6.60 Problems 5901 to 6000

Table 6.119: Main lookup table sequentially arranged

#

ODE

Mathematica

Maple

5901

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

5902

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

5903

\[ {}y^{2}+12 x^{2} y+\left (2 x y+4 x^{3}\right ) y^{\prime } = 0 \]

5904

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

5905

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

5906

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

5907

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

5908

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

5909

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

5910

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

5911

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

5912

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

5913

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

5914

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

5915

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

5916

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

5917

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

5918

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

5919

\[ {}6 y^{\prime \prime }-11 y^{\prime }+4 y = 0 \]

5920

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

5921

\[ {}y^{\prime \prime \prime }+y^{\prime \prime }-10 y^{\prime }-6 y = 0 \]

5922

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

5923

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

5924

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

5925

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

5926

\[ {}y^{\prime \prime }+4 k y^{\prime }-12 k^{2} y = 0 \]

5927

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

5928

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

5929

\[ {}3 y^{\prime \prime \prime }+5 y^{\prime \prime }+y^{\prime }-y = 0 \]

5930

\[ {}y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }-8 y = 0 \]

5931

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

5932

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

5933

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

5934

\[ {}y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }-11 y^{\prime \prime }-12 y^{\prime }+36 y = 0 \]

5935

\[ {}36 y^{\prime \prime \prime \prime }-37 y^{\prime \prime }+4 y^{\prime }+5 y = 0 \]

5936

\[ {}y^{\prime \prime \prime \prime }-8 y^{\prime \prime }+36 y = 0 \]

5937

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

5938

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

5939

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

5940

\[ {}y^{\prime \prime }-4 y^{\prime }+20 y = 0 \]

5941

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

5942

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

5943

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

5944

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

5945

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

5946

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

5947

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

5948

\[ {}y^{\prime \prime }-4 y^{\prime }+20 y = 0 \]

5949

\[ {}3 y^{\prime \prime \prime }+5 y^{\prime \prime }+y^{\prime }-y = 0 \]

5950

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

5951

\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = 12 \,{\mathrm e}^{x} \]

5952

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

5953

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

5954

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

5955

\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = 8+6 \,{\mathrm e}^{x}+2 \sin \left (x \right ) \]

5956

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

5957

\[ {}y^{\prime \prime }-2 y^{\prime }-8 y = 9 x \,{\mathrm e}^{x}+10 \,{\mathrm e}^{-x} \]

5958

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

5959

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

5960

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

5961

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

5962

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

5963

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

5964

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

5965

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

5966

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

5967

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

5968

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

5969

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

5970

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

5971

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

5972

\[ {}y^{\prime \prime }+9 y = 8 \cos \left (x \right ) \]

5973

\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = {\mathrm e}^{x} \left (2 x -3\right ) \]

5974

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

5975

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

5976

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

5977

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

5978

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

5979

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

5980

\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = 12 \,{\mathrm e}^{x} \]

5981

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

5982

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

5983

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

5984

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

5985

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

5986

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

5987

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

5988

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

5989

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

5990

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

5991

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

5992

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

5993

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

5994

\[ {}2 x^{2} y^{\prime \prime }+3 x y^{\prime }-y = \frac {1}{x} \]

5995

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

5996

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

5997

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

5998

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

5999

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

6000

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