2.3.227 Problems 22601 to 22700

Table 2.985: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

22601

7705

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

6.661

22602

7893

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

6.663

22603

7722

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

6.665

22604

11621

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

6.665

22605

1603

\begin{align*} y^{\prime }&=a y-b y^{2} \\ y \left (0\right ) &= \operatorname {y0} \\ \end{align*}

6.671

22606

4718

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

6.671

22607

16219

\begin{align*} y^{\prime }&=y^{2}+9 \\ \end{align*}

6.672

22608

17346

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

6.678

22609

24803

\begin{align*} {y^{\prime }}^{2}+4 x^{4} y^{\prime }-12 x^{4} y&=0 \\ \end{align*}

6.678

22610

9997

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

6.684

22611

17285

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

6.684

22612

11865

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

6.687

22613

11934

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

6.690

22614

11578

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

6.697

22615

10280

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

6.700

22616

20309

\begin{align*} {x^{\prime }}^{2}&=k^{2} \left (1-{\mathrm e}^{-\frac {2 g x}{k^{2}}}\right ) \\ x \left (0\right ) &= 0 \\ \end{align*}

6.707

22617

5230

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

6.714

22618

24356

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

6.719

22619

18616

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

6.722

22620

13305

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

6.723

22621

11880

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

6.724

22622

19896

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

6.725

22623

2928

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

6.727

22624

19265

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

6.729

22625

1605

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

6.732

22626

13964

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

6.733

22627

12141

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

6.735

22628

24212

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

6.738

22629

19103

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

6.739

22630

17005

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

6.742

22631

22406

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

6.742

22632

6899

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

6.750

22633

6985

\begin{align*} \left (x -\cos \left (y\right )\right ) y^{\prime }+\tan \left (y\right )&=0 \\ y \left (1\right ) &= \frac {\pi }{6} \\ \end{align*}

6.750

22634

3042

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

6.751

22635

10452

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

6.756

22636

13650

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

6.759

22637

24255

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

6.760

22638

19292

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

6.762

22639

3482

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

6.769

22640

6311

\begin{align*} a \,{\mathrm e}^{y}+y^{\prime \prime }&=0 \\ \end{align*}

6.769

22641

18627

\begin{align*} 4 x y^{\prime } y&=8 x^{2}+5 y^{2} \\ \end{align*}

6.772

22642

7555

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

6.782

22643

17281

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

6.782

22644

7031

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

6.786

22645

7744

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

6.789

22646

13251

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

6.792

22647

11877

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

6.798

22648

12179

\begin{align*} y^{\prime }&=\frac {32 x^{5}+64 x^{6}+64 x^{6} y^{2}+32 x^{4} y+4 x^{2}+64 x^{6} y^{3}+48 x^{4} y^{2}+12 x^{2} y+1}{64 x^{8}} \\ \end{align*}

6.805

22649

11693

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

6.806

22650

6907

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

6.809

22651

11805

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

6.810

22652

11902

\begin{align*} y^{\prime }&=\frac {6 y}{8 y^{4}+9 y^{3}+12 y^{2}+6 y-F \left (-\frac {y^{4}}{3}-\frac {y^{3}}{2}-y^{2}-y+x \right )} \\ \end{align*}

6.811

22653

14246

\begin{align*} x x^{\prime }&=1-t x \\ \end{align*}

6.812

22654

5148

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

6.813

22655

18574

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

6.815

22656

200

\begin{align*} y^{\prime } x&=6 y+12 x^{4} y^{{2}/{3}} \\ \end{align*}

6.816

22657

20254

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

6.819

22658

17929

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

6.821

22659

11337

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

6.823

22660

17294

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

6.832

22661

12185

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

6.833

22662

11642

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

6.835

22663

1654

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

6.839

22664

4873

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

6.839

22665

7892

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

6.841

22666

13643

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

6.846

22667

18041

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

6.846

22668

4875

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

6.850

22669

20327

\begin{align*} y^{\prime }+\frac {a x +b y+c}{b x +f y+e}&=0 \\ \end{align*}

6.853

22670

14506

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

6.854

22671

7874

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

6.857

22672

25032

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

6.857

22673

24173

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

6.861

22674

20816

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

6.862

22675

13734

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

6.863

22676

7863

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

6.865

22677

13963

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

6.865

22678

21862

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

6.867

22679

24122

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

6.872

22680

24200

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

6.874

22681

19907

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

6.881

22682

21762

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

6.882

22683

5202

\begin{align*} 8 x^{3} y y^{\prime }+3 x^{4}-6 y^{2} x^{2}-y^{4}&=0 \\ \end{align*}

6.892

22684

12103

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

6.892

22685

17295

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

6.892

22686

21286

\begin{align*} x^{\prime }+x&=\operatorname {Heaviside}\left (t -a \right ) \\ x \left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

6.896

22687

5359

\begin{align*} {y^{\prime }}^{2}+3 x^{2}&=8 y \\ \end{align*}

6.897

22688

11891

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

6.898

22689

11965

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

6.901

22690

15747

\(\left [\begin {array}{ccccc} 1 & 3 & 5 & 2 & 4 \\ 5 & 2 & 4 & 1 & 3 \\ 4 & 1 & 3 & 5 & 2 \\ 3 & 5 & 2 & 4 & 1 \\ 2 & 4 & 1 & 3 & 5 \end {array}\right ]\)

N/A

N/A

N/A

6.908

22691

7932

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

6.915

22692

2907

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

6.916

22693

20225

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

6.916

22694

19356

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

6.919

22695

24142

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

6.920

22696

17269

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

6.921

22697

19414

\begin{align*} \frac {\cos \left (y\right )}{x +3}-\left (\sin \left (y\right ) \ln \left (5 x +15\right )-\frac {1}{y}\right ) y^{\prime }&=0 \\ \end{align*}

6.928

22698

24273

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

6.928

22699

2906

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

6.933

22700

24352

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

6.933