2.3.220 Problems 21901 to 22000

Table 2.983: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

21901

15962

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

8.798

21902

7014

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

8.801

21903

11970

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

8.803

21904

12690

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

8.803

21905

9976

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

8.809

21906

11521

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

8.812

21907

17333

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

8.812

21908

16320

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

8.815

21909

803

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

8.818

21910

12573

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

8.818

21911

24157

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

8.827

21912

14370

\begin{align*} x^{\prime \prime }+4 x&=\delta \left (-2+t \right )-\delta \left (t -5\right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

8.828

21913

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*}

8.834

21914

22861

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

8.836

21915

5200

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

8.839

21916

22454

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

8.839

21917

11936

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

8.840

21918

15165

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

8.841

21919

7752

\begin{align*} \frac {r \tan \left (\theta \right ) r^{\prime }}{a^{2}-r^{2}}&=1 \\ r \left (\frac {\pi }{4}\right ) &= 0 \\ \end{align*}

8.843

21920

16685

\begin{align*} x^{2} y^{\prime \prime }+5 y^{\prime } x +4 y&=64 \ln \left (x \right ) x^{2} \\ \end{align*}

8.845

21921

11851

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

8.847

21922

17120

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

8.847

21923

19235

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

8.848

21924

9150

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

8.851

21925

24228

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

8.854

21926

4879

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

8.855

21927

25015

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

8.856

21928

22873

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

8.861

21929

17931

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

8.862

21930

11518

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

8.864

21931

5031

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

8.865

21932

7845

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

8.867

21933

6820

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

8.870

21934

11926

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

8.870

21935

15782

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

8.871

21936

13754

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

8.874

21937

22511

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

8.875

21938

20267

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

8.876

21939

24312

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

8.877

21940

12209

\begin{align*} y^{\prime }&=-\frac {16 x y^{3}-8 y^{3}-8 y+8 x y^{2}-2 x^{2} y^{3}-8+12 y x -6 y^{2} x^{2}+x^{3} y^{3}}{32 y x} \\ \end{align*}

8.881

21941

17301

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

8.882

21942

23197

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

8.882

21943

11372

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

8.885

21944

17006

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

8.885

21945

21194

\begin{align*} x^{\left (5\right )}+x&=0 \\ x \left (\infty \right ) &= 0 \\ \end{align*}

8.886

21946

5258

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

8.891

21947

10114

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

8.898

21948

5450

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

8.902

21949

22871

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

8.907

21950

11566

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

8.912

21951

11523

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

8.913

21952

12070

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

8.915

21953

25696

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

8.918

21954

25490

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

8.923

21955

115

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

8.925

21956

23970

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

8.928

21957

12152

\begin{align*} y^{\prime }&=\frac {-30 x^{3} y+12 x^{6}+70 x^{{7}/{2}}-30 x^{3}-25 \sqrt {x}\, y+50 x -25 \sqrt {x}-25}{5 \left (-5 y+2 x^{3}+10 \sqrt {x}-5\right ) x} \\ \end{align*}

8.930

21958

23954

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

8.932

21959

24955

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

8.934

21960

4863

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

8.940

21961

730

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

8.941

21962

6984

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

8.941

21963

11579

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

8.941

21964

13460

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

8.947

21965

21090

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

8.947

21966

21066

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

8.951

21967

21346

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

8.957

21968

21369

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

8.957

21969

4830

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

8.960

21970

24319

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

8.961

21971

12274

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

8.962

21972

3668

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

8.963

21973

5709

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

8.964

21974

13027

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

8.965

21975

22526

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

8.968

21976

5040

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

8.970

21977

11887

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

8.970

21978

21990

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

8.970

21979

10130

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

8.972

21980

11461

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

8.974

21981

12058

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

8.977

21982

5045

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

8.978

21983

22449

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

8.984

21984

23861

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

8.985

21985

25770

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

8.985

21986

16296

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

8.986

21987

1159

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

8.987

21988

2940

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

8.987

21989

15184

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

8.987

21990

9997

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

8.988

21991

25797

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

8.988

21992

25826

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

8.989

21993

15381

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

8.992

21994

24170

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

8.996

21995

4706

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

8.997

21996

15870

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

8.998

21997

13329

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

8.999

21998

19279

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

9.000

21999

16313

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

9.002

22000

24373

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

9.005