2.3.263 Problems 26201 to 26300

Table 2.1099: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

26201

6045

\begin{align*} \left (\operatorname {a1} +\operatorname {b1} \,x^{k}+\operatorname {c1} \,x^{2 k}\right ) y+x \left (\operatorname {a0} +\operatorname {b0} \,x^{k}\right ) y^{\prime }+x^{2} y^{\prime \prime }&=0 \\ \end{align*}

35.257

26202

3479

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

35.262

26203

13891

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

35.269

26204

13341

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

35.279

26205

8684

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

35.287

26206

1233

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

35.290

26207

19705

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

35.298

26208

5530

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

35.345

26209

24177

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

35.355

26210

5141

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

35.362

26211

5062

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

35.369

26212

11741

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

35.385

26213

19493

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

35.390

26214

6910

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

35.400

26215

12483

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

35.418

26216

4694

\begin{align*} y^{\prime }&=a_{0} +a_{1} y+a_{2} y^{2}+a_{3} y^{3} \\ \end{align*}

35.437

26217

17270

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

35.491

26218

14532

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

35.500

26219

26390

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

35.513

26220

13291

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

35.550

26221

22303

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

35.551

26222

23875

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

35.565

26223

25846

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

35.579

26224

10128

\begin{align*} y^{\prime \prime }-\frac {y^{\prime }}{x}-x^{3} y-x^{4}-\frac {1}{x}&=0 \\ \end{align*}

35.585

26225

13361

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

35.612

26226

11363

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

35.631

26227

11645

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

35.649

26228

11906

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

35.656

26229

5063

\begin{align*} \left (3-x +y\right ) y^{\prime }&=11-4 x +3 y \\ \end{align*}

35.657

26230

6916

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

35.659

26231

18580

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

35.695

26232

3682

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

35.721

26233

16292

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

35.777

26234

26401

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

35.790

26235

4851

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

35.799

26236

15353

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

35.827

26237

13905

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

35.841

26238

15352

\begin{align*} \left (7 x +5 y\right ) y^{\prime }+10 x +8 y&=0 \\ \end{align*}

35.845

26239

17348

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

35.856

26240

21978

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

35.874

26241

20237

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

35.875

26242

20320

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

35.943

26243

22572

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

35.946

26244

6806

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

35.961

26245

4747

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

35.973

26246

19314

\begin{align*} \frac {4 y^{2}-2 x^{2}}{4 x y^{2}-x^{3}}+\frac {\left (8 y^{2}-x^{2}\right ) y^{\prime }}{4 y^{3}-x^{2} y}&=0 \\ \end{align*}

36.023

26247

14006

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

36.036

26248

6400

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

36.069

26249

2913

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

36.081

26250

9975

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

36.085

26251

6912

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

36.086

26252

4356

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

36.095

26253

6425

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

36.098

26254

11990

\begin{align*} y^{\prime }&=\frac {\left (-\ln \left (-1+y\right )+\ln \left (y+1\right )+2 \ln \left (x \right )\right )^{2} x \left (y+1\right )^{2}}{16} \\ \end{align*}

36.172

26255

13333

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

36.176

26256

18053

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

36.191

26257

10432

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

36.225

26258

15619

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

36.233

26259

5105

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

36.280

26260

14016

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

36.295

26261

14470

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

36.319

26262

24363

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

36.323

26263

8704

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

36.332

26264

12872

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

36.358

26265

6816

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

36.369

26266

5005

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

36.375

26267

15615

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

36.377

26268

13795

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

36.408

26269

18600

\begin{align*} y^{\prime }&=\frac {4 y-7 x}{5 x -y} \\ \end{align*}

36.452

26270

12482

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

36.461

26271

20246

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

36.485

26272

18627

\begin{align*} 4 x y y^{\prime }&=8 x^{2}+5 y^{2} \\ \end{align*}

36.504

26273

18551

\begin{align*} y^{\prime }&=\frac {t -y}{2 t +5 y} \\ \end{align*}

36.542

26274

9153

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

36.569

26275

5502

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

36.586

26276

19300

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

36.590

26277

26449

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

36.618

26278

23902

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

36.662

26279

21285

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

Using Laplace transform method.

36.665

26280

17654

\begin{align*} 9 x^{2} y^{\prime \prime }+27 x y^{\prime }+10 y&=\frac {1}{x} \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= -1 \\ \end{align*}

36.675

26281

13501

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

36.711

26282

15356

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

36.719

26283

6583

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

36.726

26284

24572

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

36.736

26285

4671

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

36.770

26286

5262

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

36.772

26287

14550

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

36.794

26288

6886

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

36.825

26289

6037

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

36.882

26290

5501

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

36.935

26291

4393

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

36.950

26292

14043

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

36.996

26293

11927

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

37.012

26294

26681

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

37.021

26295

14466

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

37.033

26296

5263

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

37.041

26297

5179

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

37.050

26298

13377

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

37.050

26299

6335

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

37.063

26300

12006

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

37.100