2.3.256 Problems 25501 to 25600

Table 2.1043: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

25501

13866

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

88.898

25502

13375

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

89.113

25503

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*}

89.646

25504

12931

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

89.889

25505

12504

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

89.920

25506

20430

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

89.935

25507

9685

\begin{align*} x^{\prime }&=\frac {9 x}{10}+\frac {21 y}{10}+\frac {16 z}{5} \\ y^{\prime }&=\frac {7 x}{10}+\frac {13 y}{2}+\frac {21 z}{5} \\ z^{\prime }&=\frac {11 x}{10}+\frac {17 y}{10}+\frac {17 z}{5} \\ \end{align*}

89.959

25508

13290

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

90.135

25509

13913

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

90.798

25510

8323

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

90.978

25511

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*}

91.349

25512

11817

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

91.522

25513

13537

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

91.533

25514

21823

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

91.640

25515

19903

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

91.762

25516

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*}

91.907

25517

19398

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

92.088

25518

13819

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

92.341

25519

13444

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

92.391

25520

13519

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

92.425

25521

13588

\begin{align*} y^{\prime } y+\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*}

92.563

25522

13291

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

92.642

25523

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*}

93.020

25524

19819

\begin{align*} \left (x -3 y+4\right ) y^{\prime }&=5 x -7 y \\ \end{align*}

93.069

25525

6071

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

93.940

25526

21840

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

94.017

25527

11631

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

94.152

25528

13388

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

94.211

25529

20012

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

94.399

25530

13350

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

94.418

25531

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*}

94.498

25532

13399

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

94.793

25533

13510

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

94.857

25534

11503

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

94.935

25535

13546

\begin{align*} y^{\prime } y-y&=-\frac {4 x}{25}+\frac {A \left (7 \sqrt {x}+49 A +\frac {6 A^{2}}{\sqrt {x}}\right )}{50} \\ \end{align*}

94.966

25536

13609

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

95.198

25537

10154

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

95.683

25538

10372

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

95.737

25539

13486

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

95.931

25540

13544

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

96.036

25541

13476

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

96.381

25542

13538

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

96.424

25543

11806

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

96.434

25544

24166

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

96.438

25545

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*}

96.482

25546

21839

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

96.524

25547

18732

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

96.614

25548

10410

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

96.657

25549

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*}

97.168

25550

13636

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

97.182

25551

5433

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

97.200

25552

13278

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

97.312

25553

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*}

97.404

25554

12630

\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*}

97.415

25555

8833

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

97.579

25556

19120

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

97.827

25557

13386

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

97.864

25558

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*}

98.126

25559

6074

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

99.261

25560

21929

\begin{align*} \left (x^{3}+3\right ) y^{\prime }+2 y x +5 x^{2}&=0 \\ y \left (2\right ) &= 1 \\ \end{align*}

99.512

25561

21608

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

99.708

25562

4953

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

99.829

25563

6262

\begin{align*} \left (\operatorname {c2} \,x^{2}+\operatorname {b2} x +\operatorname {a2} \right ) y+\operatorname {a1} x \left (-x^{2}+1\right ) y^{\prime }+\left (-x^{2}+1\right )^{2} y^{\prime \prime }&=0 \\ \end{align*}

101.105

25564

13526

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

101.280

25565

11740

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

101.599

25566

12856

\begin{align*} y^{\prime \prime }-7 y^{\prime }-y^{{3}/{2}}+12 y&=0 \\ \end{align*}

102.039

25567

21818

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

102.067

25568

6112

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

102.152

25569

6087

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

102.343

25570

6173

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

102.491

25571

21789

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

102.660

25572

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*}

102.675

25573

13362

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

102.704

25574

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*}

102.747

25575

13307

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

102.967

25576

13583

\begin{align*} y^{\prime } y-\frac {a \left (x +1\right ) y}{2 x^{{7}/{4}}}&=\frac {a^{2} \left (x -1\right ) \left (3 x +5\right )}{4 x^{{5}/{2}}} \\ \end{align*}

103.300

25577

13627

\begin{align*} \left (A x y+B \,x^{2}+k x \right ) y^{\prime }&=A y^{2}+c x y+d \,x^{2}+\left (-A \beta +k \right ) y-c \beta x -k \beta \\ \end{align*}

103.514

25578

22020

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

104.149

25579

24195

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

105.339

25580

11847

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

105.477

25581

21819

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

106.050

25582

13447

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

106.079

25583

13225

\begin{align*} x^{n +1} y^{\prime }&=x^{2 n} a y^{2}+c \,x^{m}+d \\ \end{align*}

106.598

25584

13325

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

107.322

25585

21815

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

107.351

25586

21835

\begin{align*} 4 x +3 y+2+\left (5 x +4 y+1\right ) y^{\prime }&=0 \\ \end{align*}

107.516

25587

6265

\begin{align*} \left (\operatorname {a4} \,x^{4}+\operatorname {a2} \,x^{2}+\operatorname {a0} \right ) y-2 x \left (a^{2}-x^{2}\right ) y^{\prime }+\left (a^{2}-x^{2}\right )^{2} y^{\prime \prime }&=0 \\ \end{align*}

107.534

25588

20151

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

107.994

25589

5368

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

108.305

25590

13888

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

108.353

25591

12088

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

108.608

25592

21593

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

108.659

25593

19290

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

108.712

25594

20723

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

109.216

25595

12655

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

109.396

25596

5248

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

109.470

25597

10407

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

109.688

25598

11748

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

109.708

25599

6577

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

110.177

25600

13334

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

110.319