2.80 Problems 7901 to 8000

Table 2.80: Main lookup table

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ODE

Mathematica result

Maple result

7901

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

7902

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

7903

\[ {}\left (a x y^{3}+c \right ) x y^{\prime }+\left (b \,x^{3} y+c \right ) y = 0 \]

7904

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

7905

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

7906

\[ {}y \left (\left (b x +a y\right )^{3}+b \,x^{3}\right ) y^{\prime }+x \left (\left (b x +a y\right )^{3}+a y^{3}\right ) = 0 \]

7907

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

7908

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

7909

\[ {}y^{m} x^{n} \left (a x y^{\prime }+b y\right )+\alpha x y^{\prime }+\beta y = 0 \]

7910

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

7911

\[ {}\frac {y^{\prime } f_{\nu }\relax (x ) \left (-y+y^{p +1}\right )}{y-1}-\frac {g_{\nu }\relax (x ) \left (-y+y^{q +1}\right )}{y-1} = 0 \]

7912

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

7913

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

7914

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

7915

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

7916

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

7917

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

7918

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

7919

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

7920

\[ {}\left (\frac {\mathit {e1} \left (x +a \right )}{\left (\left (x +a \right )^{2}+y^{2}\right )^{\frac {3}{2}}}+\frac {\mathit {e2} \left (x -a \right )}{\left (\left (x -a \right )^{2}+y^{2}\right )^{\frac {3}{2}}}\right ) y^{\prime }-y \left (\frac {\mathit {e1}}{\left (\left (x +a \right )^{2}+y^{2}\right )^{\frac {3}{2}}}+\frac {\mathit {e2}}{\left (\left (x -a \right )^{2}+y^{2}\right )^{\frac {3}{2}}}\right ) = 0 \]

7921

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

7922

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

7923

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

7924

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

7925

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

7926

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

7927

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

7928

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

7929

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

7930

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

7931

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

7932

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

7933

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

7934

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

7935

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

7936

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

7937

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

7938

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

7939

\[ {}3 y^{\prime } \sin \relax (x ) \sin \relax (y)+5 \left (\cos ^{4}\relax (x )\right ) y = 0 \]

7940

\[ {}y^{\prime } \cos \left (a y\right )-b \left (1-c \cos \left (a y\right )\right ) \sqrt {\cos ^{2}\left (a y\right )-1+c \cos \left (a y\right )} = 0 \]

7941

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

7942

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

7943

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

7944

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

7945

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

7946

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

7947

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

7948

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

7949

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

7950

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

7951

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

7952

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

7953

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

7954

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

7955

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

7956

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

7957

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

7958

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

7959

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

7960

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

7961

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

7962

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

7963

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

7964

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

7965

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

7966

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

7967

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

7968

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

7969

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

7970

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

7971

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

7972

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

7973

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

7974

\[ {}\left (y^{\prime }\right )^{2}+2 f \relax (x ) y y^{\prime }+g \relax (x ) y^{2}-\left (g \relax (x )-f \relax (x )^{2}\right ) {\mathrm e}^{-2 \left (\int _{a}^{x}f \left (\mathit {xp} \right )d \mathit {xp} \right )} = 0 \]

7975

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

7976

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

7977

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

7978

\[ {}\left (y^{\prime }\right )^{2}-3 x y^{\frac {2}{3}} y^{\prime }+9 y^{\frac {5}{3}} = 0 \]

7979

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

7980

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

7981

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

7982

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

7983

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

7984

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

7985

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

7986

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

7987

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

7988

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

7989

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

7990

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

7991

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

7992

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

7993

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

7994

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

7995

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

7996

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

7997

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

7998

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

7999

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

8000

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