6.210 Problems 20901 to 21000

Table 6.419: Main lookup table sequentially arranged

#

ODE

Mathematica

Maple

Sympy

20901

\[ {} \left (x +2\right ) y^{\prime \prime }-\left (2 x +5\right ) y^{\prime }+2 y = {\mathrm e}^{x} \left (1+x \right ) \]

20902

\[ {} y^{\prime \prime }-\cot \left (x \right ) y^{\prime }-\left (1-\cot \left (x \right )\right ) y = {\mathrm e}^{x} \sin \left (x \right ) \]

20903

\[ {} \left (x \sin \left (x \right )+\cos \left (x \right )\right ) y^{\prime \prime }-x \cos \left (x \right ) y^{\prime }+y \cos \left (x \right ) = 0 \]

20904

\[ {} y^{\prime \prime }+\left (1+\frac {2 \cot \left (x \right )}{x}-\frac {2}{x^{2}}\right ) y = x \cos \left (x \right ) \]

20905

\[ {} x^{2} y^{\prime \prime }-2 \left (x^{2}+x \right ) y^{\prime }+\left (x^{2}+2 x +2\right ) y = 0 \]

20906

\[ {} x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y = 0 \]

20907

\[ {} y^{\prime \prime }+\frac {y^{\prime }}{x^{{1}/{3}}}+\left (\frac {1}{4 x^{{2}/{3}}}-\frac {1}{6 x^{{4}/{3}}}-\frac {6}{x^{2}}\right ) y = 0 \]

20908

\[ {} y^{\prime \prime }-2 \tan \left (x \right ) y^{\prime }+y = 0 \]

20909

\[ {} y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-1\right ) y = -3 \,{\mathrm e}^{x^{2}} \sin \left (2 x \right ) \]

20910

\[ {} y^{\prime \prime }-\left (8 \,{\mathrm e}^{2 x}+2\right ) y^{\prime }+4 \,{\mathrm e}^{4 x} y = {\mathrm e}^{6 x} \]

20911

\[ {} y^{\prime \prime }+\cot \left (x \right ) y^{\prime }+\frac {\csc \left (x \right )^{2} y}{2} = 0 \]

20912

\[ {} x^{6} y^{\prime \prime }+3 x^{5} y^{\prime }+a^{2} y = \frac {1}{x^{2}} \]

20913

\[ {} x y^{\prime \prime }-y^{\prime }-4 x^{3} y = 8 x^{3} \sin \left (x^{2}\right ) \]

20914

\[ {} y^{\prime \prime } \cos \left (x \right )+y^{\prime } \sin \left (x \right )-2 \cos \left (x \right )^{3} y = 2 \cos \left (x \right )^{5} \]

20915

\[ {} \left (1+x \right )^{2} y^{\prime \prime }+y^{\prime } \left (1+x \right )+y = 4 \cos \left (\ln \left (1+x \right )\right ) \]

20916

\[ {} x y^{\prime \prime }+\left (x -1\right ) y^{\prime }-y = x^{2} \]

20917

\[ {} 3 x^{2} y^{\prime \prime }+\left (-6 x^{2}+6 x +2\right ) y^{\prime }-4 y = 0 \]

20918

\[ {} y^{\prime \prime }+a^{2} y = \sec \left (a x \right ) \]

20919

\[ {} x^{2} y^{\prime \prime }+x y^{\prime }-y = x^{2} {\mathrm e}^{x} \]

20920

\[ {} 2 \left (1+x \right ) y-2 x \left (1+x \right ) y^{\prime }+x^{2} y^{\prime \prime } = x^{3} \]

20921

\[ {} y^{\prime \prime }+\left (1-\cot \left (x \right )\right ) y^{\prime }-y \cot \left (x \right ) = \sin \left (x \right )^{2} \]

20922

\[ {} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y = {\mathrm e}^{2 x} \]

20923

\[ {} [x^{\prime }\left (t \right )-7 x \left (t \right )+y \left (t \right ) = 0, y^{\prime }\left (t \right )-2 x \left (t \right )-5 y \left (t \right ) = 0] \]

20924

\[ {} [x^{\prime }\left (t \right )+5 x \left (t \right )+y \left (t \right ) = {\mathrm e}^{t}, y^{\prime }\left (t \right )-x \left (t \right )+3 y \left (t \right ) = {\mathrm e}^{2 t}] \]

