816

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

2.670

19272

11474

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

2.670

19273

14031

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

2.670

19274

20291

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

2.670

19275

21258

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

2.670

19276

5242

\begin{align*} 3 \left (x^{2}-y^{2}\right ) y^{\prime }+3 \,{\mathrm e}^{x}+6 \left (x +1\right ) x y-2 y^{3}&=0 \\ \end{align*}

2.671

19277

12396

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

2.671

19278

8357

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

2.672

19279

4323

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

2.674

19280

10314

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

2.674

19281

14895

\begin{align*} m v^{\prime }&=-m g +k v^{2} \\ \end{align*}

2.674

19282

22402

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

2.674

19283

11819

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

2.675

19284

25822

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

2.675

19285

7704

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

2.677

19286

11404

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

2.677

19287

3251

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

2.678

19288

7708

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

2.680

19289

9929

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

2.680

19290

16283

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

2.681

19291

2492

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

2.682

19292

14462

\begin{align*} \left ({\mathrm e}^{v}+1\right ) \cos \left (u \right )+{\mathrm e}^{v} \left (1+\sin \left (u \right )\right ) v^{\prime }&=0 \\ \end{align*}

2.682

19293

24235

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

2.682

19294

18533

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

2.683

19295

24350

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

2.683

19296

3528

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

2.685

19297

17148

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

2.685

19298

750

\begin{align*} x^{2} y^{\prime }+2 y x&=5 y^{4} \\ \end{align*}

2.686

19299

21758

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

2.686

19300

1121

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

2.687