2.3.243 Problems 24201 to 24300

Table 2.1059: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

24201

12087

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

12.446

24202

21403

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

12.446

24203

19781

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

12.451

24204

15349

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

12.452

24205

14517

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

12.453

24206

7532

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

12.454

24207

22449

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

12.454

24208

3646

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

12.455

24209

20264

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

12.457

24210

26399

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

12.459

24211

17965

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

12.467

24212

5627

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

12.476

24213

13725

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

12.479

24214

8776

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

12.487

24215

21791

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

12.487

24216

9150

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

12.493

24217

19712

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

12.499

24218

8469

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

12.502

24219

20434

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

12.508

24220

17295

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

12.522

24221

21386

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

12.529

24222

14914

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

12.531

24223

11352

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

12.534

24224

12197

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

12.539

24225

15643

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

12.540

24226

20306

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

12.541

24227

15966

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

12.544

24228

8235

\begin{align*} y^{\prime }&=\sqrt {y^{2}-9} \\ y \left (-1\right ) &= 1 \\ \end{align*}

12.550

24229

11874

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

12.555

24230

13971

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

12.557

24231

16265

\begin{align*} x y^{\prime }+\cos \left (x^{2}\right )&=827 y \\ \end{align*}

12.557

24232

4819

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

12.571

24233

21841

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

12.576

24234

2951

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

12.577

24235

25876

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

12.579

24236

13650

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

12.580

24237

7029

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

12.586

24238

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*}

12.587

24239

25838

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

12.588

24240

19350

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

12.591

24241

2819

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

12.592

24242

5320

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

12.599

24243

4688

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

12.605

24244

13805

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

12.613

24245

22395

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

12.613

24246

1605

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

12.619

24247

12123

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

12.619

24248

5229

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

12.620

24249

24199

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

12.621

24250

27412

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

12.625

24251

15254

\begin{align*} t^{2} y^{\prime \prime }+3 t y^{\prime }+y&=t^{7} \\ \end{align*}

12.627

24252

20989

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

12.630

24253

22541

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

12.638

24254

6557

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

12.642

24255

13248

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

12.653

24256

21997

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

12.655

24257

23198

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

12.655

24258

1662

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

12.665

24259

15255

\begin{align*} t^{2} y^{\prime \prime }-6 t y^{\prime }+\sin \left (2 t \right ) y&=\ln \left (t \right ) \\ \end{align*}

12.681

24260

12098

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

12.682

24261

22974

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

12.687

24262

15533

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

12.688

24263

5130

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

12.694

24264

7931

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

12.694

24265

25693

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

12.695

24266

115

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

12.697

24267

12130

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

12.706

24268

12276

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

12.708

24269

2882

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

12.714

24270

11702

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

12.714

24271

4932

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

12.717

24272

21362

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

12.718

24273

14887

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

12.720

24274

22489

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

12.721

24275

1231

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

12.725

24276

4418

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

12.731

24277

17294

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

12.731

24278

4423

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

12.735

24279

20225

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

12.747

24280

12056

\begin{align*} y^{\prime }&=\frac {-4 y x -x^{3}-2 a \,x^{2}-4 x +8}{8 y+2 x^{2}+4 a x +8} \\ \end{align*}

12.749

24281

14505

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

12.752

24282

22414

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

12.754

24283

21452

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

12.755

24284

26258

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

12.755

24285

8230

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

12.765

24286

8233

\begin{align*} y^{\prime }&=\sqrt {y^{2}-9} \\ y \left (5\right ) &= 3 \\ \end{align*}

12.765

24287

23221

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

12.766

24288

105

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

12.769

24289

5917

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

12.780

24290

5918

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

12.783

24291

6298

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

12.789

24292

24229

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

12.813

24293

25820

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

12.817

24294

1654

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

12.819

24295

19936

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

12.821

24296

14514

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

12.825

24297

4189

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

12.827

24298

20948

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

12.830

24299

14154

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

12.832

24300

9630

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

Using Laplace transform method.

12.833