2.3.248 Problems 24701 to 24800

Table 2.1027: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

24701

13997

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

30.588

24702

13543

\begin{align*} y^{\prime } y-y&=\frac {15 x}{4}+\frac {A}{x^{7}} \\ \end{align*}

30.602

24703

11648

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

30.617

24704

12409

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

30.635

24705

24241

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

30.679

24706

4330

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

30.691

24707

21061

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

30.706

24708

13511

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

30.742

24709

5077

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

30.756

24710

13981

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

30.759

24711

17233

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

30.786

24712

13267

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

30.819

24713

11553

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

30.875

24714

20314

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

30.915

24715

5050

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

30.956

24716

5092

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

30.968

24717

5117

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

31.006

24718

5658

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

31.026

24719

21276

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

31.033

24720

23127

\begin{align*} x^{\prime }&=\frac {a x^{{5}/{6}}}{\left (-B t +b \right )^{{3}/{2}}} \\ \end{align*}

31.041

24721

11708

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

31.042

24722

19906

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

31.047

24723

13459

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

31.048

24724

17066

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

31.080

24725

12539

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

31.083

24726

3667

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

31.095

24727

22983

\begin{align*} z^{\prime }-z \sin \left (x \right )&={\mathrm e}^{-\cos \left (x \right )} \\ z \left (2 \pi \right ) &= 2 \\ \end{align*}

31.109

24728

19915

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

31.138

24729

5172

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

31.144

24730

18610

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

31.163

24731

13283

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

31.176

24732

11399

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

31.228

24733

18611

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

31.275

24734

2669

\begin{align*} t^{2} y^{\prime \prime }+t p \left (t \right ) y^{\prime }+q \left (t \right ) y&=0 \\ \end{align*}
Series expansion around \(t=0\).

31.342

24735

11349

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

31.342

24736

13281

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

31.385

24737

11907

\begin{align*} y^{\prime }&=\frac {x^{{5}/{3}}}{y+x^{{4}/{3}}} \\ \end{align*}

31.440

24738

4250

\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*}

31.447

24739

5877

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

31.491

24740

11316

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

31.501

24741

24347

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

31.505

24742

11755

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

31.566

24743

15127

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

31.589

24744

13578

\begin{align*} y^{\prime } y-\frac {a \left (1+\frac {2 b}{x^{2}}\right ) y}{2}&=\frac {a^{2} \left (3 x +\frac {4 b}{x}\right )}{16} \\ \end{align*}

31.592

24745

14909

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

31.636

24746

11369

\begin{align*} y^{\prime }-\sqrt {\frac {a y^{4}+b y^{2}+1}{a \,x^{4}+b \,x^{2}+1}}&=0 \\ \end{align*}

31.802

24747

19810

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

31.905

24748

24340

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

31.937

24749

7248

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

31.997

24750

15629

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

32.006

24751

11326

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

32.036

24752

10114

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

32.040

24753

9126

\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*}

32.063

24754

12437

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

32.076

24755

19714

\begin{align*} x^{\prime }&=k \left (A -n x\right ) \left (M -m x\right ) \\ \end{align*}

32.093

24756

2346

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

32.154

24757

11754

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

32.190

24758

14084

\begin{align*} 8 \left (1+y^{\prime }\right )^{3}&=27 \left (x +y\right ) \left (1-y^{\prime }\right )^{3} \\ \end{align*}

32.235

24759

19386

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

32.246

24760

13615

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

32.331

24761

11405

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

32.347

24762

12622

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

32.358

24763

2351

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

32.365

24764

12862

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

32.370

24765

11350

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

32.436

24766

12558

\begin{align*} 144 x \left (x -1\right ) y^{\prime \prime }+\left (168 x -96\right ) y^{\prime }+y&=0 \\ \end{align*}

32.508

24767

11686

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

32.546

24768

24287

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

32.605

24769

24318

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

32.637

24770

12217

\begin{align*} y^{\prime }&=\frac {-2 y-2 \ln \left (2 x +1\right )-2+2 x y^{3}+y^{3}+6 y^{2} \ln \left (2 x +1\right ) x +3 y^{2} \ln \left (2 x +1\right )+6 y \ln \left (2 x +1\right )^{2} x +3 y \ln \left (2 x +1\right )^{2}+2 \ln \left (2 x +1\right )^{3} x +\ln \left (2 x +1\right )^{3}}{\left (2 x +1\right ) \left (y+\ln \left (2 x +1\right )+1\right )} \\ \end{align*}

32.639

24771

21832

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

32.661

24772

10417

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

32.663

24773

1233

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

32.668

24774

20480

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

32.674

24775

20962

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

32.688

24776

5106

\begin{align*} \left (11-11 x -4 y\right ) y^{\prime }&=62-8 x -25 y \\ \end{align*}

32.697

24777

12113

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

32.714

24778

12870

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

32.731

24779

11658

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

32.773

24780

19900

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

32.809

24781

24168

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

32.818

24782

11649

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

32.837

24783

7848

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

32.855

24784

17292

\begin{align*} 1+t -2 y+\left (4 t -3 y-6\right ) y^{\prime }&=0 \\ \end{align*}

32.895

24785

13238

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

32.911

24786

5096

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

32.937

24787

23225

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

32.969

24788

15633

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

32.981

24789

13618

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

33.041

24790

24132

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

33.050

24791

5986

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

33.084

24792

22400

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

33.115

24793

11388

\begin{align*} 2 y^{\prime }-3 y^{2}-4 a y-b -c \,{\mathrm e}^{-2 a x}&=0 \\ \end{align*}

33.122

24794

4297

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

33.135

24795

19113

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

33.165

24796

5632

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

33.328

24797

9043

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

33.349

24798

21978

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

33.362

24799

9131

\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*}

33.541

24800

2922

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

33.606