2.60 Problems 5901 to 6000

Table 2.119: Main lookup table

#

ODE

Mathematica result

Maple result

5901

\[ {}[x_{1}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )-x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 5 x_{1} \left (t \right )+2 x_{2} \left (t \right )] \]

5902

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

5903

\[ {}[x_{1}^{\prime }\left (t \right ) = -2 x_{1} \left (t \right )+x_{2} \left (t \right )+2 \,{\mathrm e}^{-t}, x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )-2 x_{2} \left (t \right )+3 t] \]

5904

\[ {}[x_{1}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )-x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 16 x_{1} \left (t \right )-5 x_{2} \left (t \right )] \]

5905

\[ {}[x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )-2 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )-4 x_{2} \left (t \right )] \]

5906

\[ {}[x_{1}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )-18 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )-9 x_{2} \left (t \right )] \]

5907

\[ {}[x_{1}^{\prime }\left (t \right ) = -x_{1} \left (t \right )+3 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -3 x_{1} \left (t \right )+5 x_{2} \left (t \right )] \]

5908

\[ {}[x_{1}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )-18 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )-9 x_{2} \left (t \right )] \]

5909

\[ {}[x_{1}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )-x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )-2 x_{2} \left (t \right )] \]

5910

\[ {}[x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )+x_{2} \left (t \right )-8, x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )+x_{2} \left (t \right )+3] \]

5911

\[ {}[x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )+x_{2} \left (t \right )-8, x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )+x_{2} \left (t \right )+3] \]

5912

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

5913

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

5914

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

5915

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

5916

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

5917

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

5918

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

5919

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

5920

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

5921

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

5922

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

5923

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

5924

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

5925

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

5926

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

5927

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

5928

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

5929

\[ {}L y^{\prime }+R y = E \]

5930

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

5931

\[ {}L y^{\prime }+R y = E \,{\mathrm e}^{i \omega x} \]

5932

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

5933

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

5934

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

5935

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

5936

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

5937

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

5938

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

5939

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

5940

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

5941

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

5942

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

5943

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

5944

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

5945

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

5946

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

5947

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

5948

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

5949

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

5950

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

5951

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

5952

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

5953

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

5954

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

5955

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

5956

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

5957

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

5958

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

5959

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

5960

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

5961

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

5962

\[ {}y^{\prime \prime }+9 y = \sin \left (3 x \right ) \]

5963

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

5964

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

5965

\[ {}y^{\prime \prime }-4 y^{\prime }+5 y = 3 \,{\mathrm e}^{-x}+2 x^{2} \]

5966

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

5967

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

5968

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

5969

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

5970

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

5971

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

5972

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

5973

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

5974

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

5975

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

5976

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

5977

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

5978

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

5979

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

5980

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

5981

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

5982

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

5983

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

5984

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

5985

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

5986

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

5987

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

5988

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

5989

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

5990

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

5991

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

5992

\[ {}y^{\prime \prime \prime }-8 y = {\mathrm e}^{i x} \]

5993

\[ {}y^{\prime \prime \prime \prime }+16 y = \cos \left (x \right ) \]

5994

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

5995

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

5996

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

5997

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

5998

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

5999

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

6000

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