2.3.251 Problems 25001 to 25100

Table 2.1033: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

25001

13534

\begin{align*} y^{\prime } y-y&=\frac {6}{25} x -A \,x^{2} \\ \end{align*}

43.417

25002

11769

\begin{align*} x y {y^{\prime }}^{2}+\left (x^{22}-y^{2}+a \right ) y^{\prime }-y x&=0 \\ \end{align*}

43.493

25003

20320

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

43.510

25004

23835

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

43.588

25005

4746

\begin{align*} 2 y^{\prime }+a x&=-\sqrt {a^{2} x^{2}-4 b \,x^{2}-4 c y} \\ \end{align*}

43.662

25006

9117

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

43.698

25007

13340

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

43.739

25008

21953

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

43.781

25009

21466

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

43.947

25010

20213

\begin{align*} x^{\prime }&=n y-m z \\ y^{\prime }&=L z-m x \\ z^{\prime }&=m x-L y \\ \end{align*}

44.079

25011

5618

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

44.204

25012

19300

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

44.345

25013

18336

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

44.346

25014

39

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

44.348

25015

6310

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

44.401

25016

11990

\begin{align*} y^{\prime }&=\frac {\left (-\ln \left (y-1\right )+\ln \left (1+y\right )+2 \ln \left (x \right )\right )^{2} x \left (1+y\right )^{2}}{16} \\ \end{align*}

44.473

25017

12881

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

44.487

25018

4745

\begin{align*} 2 y^{\prime }+a x&=\sqrt {a^{2} x^{2}-4 b \,x^{2}-4 c y} \\ \end{align*}

44.829

25019

7550

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

44.882

25020

4682

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

44.997

25021

5144

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

45.013

25022

21846

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

45.030

25023

6860

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

45.086

25024

19282

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

45.141

25025

12068

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

45.248

25026

13473

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

45.381

25027

13336

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

45.410

25028

21806

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

45.417

25029

7008

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

45.447

25030

13996

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

45.606

25031

13385

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

45.682

25032

17837

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

45.764

25033

21845

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

45.778

25034

11795

\begin{align*} 9 y^{4} \left (x^{2}-1\right ) {y^{\prime }}^{2}-6 x y^{5} y^{\prime }-4 x^{2}&=0 \\ \end{align*}

45.819

25035

13280

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

45.987

25036

13381

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

46.104

25037

18035

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

46.163

25038

19766

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

46.246

25039

4840

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

46.320

25040

13820

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

46.349

25041

13330

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

46.502

25042

11360

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

46.625

25043

13586

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

46.646

25044

13559

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

46.733

25045

6355

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

46.787

25046

13494

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

46.809

25047

13587

\begin{align*} y^{\prime } y-\frac {2 a \left (3 x -10\right ) y}{5 x^{4}}&=\frac {a^{2} \left (x -1\right ) \left (8 x -5\right )}{5 x^{7}} \\ \end{align*}

46.848

25048

11796

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

46.853

25049

13482

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

46.905

25050

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*}

46.922

25051

21849

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

46.958

25052

19351

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

47.005

25053

11787

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

47.071

25054

20483

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

47.078

25055

13483

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

47.124

25056

13428

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

47.253

25057

11927

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

47.339

25058

21861

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

47.353

25059

13613

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

47.377

25060

7518

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

47.464

25061

10119

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

47.465

25062

9782

\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*}

47.704

25063

12054

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

47.706

25064

25496

\begin{align*} y^{\prime }&=\frac {c t -a y}{A t +b y} \\ \end{align*}

47.760

25065

18352

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

47.795

25066

5569

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

47.849

25067

13423

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

47.924

25068

19314

\begin{align*} \frac {4 y^{2}-2 x^{2}}{4 x y^{2}-x^{3}}+\frac {\left (8 y^{2}-x^{2}\right ) y^{\prime }}{4 y^{3}-x^{2} y}&=0 \\ \end{align*}

47.945

25069

24180

\begin{align*} 16 x +15 y+\left (3 x +y\right ) y^{\prime }&=0 \\ y \left (1\right ) &= -3 \\ \end{align*}

47.966

25070

12118

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

48.167

25071

13395

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

48.358

25072

12125

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

48.372

25073

11989

\begin{align*} y^{\prime }&=-\frac {\left (-\ln \left (y-1\right )+\ln \left (1+y\right )+2 \ln \left (x \right )\right ) x \left (1+y\right )^{2}}{8} \\ \end{align*}

48.492

25074

24360

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

48.529

25075

21248

\begin{align*} L x^{\prime \prime }+g \sin \left (x\right )&=0 \\ \end{align*}

48.559

25076

12512

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

48.577

25077

10526

\begin{align*} \left (x^{8}+1\right ) y^{\prime \prime }-16 x^{7} y^{\prime }+72 x^{6} y&=0 \\ \end{align*}

48.697

25078

6358

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

48.875

25079

10946

\begin{align*} \left (x^{8}+1\right ) y^{\prime \prime }-16 x^{7} y^{\prime }+72 x^{6} y&=0 \\ \end{align*}

48.892

25080

12044

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

48.963

25081

24272

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

49.009

25082

11364

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

49.078

25083

21788

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

49.154

25084

6170

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

49.174

25085

13420

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

49.269

25086

13508

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

49.303

25087

21451

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

49.493

25088

15361

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

49.501

25089

20834

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

49.556

25090

19813

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

49.566

25091

21266

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

49.572

25092

599

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

49.599

25093

11909

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

49.791

25094

25516

\begin{align*} m y^{\prime \prime }+k \sin \left (y\right )&=0 \\ \end{align*}

49.859

25095

2820

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

49.891

25096

16303

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

49.898

25097

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*}

50.102

25098

4774

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

50.119

25099

12093

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

50.217

25100

11332

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

50.410