2.20 Problems 1901 to 2000

Table 2.20: Main lookup table

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ODE

Mathematica result

Maple result

1901

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

1902

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

1903

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

1904

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

1905

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

1906

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

1907

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

1908

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

1909

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

1910

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

1911

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

1912

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

1913

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

1914

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

1915

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

1916

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

1917

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

1918

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

1919

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

1920

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

1921

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

1922

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

1923

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

1924

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

1925

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

1926

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

1927

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

1928

\[ {}y^{\prime } = \arcsin \relax (x ) \]

1929

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

1930

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

1931

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

1932

\[ {}y^{\prime } \sin \relax (y) = x^{2} \]

1933

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

1934

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

1935

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

1936

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

1937

\[ {}y^{\prime } \sin \relax (x ) = 1 \]

1938

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

1939

\[ {}y^{\prime } = t \,{\mathrm e}^{2 t} \]

1940

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

1941

\[ {}y^{\prime } = \sin ^{2}\relax (t ) \]

1942

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

1943

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

1944

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

1945

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

1946

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

1947

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

1948

\[ {}y^{\prime } = t \,{\mathrm e}^{2 t} \]

1949

\[ {}y^{\prime } = \sin ^{2}\relax (t ) \]

1950

\[ {}y^{\prime } = 8 \,{\mathrm e}^{4 t}+t \]

1951

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

1952

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

1953

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

1954

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

1955

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

1956

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

1957

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

1958

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

1959

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

1960

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

1961

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

1962

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

1963

\[ {}t y^{\prime }+2 y = \sin \relax (t ) \]

1964

\[ {}y^{\prime } = \tan \relax (t ) y+\sec \relax (t ) \]

1965

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

1966

\[ {}y^{\prime } = \tan \relax (t ) y+\sec ^{3}\relax (t ) \]

1967

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

1968

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

1969

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

1970

\[ {}y^{\prime } = -\tan \relax (t ) y+\sec \relax (t ) \]

1971

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

1972

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

1973

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

1974

\[ {}t \ln \relax (t ) y^{\prime } = \ln \relax (t ) t -y \]

1975

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

1976

\[ {}y^{\prime } = -\cot \relax (t ) y+6 \left (\cos ^{2}\relax (t )\right ) \]

1977

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

1978

\[ {}\frac {y^{\prime }}{\tan \relax (x )}-\frac {y}{x^{2}+1} = 0 \]

1979

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

1980

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

1981

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

1982

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

1983

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

1984

\[ {}y^{\prime }-y \cot \relax (x )+\frac {1}{\sin \relax (x )} = 0 \]

1985

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

1986

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

1987

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

1988

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

1989

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

1990

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

1991

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

1992

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

1993

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

1994

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

1995

\[ {}y^{\prime }-y \tan \relax (x ) = 1 \]

1996

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

1997

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

1998

\[ {}y^{\prime } \sin \relax (x )+2 y \cos \relax (x ) = 1 \]

1999

\[ {}\left (5 x +y-7\right ) y^{\prime } = 3+3 x +3 y \]

2000

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