2.3.259 Problems 25801 to 25900

Table 2.1061: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

25801

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*}

106.240

25802

23868

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

106.313

25803

5071

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

106.453

25804

20597

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

106.808

25805

2890

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

106.919

25806

10063

\begin{align*} x^{\prime }&=4 A k \left (\frac {x}{A}\right )^{{3}/{4}}-3 k x \\ \end{align*}

106.986

25807

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*}

107.488

25808

20004

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

107.954

25809

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*}

108.076

25810

6114

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

108.114

25811

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

25812

5112

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

108.256

25813

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*}

108.460

25814

14023

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

108.524

25815

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*}

108.589

25816

13593

\begin{align*} y y^{\prime }+\frac {a \left (33 x +2\right ) y}{30 x^{{6}/{5}}}&=-\frac {a^{2} \left (x -1\right ) \left (9 x -4\right )}{30 x^{{7}/{5}}} \\ \end{align*}

108.883

25817

20733

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

109.024

25818

4748

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

109.112

25819

1644

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

109.165

25820

24221

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

109.472

25821

22009

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

109.721

25822

13599

\begin{align*} y y^{\prime }-\frac {a \left (x +4\right ) y}{5 x^{{8}/{5}}}&=\frac {a^{2} \left (x -1\right ) \left (3 x +7\right )}{5 x^{{11}/{5}}} \\ \end{align*}

109.728

25823

10407

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

109.769

25824

12126

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

110.018

25825

23965

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

110.168

25826

13374

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

110.293

25827

7868

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

110.374

25828

5295

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

110.432

25829

5635

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

110.450

25830

11771

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

110.491

25831

6118

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

110.605

25832

11708

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

110.951

25833

5194

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

111.226

25834

6174

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

111.316

25835

13582

\begin{align*} y y^{\prime }+\frac {3 a \left (13 x -8\right ) y}{20 x^{{7}/{5}}}&=-\frac {a^{2} \left (x -1\right ) \left (27 x -32\right )}{20 x^{{9}/{5}}} \\ \end{align*}

111.345

25836

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

25837

11687

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

111.493

25838

4389

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

111.643

25839

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*}

111.944

25840

23211

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

111.970

25841

7550

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

112.088

25842

6253

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

112.111

25843

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*}

112.284

25844

22021

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

112.462

25845

12581

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

112.510

25846

13596

\begin{align*} y y^{\prime }-\frac {2 a \left (3 x +2\right ) y}{5 x^{{8}/{5}}}&=\frac {a^{2} \left (x -1\right ) \left (8 x +1\right )}{5 x^{{11}/{5}}} \\ \end{align*}

112.799

25847

7032

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

112.868

25848

14915

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

112.909

25849

13978

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

112.917

25850

17267

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

112.920

25851

11503

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

112.961

25852

18073

\begin{align*} \left (5 x -7 y+1\right ) y^{\prime }+x +y-1&=0 \\ \end{align*}

113.291

25853

20001

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

113.313

25854

13625

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

113.432

25855

13602

\begin{align*} y y^{\prime }-\frac {3 a y}{x^{{7}/{4}}}&=\frac {a^{2} \left (x -1\right ) \left (x -9\right )}{4 x^{{5}/{2}}} \\ \end{align*}

113.692

25856

21387

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

113.827

25857

21392

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

113.851

25858

21789

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

113.887

25859

19166

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

113.899

25860

23199

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

114.076

25861

17919

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

114.188

25862

6338

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

114.581

25863

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*}

114.627

25864

3322

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

114.708

25865

12620

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

114.830

25866

11798

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

114.850

25867

13617

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

115.004

25868

20473

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

115.025

25869

5121

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

115.208

25870

3312

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

115.332

25871

15319

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

115.567

25872

20952

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

115.766

25873

5342

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

115.845

25874

20769

\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*}

116.104

25875

5405

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

116.119

25876

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*}

116.247

25877

12024

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

116.404

25878

18014

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

116.778

25879

5615

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

116.792

25880

13390

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

116.805

25881

23225

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

116.858

25882

21851

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

116.898

25883

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*}

116.906

25884

20723

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

116.973

25885

18720

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

117.312

25886

23860

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

117.408

25887

13636

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

117.459

25888

5144

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

117.463

25889

16329

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

117.573

25890

23156

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

117.594

25891

15032

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

117.747

25892

6185

\begin{align*} 2 \operatorname {a2} y+\left (\operatorname {b1} x +\operatorname {a1} \right ) y^{\prime }+\left (\operatorname {c0} \,x^{2}+\operatorname {b0} x +\operatorname {a0} \right ) y^{\prime \prime }&=0 \\ \end{align*}

117.792

25893

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*}

118.760

25894

5620

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

118.776

25895

12588

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

118.779

25896

13833

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

118.862

25897

23761

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

118.994

25898

12931

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

119.023

25899

6071

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

119.397

25900

12626

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

119.489