2.3.255 Problems 25401 to 25500

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

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

25401

13512

\begin{align*} y y^{\prime }-y&=\frac {3 x}{8}+\frac {3 \sqrt {a^{2}+x^{2}}}{8}-\frac {a^{2}}{16 \sqrt {a^{2}+x^{2}}} \\ \end{align*}

111.288

25402

5691

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

111.440

25403

18732

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

111.697

25404

11631

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

111.801

25405

13264

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

112.030

25406

6131

\begin{align*} \operatorname {a2} y+\left (\operatorname {b1} x +\operatorname {a1} \right ) y^{\prime }+x \left (\operatorname {a0} +x \right ) y^{\prime \prime }&=0 \\ \end{align*}

112.040

25407

6204

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

112.088

25408

914

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

112.112

25409

18720

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

112.118

25410

17815

\begin{align*} x^{\prime \prime }+4 x^{\prime }+13 x&=\left \{\begin {array}{cc} 1 & 0\le t <\pi \\ 1-t & \pi \le t <2 \pi \\ 0 & 2 \pi \le t \end {array}\right . \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}

112.476

25411

24887

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

112.694

25412

13572

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

112.969

25413

17919

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

112.996

25414

13397

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

113.246

25415

6171

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

113.355

25416

13304

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

113.371

25417

4113

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

113.740

25418

6203

\begin{align*} 4 y x -\left (x^{2}+7\right ) y^{\prime }+x \left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}

113.748

25419

13537

\begin{align*} y y^{\prime }-y&=2 x +2 A \left (10 \sqrt {x}+31 A +\frac {30 A^{2}}{\sqrt {x}}\right ) \\ \end{align*}

114.001

25420

13479

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

114.484

25421

13526

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

114.529

25422

24886

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

114.703

25423

12660

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

114.759

25424

13538

\begin{align*} y y^{\prime }-y&=2 x +2 A \left (-10 \sqrt {x}+19 A +\frac {30 A^{2}}{\sqrt {x}}\right ) \\ \end{align*}

115.034

25425

1681

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

115.123

25426

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 )+a \lambda \\ \end{align*}

115.431

25427

12578

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

115.626

25428

901

\begin{align*} y^{\prime \prime }-4 y&=x \,{\mathrm e}^{x} \\ \end{align*}

116.268

25429

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*}

116.730

25430

8834

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

116.844

25431

13853

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

116.981

25432

15107

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

117.114

25433

6532

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

117.398

25434

5181

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

117.400

25435

7154

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

117.827

25436

6087

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

117.868

25437

13469

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

118.092

25438

5869

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

118.095

25439

6197

\begin{align*} \operatorname {a2} y+x \left (\operatorname {b1} x +\operatorname {a1} \right ) y^{\prime }+x^{3} y^{\prime \prime }&=0 \\ \end{align*}

118.694

25440

5433

\begin{align*} {y^{\prime }}^{2}-3 x y^{{2}/{3}} y^{\prime }+9 y^{{5}/{3}}&=0 \\ \end{align*}

118.855

25441

17288

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

119.017

25442

12511

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

119.185

25443

13544

\begin{align*} y y^{\prime }-y&=-\frac {10 x}{49}+\frac {2 A \left (4 \sqrt {x}+61 A +\frac {12 A^{2}}{\sqrt {x}}\right )}{49} \\ \end{align*}

119.269

25444

13896

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

119.495

25445

6572

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

120.297

25446

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*}

120.351

25447

17654

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

120.427

25448

6369

\begin{align*} 2 y^{\prime \prime }&=1+12 y^{2} \\ \end{align*}

120.730

25449

5345

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

120.809

25450

6224

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

121.057

25451

6232

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

121.097

25452

12516

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

121.159

25453

13470

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

121.240

25454

13833

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

121.563

25455

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*}

121.627

25456

12584

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

121.881

25457

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*}

122.072

25458

12565

\begin{align*} \operatorname {A2} \left (a x +b \right )^{2} y^{\prime \prime }+\operatorname {A1} \left (a x +b \right ) y^{\prime }+\operatorname {A0} \left (a x +b \right ) y&=0 \\ \end{align*}

122.146

25459

13816

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

122.240

25460

13814

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

122.267

25461

6836

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

122.964

25462

20511

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

122.997

25463

12550

\begin{align*} \left (3 x -1\right )^{2} y^{\prime \prime }+3 \left (3 x -1\right ) y^{\prime }-9 y-\ln \left (3 x -1\right )^{2}&=0 \\ \end{align*}

123.151

25464

5952

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

123.517

25465

13548

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

124.393

25466

20777

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

125.630

25467

909

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

125.829

25468

13519

\begin{align*} y y^{\prime }-y&=-\frac {30 x}{121}+\frac {3 A \left (21 \sqrt {x}+35 A +\frac {6 A^{2}}{\sqrt {x}}\right )}{242} \\ \end{align*}

125.942

25469

7868

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

125.964

25470

912

\begin{align*} m x^{\prime \prime }+k x&=F_{0} \cos \left (\omega t \right ) \\ \end{align*}

126.010

25471

6198

\begin{align*} \left (\operatorname {b2} x +\operatorname {a2} \right ) y+x \left (\operatorname {b1} x +\operatorname {a1} \right ) y^{\prime }+x^{3} y^{\prime \prime }&=0 \\ \end{align*}

126.292

25472

13406

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

127.190

25473

13509

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

127.716

25474

20004

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

127.787

25475

6234

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

127.792

25476

12072

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

127.948

25477

5248

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

128.161

25478

2820

\begin{align*} z^{\prime \prime }+z+z^{5}&=0 \\ \end{align*}

128.317

25479

13609

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

128.497

25480

13848

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

128.622

25481

7725

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

128.743

25482

13897

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

128.777

25483

2330

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

129.258

25484

11584

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

129.281

25485

192

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

129.730

25486

13849

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

130.665

25487

13588

\begin{align*} y y^{\prime }+\frac {a \left (39 x -4\right ) y}{42 x^{{9}/{7}}}&=-\frac {a^{2} \left (x -1\right ) \left (9 x -1\right )}{42 x^{{11}/{7}}} \\ \end{align*}

130.854

25488

5624

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

131.030

25489

385

\begin{align*} x^{\prime \prime }+100 x&=225 \cos \left (5 t \right )+300 \sin \left (5 t \right ) \\ x \left (0\right ) &= 375 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}

131.331

25490

5232

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

131.588

25491

20524

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

132.480

25492

4153

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

132.594

25493

4922

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

132.893

25494

2502

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

133.092

25495

2521

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

133.378

25496

24155

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

133.682

25497

6172

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

133.726

25498

13515

\begin{align*} y y^{\prime }-y&=-\frac {12 x}{49}+\frac {2 A \left (5 \sqrt {x}+34 A +\frac {15 A^{2}}{\sqrt {x}}\right )}{49} \\ \end{align*}

133.770

25499

13518

\begin{align*} y y^{\prime }-y&=-\frac {12 x}{49}+\frac {6 A \left (-3 \sqrt {x}+23 A +\frac {12 A^{2}}{\sqrt {x}}\right )}{49} \\ \end{align*}

133.897

25500

1165

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

133.943