2.3.234 Problems 23301 to 23400

Table 2.1041: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

23301

23178

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

7.946

23302

15490

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

7.947

23303

16436

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

7.955

23304

8408

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

7.957

23305

19133

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

7.958

23306

22359

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

7.959

23307

11979

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

7.960

23308

21764

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

7.964

23309

1204

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

7.965

23310

25752

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

7.968

23311

5334

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

7.969

23312

26254

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

7.970

23313

4931

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

7.974

23314

27230

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

7.974

23315

5462

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

7.985

23316

11652

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

7.986

23317

19279

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

7.988

23318

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*}

7.996

23319

12335

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

7.999

23320

19375

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

8.000

23321

15792

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

8.003

23322

26899

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

8.003

23323

12365

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

8.007

23324

16978

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

8.007

23325

12330

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

8.008

23326

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*}

8.009

23327

5874

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

8.010

23328

17327

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

8.010

23329

20466

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

8.010

23330

20570

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

8.010

23331

11412

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

8.011

23332

7024

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

8.013

23333

21990

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

8.016

23334

27307

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

8.016

23335

3774

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

8.017

23336

11595

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

8.018

23337

7497

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

8.022

23338

17963

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

8.025

23339

19075

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

8.029

23340

11783

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

8.030

23341

26356

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

8.030

23342

16377

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

8.033

23343

16202

\begin{align*} y^{3}-25 y+y^{\prime }&=0 \\ \end{align*}

8.035

23344

2517

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

8.036

23345

6907

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

8.036

23346

24954

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

8.043

23347

3660

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

8.044

23348

15923

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

8.048

23349

12374

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

8.053

23350

11576

\begin{align*} \left (-1+3 x +y\right )^{2} y^{\prime }-\left (-1+2 y\right ) \left (4 y+6 x -3\right )&=0 \\ \end{align*}

8.056

23351

4688

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

8.059

23352

22410

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

8.060

23353

25788

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

8.062

23354

27463

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

8.065

23355

13677

\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*}

8.068

23356

21185

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

8.073

23357

24232

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

8.074

23358

18561

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

8.076

23359

27226

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

8.076

23360

7245

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

8.081

23361

23876

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

8.081

23362

7927

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

8.087

23363

8310

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

8.092

23364

8713

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

8.092

23365

19672

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

8.092

23366

20544

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

8.098

23367

19915

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

8.099

23368

7507

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

8.101

23369

8751

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

8.102

23370

14442

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

8.102

23371

4906

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

8.113

23372

13013

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

8.115

23373

15541

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

8.115

23374

20976

\begin{align*} y^{\prime }-y+y^{2} {\mathrm e}^{x}+5 \,{\mathrm e}^{-x}&=0 \\ y \left (0\right ) &= \eta \\ \end{align*}

8.115

23375

19202

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

8.116

23376

26190

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

8.118

23377

17730

\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (16 x^{2}-25\right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

8.120

23378

9791

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

8.125

23379

12373

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

8.129

23380

19738

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

8.130

23381

17920

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

8.131

23382

26891

\begin{align*} 4 y^{4}-1+12 x y^{3} y^{\prime }&=0 \\ y \left (1\right ) &= 2 \\ \end{align*}

8.134

23383

12089

\begin{align*} y^{\prime }&=-\frac {1}{-x -\textit {\_F1} \left (y-\ln \left (x \right )\right ) y \,{\mathrm e}^{y}} \\ \end{align*}

8.136

23384

19413

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

8.145

23385

20636

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

8.151

23386

12329

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

8.152

23387

12704

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

8.155

23388

24296

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

8.159

23389

6415

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

8.166

23390

26378

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

8.168

23391

12521

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

8.169

23392

17120

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

8.171

23393

23209

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

8.172

23394

9162

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

8.173

23395

24299

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

8.174

23396

7499

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

8.178

23397

5756

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

8.180

23398

12259

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

8.180

23399

18559

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

8.186

23400

14554

\begin{align*} 2 x +3 y+1+\left (4 x +6 y+1\right ) y^{\prime }&=0 \\ y \left (-2\right ) &= 2 \\ \end{align*}

8.187