2.3.209 Problems 20801 to 20900

Table 2.949: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

20801

15556

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

10.559

20802

19288

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

10.563

20803

14869

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

10.566

20804

23325

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

10.568

20805

20626

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

10.572

20806

11471

\begin{align*} x^{3} y^{\prime }-y^{2} x^{4}+x^{2} y+20&=0 \\ \end{align*}

10.573

20807

7597

\begin{align*} y^{\prime \prime }-4 y^{\prime }-5 y&=0 \\ y \left (-1\right ) &= 3 \\ y^{\prime }\left (-1\right ) &= 9 \\ \end{align*}

10.583

20808

24353

\begin{align*} 3 x +2 y+7+\left (2 x -y\right ) y^{\prime }&=0 \\ \end{align*}

10.587

20809

5680

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

10.589

20810

20274

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

10.594

20811

4890

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

10.603

20812

6453

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

10.609

20813

21130

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

10.611

20814

15017

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

10.612

20815

817

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

10.623

20816

18934

\begin{align*} u^{\prime \prime }+\frac {u^{\prime }}{4}+u&=\frac {\left (\left \{\begin {array}{cc} 1 & \frac {3}{2}\le t <\frac {5}{2} \\ 0 & \operatorname {otherwise} \end {array}\right .\right )}{2} \\ u \left (0\right ) &= 0 \\ u^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

10.627

20817

13416

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

10.634

20818

20353

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

10.642

20819

25720

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

10.656

20820

17783

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

10.663

20821

24174

\begin{align*} y^{2}+7 y x +16 x^{2}+x^{2} y^{\prime }&=0 \\ y \left (1\right ) &= 1 \\ \end{align*}

10.666

20822

18761

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

10.675

20823

23282

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

10.681

20824

22554

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

10.689

20825

8699

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

10.690

20826

14270

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

10.690

20827

22551

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

10.691

20828

17886

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

10.696

20829

14468

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

10.700

20830

22609

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

10.700

20831

10147

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

10.707

20832

2913

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

10.713

20833

7932

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

10.713

20834

17948

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

10.713

20835

23149

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

10.713

20836

24321

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

10.715

20837

876

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

10.716

20838

13553

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

10.718

20839

770

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

10.724

20840

687

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

10.725

20841

10314

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

10.731

20842

20221

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

10.734

20843

25534

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

10.735

20844

17910

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

10.740

20845

12243

\begin{align*} y^{\prime }&=\frac {-4 \cos \left (x \right ) x +4 x^{2} \sin \left (x \right )+4 x +4+4 y^{2}+8 y \cos \left (x \right ) x -8 y x +2 x^{2} \cos \left (2 x \right )+6 x^{2}-8 \cos \left (x \right ) x^{2}+4 y^{3}+12 y^{2} \cos \left (x \right ) x -12 x y^{2}+6 y x^{2} \cos \left (2 x \right )+18 x^{2} y-24 y \cos \left (x \right ) x^{2}+x^{3} \cos \left (3 x \right )+15 \cos \left (x \right ) x^{3}-6 x^{3} \cos \left (2 x \right )-10 x^{3}}{4 x} \\ \end{align*}

10.744

20846

10126

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

10.748

20847

24312

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

10.751

20848

8711

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

10.756

20849

15140

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

10.763

20850

19250

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

10.765

20851

14271

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

10.766

20852

19284

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

10.766

20853

17781

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

10.769

20854

4391

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

10.771

20855

16516

\begin{align*} 9 y^{\prime \prime }+18 y^{\prime }+10 y&=0 \\ \end{align*}

10.778

20856

23335

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

10.779

20857

7852

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

10.799

20858

4419

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

10.806

20859

1709

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

10.808

20860

2558

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

10.808

20861

21067

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

10.810

20862

9165

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

10.816

20863

17975

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

10.816

20864

8793

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

10.820

20865

2885

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

10.822

20866

5113

\begin{align*} \left (1+x +9 y\right ) y^{\prime }+1+x +5 y&=0 \\ \end{align*}

10.827

20867

14466

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

10.827

20868

21300

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

10.828

20869

1644

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

10.837

20870

22587

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

10.838

20871

20046

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

10.843

20872

18596

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

10.847

20873

19913

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

10.866

20874

11930

\begin{align*} y^{\prime }&=\frac {\left (a y^{2}+b \,x^{2}\right )^{2} x}{a^{{5}/{2}} y} \\ \end{align*}

10.868

20875

1801

\begin{align*} \left (3 x -1\right ) \left (y^{\prime }+y^{2}\right )-\left (3 x +2\right ) y-6 x +8&=0 \\ \end{align*}

10.869

20876

21170

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

10.869

20877

17985

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

10.870

20878

4853

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

10.882

20879

7744

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

10.883

20880

4082

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

10.887

20881

20371

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

10.895

20882

19383

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

10.898

20883

7893

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

10.900

20884

1725

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

10.902

20885

10039

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

10.902

20886

7874

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

10.906

20887

19369

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

10.911

20888

25770

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

10.914

20889

15585

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

10.917

20890

5867

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

10.918

20891

23874

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

10.925

20892

11978

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

10.927

20893

15334

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

10.927

20894

12887

\begin{align*} 9 {y^{\prime }}^{4}+8 y^{\prime \prime }&=0 \\ \end{align*}

10.932

20895

23208

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

10.933

20896

17663

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

10.950

20897

5256

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

10.954

20898

24881

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

10.956

20899

145

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

10.961

20900

4694

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

10.961