2.10 Problems 901 to 1000

Table 2.19: Main lookup table

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ODE

Mathematica result

Maple result

901

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

902

\[ {}y^{\prime }+\frac {y}{x} = \frac {7}{x^{2}}+3 \]

903

\[ {}y^{\prime }+\frac {4 y}{x -1} = \frac {1}{\left (x -1\right )^{5}}+\frac {\sin \left (x \right )}{\left (x -1\right )^{4}} \]

904

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

905

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

906

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

907

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

908

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

909

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

910

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

911

\[ {}y^{\prime }+7 y = {\mathrm e}^{3 x} \]

912

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

913

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

914

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

915

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

916

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

917

\[ {}2 y+x y^{\prime } = 8 x^{2} \]

918

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

919

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

920

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

921

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

922

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

923

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

924

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

925

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

926

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

927

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

928

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

929

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

930

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

931

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

932

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

933

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

934

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

935

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

936

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

937

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

938

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

939

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

940

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

941

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

942

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

943

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

944

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

945

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

946

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

947

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

948

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

949

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

950

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

951

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

952

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

953

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

954

\[ {}y+y^{\prime } = \frac {2 x \,{\mathrm e}^{-x}}{1+y \,{\mathrm e}^{x}} \]

955

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

956

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

957

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

958

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

959

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

960

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

961

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

962

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

963

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

964

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

965

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

966

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

967

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

968

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

969

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

970

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

971

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

972

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

973

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

974

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

975

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

976

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

977

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

978

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

979

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

980

\[ {}7 x y^{\prime }-2 y = -\frac {x^{2}}{y^{6}} \]

981

\[ {}x^{2} y^{\prime }+2 y = 2 \,{\mathrm e}^{\frac {1}{x}} \sqrt {y} \]

982

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

983

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

984

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

985

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

986

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

987

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

988

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

989

\[ {}y^{\prime }-4 y = \frac {48 x}{y^{2}} \]

990

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

991

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

992

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

993

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

994

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

995

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

996

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

997

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

998

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

999

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

1000

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