6.70 Problems 6901 to 7000

Table 6.139: Main lookup table sequentially arranged

#

ODE

Mathematica

Maple

6901

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

6902

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

6903

\[ {}y^{\prime }+2 x y = 1 \]

6904

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

6905

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

6906

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

6907

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

6908

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

6909

\[ {}2 y^{\prime \prime }+7 y^{\prime }-4 y = 0 \]

6910

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

6911

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

6912

\[ {}x^{2} y^{\prime \prime }-7 x y^{\prime }+15 y = 0 \]

6913

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

6914

\[ {}3 x y^{\prime }+5 y = 10 \]

6915

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

6916

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

6917

\[ {}y^{\prime \prime }+4 y^{\prime }+6 y = 10 \]

6918

\[ {}{y^{\prime }}^{2} = 4 y \]

6919

\[ {}{y^{\prime }}^{2} = 9-y^{2} \]

6920

\[ {}y y^{\prime }+\sqrt {16-y^{2}} = 0 \]

6921

\[ {}{y^{\prime }}^{2}-2 y^{\prime }+4 y = 4 x -1 \]

6922

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

6923

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

6924

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

6925

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

6926

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

6927

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

6928

\[ {}x {y^{\prime }}^{2}-4 y^{\prime }-12 x^{3} = 0 \]

6929

\[ {}y^{\prime } = 5-y \]

6930

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

6931

\[ {}y^{\prime \prime \prime \prime }-20 y^{\prime \prime \prime }+158 y^{\prime \prime }-580 y^{\prime }+841 y = 0 \]

6932

\[ {}x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }+20 x y^{\prime }-78 y = 0 \]

6933

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

6934

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

6935

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

6936

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

6937

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

6938

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

6939

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

6940

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

6941

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

6942

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

6943

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

6944

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

6945

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

6946

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

6947

\[ {}y^{\prime } = 3 y^{{2}/{3}} \]

6948

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

6949

\[ {}y^{\prime } = y^{{2}/{3}} \]

6950

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

6951

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

6952

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

6953

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

6954

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

6955

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

6956

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

6957

\[ {}y^{\prime } = \sqrt {y^{2}-9} \]

6958

\[ {}y^{\prime } = \sqrt {y^{2}-9} \]

6959

\[ {}y^{\prime } = \sqrt {y^{2}-9} \]

6960

\[ {}y^{\prime } = \sqrt {y^{2}-9} \]

6961

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

6962

\[ {}y^{\prime } = 1+y^{2} \]

6963

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

6964

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

6965

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

6966

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

6967

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

6968

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

6969

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

6970

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

6971

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

6972

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

6973

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

6974

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

6975

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

6976

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

6977

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

6978

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

6979

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

6980

\[ {}y^{\prime }+2 y = 3 x -6 \]

6981

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

6982

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

6983

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

6984

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

6985

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

6986

\[ {}y^{\prime \prime }+9 y = 18 \]

6987

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

6988

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

6989

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

6990

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

6991

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

6992

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

6993

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

6994

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

6995

\[ {}y^{\prime } = 6 \sqrt {y}+5 x^{3} \]

6996

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

6997

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

6998

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

6999

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

7000

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