2.80 Problems 7901 to 8000

Table 2.159: Main lookup table

#

ODE

Mathematica result

Maple result

7901

\[ {}t y^{\prime \prime }+\left (t^{2}-1\right ) y^{\prime }+t^{3} y = 0 \]

7902

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

7903

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

7904

\[ {}x^{2} y^{\prime \prime }-\left (x -\frac {3}{16}\right ) y = 0 \]

7905

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

7906

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

7907

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

7908

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

7909

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

7910

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

7911

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

7912

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

7913

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

7914

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

7915

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

7916

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

7917

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

7918

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

7919

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

7920

\[ {}4 x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (-16 x^{2}+3\right ) y = 0 \]

7921

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

7922

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

7923

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

7924

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

7925

\[ {}4 x^{2} y^{\prime \prime }+\left (-8 x^{2}+4 x \right ) y^{\prime }+\left (4 x^{2}-4 x -1\right ) y = 0 \]

7926

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

7927

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

7928

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

7929

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

7930

\[ {}2 x y^{\prime \prime }+\left (4 x +1\right ) y^{\prime }+\left (1+2 x \right ) y = 0 \]

7931

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

7932

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

7933

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

7934

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

7935

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

7936

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

7937

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

7938

\[ {}4 x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (-16 x^{2}+3\right ) y = 0 \]

7939

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

7940

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

7941

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

7942

\[ {}\left (3 x -1\right ) y^{\prime \prime }-\left (2+3 x \right ) y^{\prime }-\left (6 x -8\right ) y = 0 \]

7943

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

7944

\[ {}4 x^{2} y^{\prime \prime }+\left (-8 x^{2}+4 x \right ) y^{\prime }+\left (4 x^{2}-4 x -1\right ) y = 0 \]

7945

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

7946

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

7947

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

7948

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

7949

\[ {}4 x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (-16 x^{2}+3\right ) y = 0 \]

7950

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

7951

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

7952

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

7953

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

7954

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

7955

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

7956

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

7957

\[ {}\left (3 x -1\right ) y^{\prime \prime }-\left (2+3 x \right ) y^{\prime }-\left (6 x -8\right ) y = 0 \]

7958

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

7959

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

7960

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

7961

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

7962

\[ {}x^{2} \left (x^{2}+2\right ) y^{\prime \prime }+2 x \left (x^{2}+5\right ) y^{\prime }+2 \left (-x^{2}+3\right ) y = 0 \]

7963

\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+6 x y^{\prime }+6 y = 0 \]

7964

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

7965

\[ {}\left (x^{2}+1\right ) y^{\prime \prime }-8 x y^{\prime }+20 y = 0 \]

7966

\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-8 x y^{\prime }-12 y = 0 \]

7967

\[ {}\left (2 x^{2}+1\right ) y^{\prime \prime }+7 x y^{\prime }+2 y = 0 \]

7968

\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-5 x y^{\prime }-4 y = 0 \]

7969

\[ {}\left (x^{2}+1\right ) y^{\prime \prime }-10 x y^{\prime }+28 y = 0 \]

7970

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

7971

\[ {}\left (2 x^{2}-8 x +11\right ) y^{\prime \prime }-16 \left (-2+x \right ) y^{\prime }+36 y = 0 \]

7972

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

7973

\[ {}\left (x^{2}-8 x +14\right ) y^{\prime \prime }-8 \left (x -4\right ) y^{\prime }+20 y = 0 \]

7974

\[ {}\left (2 x^{2}+4 x +5\right ) y^{\prime \prime }-20 \left (1+x \right ) y^{\prime }+60 y = 0 \]

7975

\[ {}\left (x^{3}+1\right ) y^{\prime \prime }+7 x^{2} y^{\prime }+9 x y = 0 \]

7976

\[ {}\left (2 x^{5}+1\right ) y^{\prime \prime }+14 x^{4} y^{\prime }+10 x^{3} y = 0 \]

7977

\[ {}y^{\prime \prime }+x^{6} y^{\prime }+7 x^{5} y = 0 \]

7978

\[ {}\left (x^{8}+1\right ) y^{\prime \prime }-16 x^{7} y^{\prime }+72 x^{6} y = 0 \]

7979

\[ {}y^{\prime \prime }+x^{5} y^{\prime }+6 x^{4} y = 0 \]

7980

\[ {}\left (1+3 x \right ) y^{\prime \prime }+x y^{\prime }+2 y = 0 \]

7981

\[ {}\left (3 x^{2}+x +1\right ) y^{\prime \prime }+\left (2+15 x \right ) y^{\prime }+12 y = 0 \]

7982

\[ {}\left (2+x \right ) y^{\prime \prime }+\left (1+x \right ) y^{\prime }+3 y = 0 \]

7983

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

7984

\[ {}\left (2 x^{2}+3 x \right ) y^{\prime \prime }+10 \left (1+x \right ) y^{\prime }+8 y = 0 \]

7985

\[ {}x^{2} y^{\prime \prime }-\left (6-7 x \right ) y^{\prime }+8 y = 0 \]

7986

\[ {}\left (2 x^{2}+x +1\right ) y^{\prime \prime }+\left (1+7 x \right ) y^{\prime }+2 y = 0 \]

7987

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

7988

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

7989

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

7990

\[ {}y^{\prime \prime }-3 x y^{\prime }+\left (2 x^{2}+5\right ) y = 0 \]

7991

\[ {}2 y^{\prime \prime }+5 x y^{\prime }+\left (2 x^{2}+4\right ) y = 0 \]

7992

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

7993

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

7994

\[ {}2 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+x \left (11 x^{2}+11 x +9\right ) y^{\prime }+\left (7 x^{2}+10 x +6\right ) y = 0 \]

7995

\[ {}3 x^{2} y^{\prime \prime }+2 x \left (-2 x^{2}+x +1\right ) y^{\prime }+\left (-8 x^{2}+2 x \right ) y = 0 \]

7996

\[ {}12 x^{2} \left (1+x \right ) y^{\prime \prime }+x \left (3 x^{2}+35 x +11\right ) y^{\prime }-\left (-5 x^{2}-10 x +1\right ) y = 0 \]

7997

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

7998

\[ {}18 x^{2} \left (1+x \right ) y^{\prime \prime }+3 x \left (x^{2}+11 x +5\right ) y^{\prime }-\left (-5 x^{2}-2 x +1\right ) y = 0 \]

7999

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

8000

\[ {}2 x^{2} y^{\prime \prime }+x \left (5+x \right ) y^{\prime }-\left (2-3 x \right ) y = 0 \]