2.3.274 Problems 27301 to 27400

Table 2.1121: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

27301

6072

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

98.070

27302

5635

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

98.105

27303

1644

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

98.177

27304

20597

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

98.262

27305

19395

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

98.308

27306

26349

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

98.398

27307

13507

\begin{align*} y y^{\prime }-y&=-\frac {3 x}{16}+\frac {5 A}{x^{{1}/{3}}}-\frac {12 A^{2}}{x^{{5}/{3}}} \\ \end{align*}

98.482

27308

26663

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

98.677

27309

19999

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

98.914

27310

6074

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

99.138

27311

13589

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

99.185

27312

6257

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

99.235

27313

13923

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

99.291

27314

11771

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

99.341

27315

13569

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

99.705

27316

2915

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

99.769

27317

21392

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

99.834

27318

11797

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

100.556

27319

21813

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

100.565

27320

13570

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

100.633

27321

5674

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

101.128

27322

22605

\begin{align*} y^{\prime }&=\sqrt {\frac {5 x -6 y}{5 x +6 y}} \\ \end{align*}

101.184

27323

20443

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

101.198

27324

5342

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

101.317

27325

12940

\begin{align*} y y^{\prime \prime }+a {y^{\prime }}^{2}+b y^{2} y^{\prime }+c y^{4}&=0 \\ \end{align*}

101.552

27326

24178

\begin{align*} y \left (9 x -2 y\right )-x \left (6 x -y\right ) y^{\prime }&=0 \\ y \left (1\right ) &= 1 \\ \end{align*}

101.601

27327

26412

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

101.651

27328

6082

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

101.835

27329

15357

\begin{align*} 3 y-7 x +7-\left (3 x -7 y-3\right ) y^{\prime }&=0 \\ \end{align*}

101.931

27330

13590

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

101.948

27331

12636

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

102.206

27332

15594

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

102.325

27333

22400

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

102.507

27334

13622

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

102.620

27335

11998

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

102.932

27336

6442

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

102.979

27337

12631

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

103.131

27338

11503

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

103.133

27339

22346

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

103.142

27340

13520

\begin{align*} y y^{\prime }-y&=-\frac {3 x}{16}+\frac {A}{x^{{5}/{3}}} \\ \end{align*}

103.210

27341

11844

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

103.264

27342

12523

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

103.284

27343

12931

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

103.480

27344

12635

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

103.530

27345

13513

\begin{align*} y y^{\prime }-y&=-\frac {4 x}{25}+\frac {A}{\sqrt {x}} \\ \end{align*}

103.614

27346

11609

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

103.984

27347

607

\begin{align*} x^{\prime }&=3 x-4 y+z+t \\ y^{\prime }&=x-3 z+t^{2} \\ z^{\prime }&=6 y-7 z+t^{3} \\ \end{align*}

104.161

27348

18342

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

104.433

27349

5620

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

104.464

27350

5513

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

104.534

27351

26447

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

104.589

27352

13571

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

104.627

27353

13530

\begin{align*} y y^{\prime }-y&=-\frac {3 x}{16}+\frac {3 A}{x^{{1}/{3}}}-\frac {12 A^{2}}{x^{{5}/{3}}} \\ \end{align*}

104.700

27354

3312

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

104.724

27355

13559

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

104.989

27356

12619

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

105.367

27357

10007

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

105.909

27358

21387

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

105.995

27359

22009

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

106.064

27360

13558

\begin{align*} y y^{\prime }&=\frac {3 y}{\sqrt {a \,x^{{3}/{2}}+8 x}}+1 \\ \end{align*}

106.117

27361

13480

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

106.123

27362

23868

\begin{align*} y^{\prime }&=\frac {y x +3}{5 x -y} \\ \end{align*}

106.313

27363

13556

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

106.410

27364

13343

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

106.514

27365

26427

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

106.714

27366

14065

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

106.999

27367

5615

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

107.199

27368

22408

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

107.552

27369

13371

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

107.712

27370

7966

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

107.757

27371

6920

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

107.801

27372

23127

\begin{align*} x^{\prime }&=\frac {a x^{{5}/{6}}}{\left (-B t +b \right )^{{3}/{2}}} \\ \end{align*}

108.157

27373

13886

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

108.167

27374

19739

\begin{align*} \phi ^{\prime \prime }&=\frac {4 \pi n c}{\sqrt {v_{0}^{2}+\frac {2 e \left (\phi -V_{0} \right )}{m}}} \\ \end{align*}

108.207

27375

5071

\begin{align*} \left (4 x -y\right ) y^{\prime }+2 x -5 y&=0 \\ \end{align*}

108.333

27376

11770

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

108.440

27377

13504

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

108.650

27378

21461

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

108.706

27379

20473

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

108.727

27380

13614

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

108.746

27381

5248

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

108.831

27382

6139

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

109.260

27383

5460

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

109.273

27384

13547

\begin{align*} y y^{\prime }-y&=\frac {15 x}{4}+\frac {6 A}{x^{{1}/{3}}}-\frac {3 A^{2}}{x^{{5}/{3}}} \\ \end{align*}

109.430

27385

24221

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

109.472

27386

13540

\begin{align*} y y^{\prime }-y&=-\frac {12 x}{49}+A \sqrt {x} \\ \end{align*}

109.806

27387

18014

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

109.871

27388

2912

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

109.997

27389

25715

\begin{align*} y^{\prime }&=\sqrt {y^{2}-9} \\ y \left (1\right ) &= 4 \\ \end{align*}

110.140

27390

11296

\begin{align*} y^{\prime \prime }&=-\frac {\left (5 x^{2}+27\right ) y}{36 \left (x^{2}-1\right )^{2}} \\ \end{align*}

110.187

27391

20296

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

110.355

27392

13845

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

110.684

27393

13508

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

111.070

27394

6224

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

111.234

27395

13914

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

111.360

27396

13817

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

111.794

27397

13536

\begin{align*} y y^{\prime }-y&=\frac {63 x}{4}+\frac {A}{x^{{5}/{3}}} \\ \end{align*}

111.898

27398

23211

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

111.970

27399

5673

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

112.394

27400

6983

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

112.611