2.3.239 Problems 23801 to 23900

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

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

23801

21841

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

16.461

23802

25839

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

16.468

23803

8692

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

16.469

23804

17214

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

16.473

23805

6819

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

16.475

23806

12111

\begin{align*} y^{\prime }&=\frac {1+2 \sqrt {4 x^{2} y+1}\, x^{3}+2 x^{5} \sqrt {4 x^{2} y+1}+2 x^{6} \sqrt {4 x^{2} y+1}}{2 x^{3}} \\ \end{align*}

16.483

23807

5502

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

16.487

23808

8785

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

16.490

23809

6881

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

16.493

23810

8235

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

16.511

23811

4800

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

16.514

23812

5070

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

16.520

23813

19950

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

16.523

23814

4352

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

16.534

23815

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*}

16.536

23816

17281

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

16.538

23817

5052

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

16.540

23818

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*}

16.563

23819

4692

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

16.574

23820

12087

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

16.581

23821

12043

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

16.583

23822

5179

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

16.588

23823

4697

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

16.592

23824

23204

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

16.595

23825

4690

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

16.598

23826

4855

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

16.602

23827

21594

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

16.614

23828

24391

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

16.626

23829

21622

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

16.632

23830

3886

\begin{align*} x_{1}^{\prime }&=x_{2}+3 x_{3} \\ x_{2}^{\prime }&=2 x_{1}+3 x_{2}-2 x_{3} \\ x_{3}^{\prime }&=2 x_{2}+2 x_{3} \\ \end{align*}

16.637

23831

20510

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

16.638

23832

1707

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

16.639

23833

11997

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

16.659

23834

11967

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

16.673

23835

5080

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

16.674

23836

5083

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

16.683

23837

15568

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

16.690

23838

5309

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

16.693

23839

13458

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

16.700

23840

24405

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

16.724

23841

22462

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

16.737

23842

13370

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

16.742

23843

25507

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

16.744

23844

17958

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

16.746

23845

22530

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

16.747

23846

1658

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

16.749

23847

13713

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

16.754

23848

11969

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

16.757

23849

13754

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

16.760

23850

5081

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

16.766

23851

26383

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

16.772

23852

15943

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

16.783

23853

25878

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

16.793

23854

15555

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

16.798

23855

13445

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

16.800

23856

24396

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

16.805

23857

7515

\begin{align*} r^{\prime }&=r^{2}+\frac {2 r}{t} \\ \end{align*}

16.806

23858

7143

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

16.813

23859

15381

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

16.843

23860

2517

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

16.855

23861

5331

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

16.895

23862

8839

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

16.897

23863

15057

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

16.905

23864

4921

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

16.913

23865

4875

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

16.942

23866

18552

\begin{align*} y^{\prime }&=\sqrt {1-t^{2}-y^{2}} \\ \end{align*}

16.949

23867

2953

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

16.953

23868

2345

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

16.965

23869

13660

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

16.974

23870

18559

\begin{align*} y^{\prime }&=-\frac {4 t}{y} \\ y \left (0\right ) &= y_{0} \\ \end{align*}

16.977

23871

4695

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

16.978

23872

24784

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

16.983

23873

19916

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

16.990

23874

25899

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

16.996

23875

5358

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

17.007

23876

13980

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

17.010

23877

9014

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

17.028

23878

21358

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

17.029

23879

26276

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

17.030

23880

6294

\begin{align*} \left (\operatorname {a2} +\operatorname {b2} \,x^{k}\right ) y+x \left (\operatorname {a1} +\operatorname {b1} \,x^{k}\right ) y^{\prime }+x^{2} \left (\operatorname {a0} +\operatorname {b0} \,x^{k}\right ) y^{\prime \prime }&=0 \\ \end{align*}

17.044

23881

15826

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

17.053

23882

18561

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

17.062

23883

12195

\begin{align*} y^{\prime }&=-\frac {-y^{3}-y+4 y^{2} \ln \left (x \right )-4 \ln \left (x \right )^{2} y^{3}-1+6 y \ln \left (x \right )-12 \ln \left (x \right )^{2} y^{2}+8 \ln \left (x \right )^{3} y^{3}}{y x} \\ \end{align*}

17.064

23884

1650

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

17.065

23885

22328

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

17.071

23886

19960

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

17.075

23887

11837

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

17.079

23888

13651

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

17.083

23889

13982

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

17.089

23890

14439

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

17.089

23891

12273

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

17.090

23892

11370

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

17.100

23893

23163

\begin{align*} y y^{\prime }-7 y&=6 x \\ \end{align*}

17.121

23894

1701

\begin{align*} 7 x +4 y+\left (4 x +3 y\right ) y^{\prime }&=0 \\ \end{align*}

17.125

23895

2879

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

17.125

23896

13422

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

17.129

23897

19411

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

17.148

23898

4738

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

17.158

23899

24403

\begin{align*} 4 x +3 y-7+\left (4 x +3 y+1\right ) y^{\prime }&=0 \\ \end{align*}

17.164

23900

22554

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

17.171