2.3.213 Problems 21201 to 21300

Table 2.975: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

21201

13979

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

6.491

21202

14001

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

6.492

21203

15802

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

6.496

21204

12255

\begin{align*} y^{\prime }&=y^{3}+y^{2} x^{2}+\frac {x^{4} y}{3}+\frac {x^{6}}{27}-\frac {2 x}{3} \\ \end{align*}

6.497

21205

13449

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

6.499

21206

20310

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

6.504

21207

1626

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

6.505

21208

11593

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

6.505

21209

26464

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

6.506

21210

4092

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

6.509

21211

11333

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

6.516

21212

21432

\begin{align*} y^{\prime }+q \left (x \right ) y&=0 \\ y \left (\textit {x\_0} \right ) &= y_{0} \\ \end{align*}

6.516

21213

7630

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

6.521

21214

12537

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

6.525

21215

18533

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

6.527

21216

17326

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

6.528

21217

24028

\begin{align*} y^{\left (8\right )}+y&=x^{15} \\ \end{align*}

6.531

21218

6594

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

6.532

21219

25768

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

6.533

21220

5610

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

6.534

21221

12180

\begin{align*} y^{\prime }&=\frac {2 a \left (-y^{2}+4 a x -1\right )}{-y^{3}+4 a x y-y-2 y^{6} a +24 y^{4} a^{2} x -96 y^{2} a^{3} x^{2}+128 a^{4} x^{3}} \\ \end{align*}

6.534

21222

22963

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

6.537

21223

4936

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

6.538

21224

4981

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

6.539

21225

24146

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

6.539

21226

11870

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

6.542

21227

20110

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

6.543

21228

21347

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

6.545

21229

15084

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

6.546

21230

20233

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

6.548

21231

26208

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

6.553

21232

4605

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

6.554

21233

3665

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

6.558

21234

18496

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

6.562

21235

11902

\begin{align*} y^{\prime }&=\frac {6 y}{8 y^{4}+9 y^{3}+12 y^{2}+6 y-F \left (-\frac {y^{4}}{3}-\frac {y^{3}}{2}-y^{2}-y+x \right )} \\ \end{align*}

6.563

21236

26324

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

6.563

21237

14506

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

6.566

21238

17878

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

6.569

21239

17880

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

6.569

21240

26402

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

6.570

21241

7734

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

6.571

21242

13959

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

6.572

21243

5300

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

6.573

21244

2329

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

6.575

21245

19235

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

6.577

21246

5459

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

6.579

21247

4768

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

6.582

21248

4755

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

6.583

21249

17905

\begin{align*} \left (x^{2}+1\right ) y^{\prime }-\frac {\cos \left (2 y\right )^{2}}{2}&=0 \\ y \left (-\infty \right ) &= \frac {7 \pi }{2} \\ \end{align*}

6.583

21250

528

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

6.584

21251

12244

\begin{align*} y^{\prime }&=-\frac {8 x \left (-1+a \right ) \left (1+a \right )}{8+2 x^{4}-8 y-8 y^{2} a^{2} x^{2}-9 y^{2} a^{2} x^{4}+2 y^{4}+3 x^{2} y^{4}+y^{6}+3 a^{4} y^{4} x^{2}-3 a^{6} y^{2} x^{4}+9 y^{2} a^{4} x^{4}-8 a^{2}+4 y^{2} x^{2}+3 y^{2} x^{4}+x^{6}-6 a^{2} x^{4}-2 y^{4} a^{2}+a^{8} x^{6}-4 a^{6} x^{6}+6 a^{4} x^{6}+4 a^{4} y^{2} x^{2}-2 a^{6} x^{4}+6 a^{4} x^{4}-6 y^{4} a^{2} x^{2}-4 a^{2} x^{6}-y^{6} a^{2}} \\ \end{align*}

6.585

21252

12606

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

6.586

21253

15851

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

6.587

21254

7438

\begin{align*} \cos \left (x \right ) y^{\prime }+\sin \left (x \right ) y&=2 x \cos \left (x \right )^{2} \\ y \left (\frac {\pi }{4}\right ) &= -\frac {15 \sqrt {2}\, \pi ^{2}}{32} \\ \end{align*}

6.590

21255

4599

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

6.591

21256

6345

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

6.591

21257

17174

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

6.592

21258

22962

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

6.593

21259

4636

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

6.594

21260

7404

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

6.595

21261

4907

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

6.597

21262

7891

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

6.597

21263

7332

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

6.600

21264

17938

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

6.600

21265

4769

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

6.603

21266

19375

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

6.603

21267

17842

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

6.604

21268

4367

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

6.605

21269

23948

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

6.607

21270

21761

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

6.611

21271

25781

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

6.612

21272

25906

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

6.613

21273

4441

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

6.615

21274

9010

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

6.615

21275

4116

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

6.616

21276

4614

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

6.618

21277

21343

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

6.618

21278

19391

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

6.627

21279

8657

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

6.635

21280

19321

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

6.636

21281

22384

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

6.636

21282

25837

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

6.638

21283

5178

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

6.639

21284

18488

\begin{align*} r^{\prime }&=\frac {r^{2}}{\theta } \\ r \left (1\right ) &= 2 \\ \end{align*}

6.641

21285

22374

\begin{align*} r^{\prime }&=\frac {\sin \left (t \right )+{\mathrm e}^{r} \sin \left (t \right )}{3 \,{\mathrm e}^{r}+{\mathrm e}^{r} \cos \left (2 t \right )} \\ r \left (\frac {\pi }{2}\right ) &= 0 \\ \end{align*}

6.645

21286

26168

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

6.645

21287

13234

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

6.648

21288

22957

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

6.649

21289

22537

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

6.650

21290

17064

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

6.653

21291

15605

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

6.654

21292

5338

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

6.655

21293

15866

\begin{align*} y^{\prime }&=y^{2}-4 y-12 \\ y \left (0\right ) &= 6 \\ \end{align*}

6.655

21294

13222

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

6.656

21295

19951

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

6.658

21296

21056

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

6.658

21297

17080

\begin{align*} \left (5 x^{5}-4 \cos \left (x\right )\right ) x^{\prime }+2 \cos \left (9 t \right )+2 \sin \left (7 t \right )&=0 \\ \end{align*}

6.659

21298

20322

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

6.662

21299

20481

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

6.668

21300

3327

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

6.669