20925

\[ {} [4 x^{\prime }\left (t \right )+9 y^{\prime }\left (t \right )+11 x \left (t \right )+31 y \left (t \right ) = {\mathrm e}^{t}, 3 x^{\prime }\left (t \right )+7 y^{\prime }\left (t \right )+8 x \left (t \right )+24 y \left (t \right ) = {\mathrm e}^{2 t}] \]

20926

\[ {} [t x^{\prime }\left (t \right ) = t -2 x \left (t \right ), t y^{\prime }\left (t \right ) = t x \left (t \right )+t y \left (t \right )+2 x \left (t \right )-t] \]

20927

\[ {} y^{\prime } = \frac {{\mathrm e}^{x}}{2 y} \]

20928

\[ {} y^{\prime } = y^{2} \left (t^{2}+1\right ) \]

20929

\[ {} y^{\prime } = \frac {\sqrt {1-y^{2}}}{x} \]

20930

\[ {} x y^{\prime } = y \left (1-2 y\right ) \]

20931

\[ {} y^{\prime }-\sin \left (x \right ) y = \sin \left (x \right ) \]

20932

\[ {} -2 y+x y^{\prime } = x^{2} \]

20933

\[ {} s^{\prime }+2 s = s t^{2} \]

20934

\[ {} x^{\prime }-2 x = t \,{\mathrm e}^{2 t} \]

20935

\[ {} y^{\prime }+y = \sin \left (x \right ) \]

20936

\[ {} y^{\prime }-\frac {3 y}{x} = x^{3} \]

20937

\[ {} 3 x^{2}+6 x y^{2}+\left (6 x^{2}+4 y^{3}\right ) y^{\prime } = 0 \]

20938

\[ {} x +y^{2}-2 y y^{\prime } x = 0 \]

20939

\[ {} \sin \left (x y\right )+x y \cos \left (x y\right )+x^{2} \cos \left (x y\right ) y^{\prime } = 0 \]

20940

\[ {} x^{2}+y-x y^{\prime } = 0 \]

20941

\[ {} 2 x y^{2}-3 y^{3}+\left (7-3 x y^{2}\right ) y^{\prime } = 0 \]

20942

\[ {} y^{\prime } = \frac {x}{y}-\frac {x}{1+y} \]

20943

\[ {} y = x y^{\prime }+\frac {1}{y^{\prime }} \]

20944

\[ {} y = 2 x y^{\prime }+\ln \left (y^{\prime }\right ) \]

20945

\[ {} y^{\prime }+2 x y = 2 x y^{2} \]

20946

\[ {} y^{\prime }+2 x y = y^{2} {\mathrm e}^{x^{2}} \]

20947

\[ {} x y^{\prime }-y^{2}+\left (2 x +1\right ) y = x^{2}+2 x \]

20948

\[ {} {\mathrm e}^{-x} y^{\prime }+y^{2}-2 y \,{\mathrm e}^{x} = 1-{\mathrm e}^{2 x} \]

20949

\[ {} y^{\prime } = \frac {x y+y^{2}}{x^{2}} \]

20950

\[ {} x^{2}-x y+y^{2}-y y^{\prime } x = 0 \]

20951

\[ {} x y-\left (x^{2}+y^{2}\right ) y^{\prime } = 0 \]

20952

\[ {} x^{2}+2 x y-4 y^{2}-\left (x^{2}-8 x y-4 y^{2}\right ) y^{\prime } = 0 \]

20953

\[ {} 20 y-9 y^{\prime }+y^{\prime \prime } = 0 \]

20954

\[ {} y^{\prime \prime }-3 y^{\prime }+4 y = 0 \]

20955

\[ {} 8 y^{\prime \prime }+4 y^{\prime }+y = 0 \]

20956

\[ {} x^{\prime \prime }-x^{\prime }-6 x = 0 \]

20957

\[ {} x^{2} y^{\prime \prime }-2 x y^{\prime }-4 y = 0 \]

20958

\[ {} x y^{\prime \prime }-y^{\prime }+4 x^{3} y = 0 \]

20959

\[ {} \left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0 \]

20960

\[ {} \left (x -1\right ) y^{\prime \prime }-x y^{\prime }+y = 0 \]

20961

\[ {} -y+y^{\prime \prime } = 0 \]

