2.3.234 Problems 23301 to 23400

Table 2.999: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

23301

14227

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

9.395

23302

13979

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

9.399

23303

21081

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

9.403

23304

13216

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

9.408

23305

24172

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

9.408

23306

21059

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

9.409

23307

127

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

9.424

23308

19740

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

9.432

23309

5460

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

9.444

23310

12484

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

9.446

23311

19910

\begin{align*} \left (2 x^{2} y+4 x^{3}-12 x y^{2}+3 y^{2}-x \,{\mathrm e}^{y}+{\mathrm e}^{2 x}\right ) y^{\prime }+12 x^{2} y+2 x y^{2}+4 x^{3}-4 y^{3}+2 y \,{\mathrm e}^{2 x}-{\mathrm e}^{y}&=0 \\ \end{align*}

9.449

23312

7876

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

9.454

23313

12117

\begin{align*} y^{\prime }&=-\frac {1}{-\left (y^{3}\right )^{{2}/{3}} x -\textit {\_F1} \left (y^{3}-3 \ln \left (x \right )\right ) \left (y^{3}\right )^{{1}/{3}} x} \\ \end{align*}

9.454

23314

13309

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

9.474

23315

17891

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

9.485

23316

15894

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

9.499

23317

13310

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

9.502

23318

12183

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

9.509

23319

214

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

9.522

23320

21404

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

9.528

23321

14469

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

9.530

23322

4280

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

9.531

23323

3649

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

9.539

23324

753

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

9.540

23325

15480

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

9.540

23326

21079

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

9.540

23327

13863

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

9.544

23328

13460

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

9.547

23329

16198

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

9.549

23330

144

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

9.554

23331

6873

\begin{align*} \frac {\sqrt {f \,x^{4}+c \,x^{3}+c \,x^{2}+b x +a}\, y^{\prime }}{\sqrt {a +b y+c y^{2}+c y^{3}+f y^{4}}}&=-1 \\ \end{align*}

9.562

23332

5105

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

9.579

23333

6573

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

9.580

23334

11972

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

9.589

23335

12115

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

9.592

23336

13616

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

9.609

23337

21166

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

9.632

23338

13365

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

9.664

23339

4242

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

9.674

23340

12203

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

9.682

23341

13314

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

9.684

23342

19377

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

9.693

23343

19324

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

9.695

23344

2872

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

9.710

23345

11920

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

9.712

23346

18053

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

9.713

23347

13555

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

9.717

23348

7955

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

9.721

23349

12219

\begin{align*} y^{\prime }&=\frac {-32 y x +16 x^{3}+16 x^{2}-32 x -64 y^{3}+48 y^{2} x^{2}+96 x y^{2}-12 x^{4} y-48 x^{3} y-48 x^{2} y+x^{6}+6 x^{5}+12 x^{4}}{-64 y+16 x^{2}+32 x -64} \\ \end{align*}

9.725

23350

17959

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

9.736

23351

17091

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

9.737

23352

18602

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

9.738

23353

13462

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

9.740

23354

19956

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

9.743

23355

6831

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

9.751

23356

12192

\begin{align*} y^{\prime }&=\frac {2 a x}{-x^{3} y+2 a \,x^{3}+2 a y^{4} x^{3}-16 y^{2} a^{2} x^{2}+32 a^{3} x +2 a y^{6} x^{3}-24 y^{4} a^{2} x^{2}+96 y^{2} x \,a^{3}-128 a^{4}} \\ \end{align*}

9.753

23357

13419

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

9.769

23358

7523

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

9.771

23359

12260

\begin{align*} y^{\prime }&=\frac {x^{3} y^{3}+6 y^{2} x^{2}+12 y x +8+2 x}{x^{3}} \\ \end{align*}

9.788

23360

129

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

9.792

23361

8256

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

9.802

23362

11968

\begin{align*} y^{\prime }&=\frac {y+\ln \left (\left (x -1\right ) \left (x +1\right )\right ) x^{3}+7 \ln \left (\left (x -1\right ) \left (x +1\right )\right ) x y^{2}}{x} \\ \end{align*}

9.810

23363

13795

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

9.820

23364

14139

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

9.825

23365

13811

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

9.827

23366

13262

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

9.829

23367

21349

\begin{align*} \cos \left (x \right ) x +\left (1-6 y^{5}\right ) y^{\prime }&=0 \\ y \left (\pi \right ) &= 0 \\ \end{align*}

9.846

23368

12189

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

9.852

23369

11913

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

9.869

23370

11978

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

9.882

23371

21620

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

9.883

23372

17348

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

9.886

23373

12598

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

9.888

23374

3657

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

9.891

23375

5308

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

9.891

23376

11915

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

9.891

23377

13380

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

9.894

23378

3001

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

9.896

23379

12224

\begin{align*} y^{\prime }&=\frac {-32 a x y-8 a^{2} x^{3}-16 b \,x^{2} a -32 a x +64 y^{3}+48 a \,x^{2} y^{2}+96 b x y^{2}+12 a^{2} x^{4} y+48 y a \,x^{3} b +48 b^{2} x^{2} y+a^{3} x^{6}+6 a^{2} x^{5} b +12 a \,x^{4} b^{2}+8 b^{3} x^{3}}{64 y+16 a \,x^{2}+32 b x +64} \\ \end{align*}

9.901

23380

5150

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

9.906

23381

5879

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

9.916

23382

20831

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

9.926

23383

21261

\begin{align*} x^{\prime \prime }+x+8 x^{7}&=0 \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= a \\ \end{align*}

9.929

23384

22346

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

9.936

23385

19952

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

9.941

23386

17966

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

9.950

23387

12221

\begin{align*} y^{\prime }&=\frac {-32 y x -72 x^{3}+32 x^{2}-32 x +64 y^{3}+48 y^{2} x^{2}-192 x y^{2}+12 x^{4} y-96 x^{3} y+192 x^{2} y+x^{6}-12 x^{5}+48 x^{4}}{64 y+16 x^{2}-64 x +64} \\ \end{align*}

9.956

23388

12057

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

9.963

23389

17979

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

9.967

23390

13807

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

9.970

23391

769

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

9.991

23392

21445

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

9.992

23393

22293

\begin{align*} r^{\prime }&=\sqrt {r t} \\ \end{align*}

9.996

23394

13306

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

10.000

23395

751

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

10.001

23396

11641

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

10.004

23397

19313

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

10.005

23398

11705

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

10.007

23399

17272

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

10.013

23400

3556

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

10.017