6.240 Problems 23901 to 24000

Table 6.479: Main lookup table sequentially arranged

#

ODE

Mathematica

Maple

Sympy

23901

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

23902

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

23903

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

23904

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

23905

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

23906

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

23907

\[ {} [x^{\prime }\left (t \right ) = 5 x \left (t \right )-6 y \left (t \right ), y^{\prime }\left (t \right ) = 6 x \left (t \right )-7 y \left (t \right )] \]

23908

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

23909

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

23910

\[ {} [x^{\prime }\left (t \right ) = 4 x \left (t \right )-6 y \left (t \right ), y^{\prime }\left (t \right ) = 8 x \left (t \right )-10 y \left (t \right )] \]

23911

\[ {} [x^{\prime }\left (t \right ) = 5 x \left (t \right )-6 y \left (t \right )+1, y^{\prime }\left (t \right ) = 6 x \left (t \right )-7 y \left (t \right )+1] \]

23912

\[ {} [x^{\prime }\left (t \right ) = 5 x \left (t \right )-6 y \left (t \right )+x \left (t \right ) y \left (t \right ), y^{\prime }\left (t \right ) = 6 x \left (t \right )-7 y \left (t \right )-x \left (t \right ) y \left (t \right )] \]

23913

\[ {} [x^{\prime }\left (t \right ) = 3 x \left (t \right )-2 y \left (t \right )+\left (x \left (t \right )^{2}+y \left (t \right )^{2}\right )^{2}, y^{\prime }\left (t \right ) = 4 x \left (t \right )-y \left (t \right )+\left (x \left (t \right )^{2}-y \left (t \right )^{2}\right )^{5}] \]

23914

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

23915

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

23916

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

23917

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

23918

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

23919

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

23920

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

23921

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

23922

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

23923

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

23924

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

23925

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

23926

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

23927

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

23928

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

23929

\[ {} [x^{\prime }\left (t \right ) = 4 x \left (t \right )+6 y \left (t \right ), y^{\prime }\left (t \right ) = -7 x \left (t \right )-9 y \left (t \right )] \]

23930

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

23931

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

23932

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

23933

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

23934

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

23935

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

23936

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

23937

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

23938

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

23939

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

23940

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

23941

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

23942

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

23943

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

23944

\[ {} y^{\prime } = \frac {1}{t^{2}} \]

23945

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

23946

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

23947

\[ {} y^{\prime } = t \,{\mathrm e}^{t} \]

23948

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

23949

\[ {} y^{\prime } = t \ln \left (t \right ) \]

23950

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

23951

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

23952

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

23953

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

23954

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

23955

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

23956

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

23957

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

23958

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

23959

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

23960

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

23961

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

23962

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

23963

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

23964

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

23965

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

23966

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

23967

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

23968

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

23969

\[ {} y^{3}+y^{\prime } \sqrt {-x^{2}+1} = 0 \]

23970

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

23971

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

23972

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

23973

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

23974

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

23975

\[ {} y y^{\prime } x +x^{6}-2 y^{2} = 0 \]

23976

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

23977

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

23978

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

23979

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

23980

\[ {} x \left (6 x^{2}+14 y^{2}\right )+y \left (13 x^{2}+30 y^{2}\right ) y^{\prime } = 0 \]

23981

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

23982

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

23983

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

23984

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

23985

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

23986

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

23987

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

23988

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

23989

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

23990

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

23991

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

23992

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

23993

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

23994

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

23995

\[ {} y^{\prime } = \frac {4 x -3 y-17}{3 x +y-3} \]

23996

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

23997

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

23998

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

23999

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

24000

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