2.3.249 Problems 24801 to 24900

Table 2.1029: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

24801

11767

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

33.668

24802

20695

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

33.697

24803

21367

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

33.735

24804

11741

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

33.736

24805

13284

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

33.744

24806

4671

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

33.747

24807

11511

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

33.748

24808

20718

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

33.766

24809

12483

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

33.793

24810

6047

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

33.819

24811

4788

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

33.851

24812

20717

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

33.861

24813

11832

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

33.868

24814

13394

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

33.868

24815

6065

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

33.898

24816

22605

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

33.900

24817

13612

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

33.967

24818

1664

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

34.039

24819

204

\begin{align*} 9 \sqrt {x}\, y^{{4}/{3}}-12 x^{{1}/{5}} y^{{3}/{2}}+\left (8 x^{{3}/{2}} y^{{1}/{3}}-15 x^{{6}/{5}} \sqrt {y}\right ) y^{\prime }&=0 \\ \end{align*}

34.053

24820

20836

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

34.056

24821

22442

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

34.138

24822

12066

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

34.141

24823

19811

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

34.142

24824

2995

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

34.183

24825

7470

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

34.220

24826

15153

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

34.237

24827

5122

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

34.402

24828

24234

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

34.420

24829

11363

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

34.438

24830

21596

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

34.476

24831

21264

\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*}

34.511

24832

13558

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

34.557

24833

19718

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

34.640

24834

11502

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

34.645

24835

24359

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

34.742

24836

13994

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

34.774

24837

18620

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

34.780

24838

15016

\begin{align*} 12 x +6 y-9+\left (5 x +2 y-3\right ) y^{\prime }&=0 \\ \end{align*}

34.825

24839

17974

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

34.829

24840

20035

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

34.830

24841

13501

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

34.841

24842

22932

\begin{align*} x^{\prime }-x+2 y-z&=t^{2} \\ y^{\prime }+3 x-y+4 z&={\mathrm e}^{t} \\ z^{\prime }-2 x+y-z&=0 \\ \end{align*}

34.880

24843

12251

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

35.019

24844

22416

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

35.122

24845

22376

\begin{align*} U^{\prime }&=\frac {U+1}{\sqrt {s}+\sqrt {s U}} \\ \end{align*}

35.131

24846

11916

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

35.224

24847

5236

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

35.259

24848

12569

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

35.273

24849

13847

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

35.286

24850

4668

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

35.309

24851

12915

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

35.336

24852

19716

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

35.377

24853

12138

\begin{align*} y^{\prime }&=-\frac {x}{4}+\frac {1}{4}+\sqrt {x^{2}-2 x +1+8 y}+x^{2} \sqrt {x^{2}-2 x +1+8 y}+x^{3} \sqrt {x^{2}-2 x +1+8 y} \\ \end{align*}

35.384

24854

22982

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

35.402

24855

21449

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

35.495

24856

22397

\begin{align*} \left (3 x -y-9\right ) y^{\prime }&=10-2 x +2 y \\ \end{align*}

35.505

24857

5379

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

35.540

24858

4255

\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*}

35.638

24859

10277

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

35.672

24860

20319

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

35.711

24861

13967

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

35.716

24862

12482

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

35.760

24863

19938

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

35.825

24864

17250

\begin{align*} 2 t +\frac {19 y}{10}+\left (\frac {19 t}{10}+2 y\right ) y^{\prime }&=0 \\ \end{align*}

35.899

24865

19137

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

35.919

24866

13404

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

35.927

24867

17052

\begin{align*} y^{\prime }&=\sqrt {25-y^{2}} \\ y \left (4\right ) &= -5 \\ \end{align*}

35.981

24868

13985

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

36.072

24869

25089

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

36.077

24870

12139

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

36.102

24871

12132

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

36.129

24872

12128

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

36.147

24873

6049

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

36.211

24874

12133

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

36.254

24875

12651

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

36.263

24876

9134

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

36.268

24877

5672

\begin{align*} {y^{\prime }}^{4}-4 x^{2} y {y^{\prime }}^{2}+16 y^{2} y^{\prime } x -16 y^{3}&=0 \\ \end{align*}

36.336

24878

6147

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

36.353

24879

19668

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

36.364

24880

6191

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

36.371

24881

6590

\begin{align*} 6 y y^{\prime \prime }-6 \left (1-6 x \right ) x y^{\prime } y^{\prime \prime }+\left (2-9 x \right ) x^{2} {y^{\prime \prime }}^{2}&=36 x {y^{\prime }}^{2} \\ \end{align*}

36.395

24882

21794

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

36.431

24883

7560

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

36.448

24884

8322

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

36.454

24885

21826

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

36.465

24886

4258

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

36.487

24887

20100

\begin{align*} \left (5+2 x \right )^{2} y^{\prime \prime }-6 \left (5-2 x \right ) y^{\prime }+8 y&=0 \\ \end{align*}

36.507

24888

19932

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

36.508

24889

23242

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

36.678

24890

19812

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

36.690

24891

5347

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

36.695

24892

5876

\begin{align*} \left (\operatorname {a0} -\operatorname {a2} \operatorname {csch}\left (x \right )^{2}+4 \operatorname {a1} \sinh \left (x \right )^{2}\right ) y+\coth \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}

36.720

24893

13335

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

36.842

24894

22415

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

36.905

24895

13360

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

36.909

24896

22556

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

36.920

24897

13620

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

37.094

24898

19804

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

37.123

24899

13241

\begin{align*} y^{\prime } x +a_{3} x y^{2}+a_{2} y+a_{1} x +a_{0}&=0 \\ \end{align*}

37.207

24900

19296

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

37.214