2.3.238 Problems 23701 to 23800

Table 2.1049: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

23701

12039

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

10.661

23702

136

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

10.667

23703

26274

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

10.667

23704

3286

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

10.668

23705

9042

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

10.668

23706

12275

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

10.676

23707

15252

\begin{align*} y^{\prime \prime \prime \prime }-5 y^{\prime \prime }+4 y&=12 \operatorname {Heaviside}\left (t \right )-12 \operatorname {Heaviside}\left (t -1\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ y^{\prime \prime \prime }\left (0\right ) &= 0 \\ \end{align*}

Using Laplace transform method.

10.677

23708

1697

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

10.685

23709

15156

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

10.687

23710

21732

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

10.689

23711

27231

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

10.690

23712

15880

\begin{align*} w^{\prime }&=3 w^{3}-12 w^{2} \\ \end{align*}

10.692

23713

24151

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

10.698

23714

25797

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

10.704

23715

803

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

10.707

23716

8222

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

10.707

23717

19155

\begin{align*} x \left (x^{2} y^{\prime }+2 y x \right ) y^{\prime \prime }+4 {y^{\prime }}^{2} x +8 x y y^{\prime }+4 y^{2}-1&=0 \\ \end{align*}

10.712

23718

1628

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

10.716

23719

14139

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

10.722

23720

25906

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

10.726

23721

7714

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

10.731

23722

12257

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

10.732

23723

19099

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

10.740

23724

5902

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

10.741

23725

606

\begin{align*} x^{\prime }&=2 x-3 y \\ y^{\prime }&=x+y+2 z \\ z^{\prime }&=5 y-7 z \\ \end{align*}

10.743

23726

6691

\begin{align*} y+x y^{\prime }+\left (\operatorname {b1} x +\operatorname {a1} \right ) y^{\prime \prime }+x \left (\operatorname {b0} x +\operatorname {a0} \right ) y^{\prime \prime \prime }&=f \left (x \right ) \\ \end{align*}

10.744

23727

16354

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

10.744

23728

5680

\begin{align*} {y^{\prime }}^{6}+f \left (x \right ) \left (y-a \right )^{5} \left (y-b \right )^{4}&=0 \\ \end{align*}

10.750

23729

4855

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

10.751

23730

4821

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

10.758

23731

13904

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

10.758

23732

4763

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

10.760

23733

21861

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

10.760

23734

4248

\begin{align*} y^{\prime }&=\frac {x +y+4}{x +y-6} \\ \end{align*}

10.762

23735

6817

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

10.763

23736

25694

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

10.764

23737

5020

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

10.766

23738

27382

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

10.766

23739

23944

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

10.767

23740

26406

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

10.767

23741

15044

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

10.768

23742

20757

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

10.775

23743

3005

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

10.779

23744

19355

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

10.780

23745

12251

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

10.782

23746

21795

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

10.782

23747

5234

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

10.787

23748

27490

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

10.792

23749

2479

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

10.796

23750

24341

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

10.796

23751

3776

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

10.797

23752

17204

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

10.802

23753

12049

\begin{align*} y^{\prime }&=\frac {-8 y x -x^{3}+2 x^{2}-8 x +32}{32 y+4 x^{2}-8 x +32} \\ \end{align*}

10.803

23754

7870

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

10.808

23755

22338

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

10.814

23756

17223

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

10.822

23757

22404

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

10.822

23758

17336

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

10.825

23759

11424

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

10.833

23760

25696

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

10.834

23761

11959

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

10.836

23762

4927

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

10.839

23763

20243

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

10.839

23764

15591

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

10.841

23765

5196

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

10.845

23766

18061

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

10.851

23767

5824

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

10.855

23768

13005

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

10.856

23769

25783

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

10.871

23770

25662

\begin{align*} y^{\prime }&=25+y^{2} \\ \end{align*}

10.872

23771

23149

\begin{align*} x^{\prime }&=k \left (a -x\right ) \left (b -x\right ) \\ \end{align*}

10.875

23772

12234

\begin{align*} y^{\prime }&=\frac {150 x^{3}+125 \sqrt {x}+125+125 y^{2}-100 x^{3} y-500 y \sqrt {x}+20 x^{6}+200 x^{{7}/{2}}+500 x +125 y^{3}-150 x^{3} y^{2}-750 y^{2} \sqrt {x}+60 x^{6} y+600 y x^{{7}/{2}}+1500 y x -8 x^{9}-120 x^{{13}/{2}}-600 x^{4}-1000 x^{{3}/{2}}}{125 x} \\ \end{align*}

10.876

23773

3549

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

10.879

23774

13459

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

10.881

23775

4921

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

10.882

23776

5455

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

10.888

23777

7244

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

10.891

23778

11521

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

10.893

23779

22366

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

10.897

23780

13306

\begin{align*} y^{\prime }&=a \,{\mathrm e}^{\lambda x} y^{2}-a b \,x^{n} {\mathrm e}^{\lambda x} y+b n \,x^{n -1} \\ \end{align*}

10.898

23781

13438

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

10.900

23782

27210

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

10.907

23783

25798

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

10.910

23784

20469

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

10.911

23785

22051

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

10.912

23786

25661

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

10.917

23787

25013

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

10.927

23788

20731

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

10.938

23789

14034

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

10.939

23790

11991

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

10.945

23791

20713

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

10.946

23792

21354

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

10.948

23793

2519

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

10.951

23794

8268

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

10.951

23795

4818

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

10.956

23796

14455

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

10.958

23797

1815

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

10.961

23798

24330

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

10.962

23799

14278

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

10.963

23800

21336

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

10.963