20962

\[ {} x^{\prime \prime }-3 x^{\prime }+2 x = 6 \,{\mathrm e}^{3 t} \]

20963

\[ {} 2 y-3 y^{\prime }+y^{\prime \prime } = 10 \]

20964

\[ {} y+2 y^{\prime }+y^{\prime \prime } = 5+10 \sin \left (2 x \right ) \]

20965

\[ {} 6 y-5 y^{\prime }+y^{\prime \prime } = 3 \,{\mathrm e}^{x} \]

20966

\[ {} y^{\prime \prime }+5 y^{\prime }-6 y = 3 \,{\mathrm e}^{x} \]

20967

\[ {} y^{\prime \prime }+y = \sec \left (x \right )^{3} \]

20968

\[ {} y^{\prime \prime }+y^{\prime } = 3 x^{2} \]

20969

\[ {} -y+y^{\prime \prime } = {\mathrm e}^{x}+1 \]

20970

\[ {} y^{\prime \prime }+y = \tan \left (x \right ) \]

20971

\[ {} 4 y-4 y^{\prime }+y^{\prime \prime } = 6 x \,{\mathrm e}^{2 x} \]

20972

\[ {} y-2 y^{\prime }+y^{\prime \prime } = \frac {{\mathrm e}^{2 x}}{\left ({\mathrm e}^{x}+1\right )^{2}} \]

20973

\[ {} 2 y-3 y^{\prime }+y^{\prime \prime } = \cos \left ({\mathrm e}^{x}\right ) \]

20974

\[ {} x^{2} y^{\prime \prime }+3 x y^{\prime }+2 y = 0 \]

20975

\[ {} x^{2} y^{\prime \prime }-3 x y^{\prime }+3 y = 0 \]

20976

\[ {} x^{2} y^{\prime \prime }+5 x y^{\prime }+4 y = 0 \]

20977

\[ {} x^{2} y^{\prime \prime }-2 x y^{\prime }+3 y = 0 \]

20978

\[ {} x^{2} y^{\prime \prime }+3 x y^{\prime }-3 y = 0 \]

20979

\[ {} x^{2} y^{\prime \prime }+3 x y^{\prime }-3 y = 0 \]

20980

\[ {} 2 x^{2} y^{\prime \prime }+5 x y^{\prime }+y = 0 \]

20981

\[ {} 4 x^{2} y^{\prime \prime }+y = 0 \]

20982

\[ {} -y+x y^{\prime }+x^{3} y^{\prime \prime \prime } = 0 \]

20983

\[ {} x^{2} y^{\prime \prime }+3 x y^{\prime }-3 y = 3 x^{2} \]

20984

\[ {} 2 x^{2} y^{\prime \prime }+5 x y^{\prime }+y = x^{2}+x \]

20985

\[ {} x^{2} y^{\prime \prime }+5 x y^{\prime }+4 y = 2 x^{3} \]

20986

\[ {} x^{2} y^{\prime \prime }-2 x y^{\prime }+3 y = 5 x^{2} \]

20987

\[ {} 2 y-3 y^{\prime }+y^{\prime \prime } = 20 \,{\mathrm e}^{-2 x} \]

20988

\[ {} y^{\prime \prime }+y = 2 \sin \left (3 x \right ) \]

20989

\[ {} y^{\prime \prime }+y = 1+2 \cos \left (x \right ) \]

20990

\[ {} x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = 3 x^{2}-x \]

20991

\[ {} x^{\prime \prime }+x = 5 t^{2} \]

20992

\[ {} x^{\prime \prime }+x = 2 \tan \left (t \right ) \]

20993

\[ {} y^{\prime \prime }-k^{2} y = f \left (x \right ) \]

20994

\[ {} -y+y^{\prime \prime } = {\mathrm e}^{-x} \]

20995

\[ {} y^{\prime \prime }-4 y = {\mathrm e}^{2 x} \]

20996

\[ {} x^{2} y^{\prime \prime }+3 x y^{\prime }-15 y = x^{4} {\mathrm e}^{x} \]

20997

\[ {} y^{\prime } = y \]

20998

\[ {} y^{\prime } = 2 x y-x^{3} \]

20999

\[ {} y^{\prime } \left (1+x \right ) = p y \]

21000

\[ {} y^{\prime } = \sqrt {x^{2}+y^{2}} \]