6.220 Problems 21901 to 22000

Table 6.439: Main lookup table sequentially arranged

#

ODE

Mathematica

Maple

Sympy

21901

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

21902

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

21903

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

21904

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

21905

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

21906

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

21907

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

21908

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

21909

\[ {} y^{\prime \prime }+y^{\prime } = 6 y+5 \,{\mathrm e}^{2 x} \]

21910

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

21911

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

21912

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

21913

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

21914

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

21915

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

21916

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

21917

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

21918

\[ {} r^{\prime } = r \tan \left (t \right ) \]

21919

\[ {} {\mathrm e}^{x} \sec \left (y\right )+\left ({\mathrm e}^{x}+1\right ) \sec \left (y\right ) \tan \left (y\right ) y^{\prime } = 0 \]

21920

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

21921

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

21922

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

21923

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

21924

\[ {} 3 x^{2}+2 x y+4 y^{2}+\left (20 x^{2}+6 x y+y^{2}\right ) y^{\prime } = 0 \]

21925

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

21926

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

21927

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

21928

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

21929

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

21930

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

21931

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

21932

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

21933

\[ {} 4 x -2 y+3+\left (5 y-2 x +7\right ) y^{\prime } = 0 \]

21934

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

21935

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

21936

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

21937

\[ {} x^{3} y^{\prime }-x^{2} y = x^{5} y \]

21938

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

21939

\[ {} 3 y+2 x y^{\prime }+4 x y^{2}+3 x^{2} y y^{\prime } = 0 \]

21940

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

21941

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

21942

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

21943

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

21944

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

21945

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

21946

\[ {} x y+x^{2} y^{\prime } = 8 x^{2} \cos \left (x \right )^{2} \]

21947

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

21948

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

21949

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

21950

\[ {} 2+3 x -5 y+7 y^{\prime } = 0 \]

21951

\[ {} 4 x +3 y+2+\left (5 x +4 y+1\right ) y^{\prime } = 0 \]

21952

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

21953

\[ {} 2 x -y-1+\left (3 x +2 y-5\right ) y^{\prime } = 0 \]

21954

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

21955

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

21956

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

21957

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

21958

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

21959

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

21960

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

21961

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

21962

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

21963

\[ {} R q^{\prime }+\frac {q}{c} = E \]

21964

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

21965

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

21966

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

21967

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

21968

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

21969

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

21970

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

21971

\[ {} {y^{\prime }}^{2}-4 y^{\prime }+2 = 0 \]

21972

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

21973

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

21974

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

21975

\[ {} 2 a \,x^{3} y-a \,x^{2} y^{\prime }+c {y^{\prime }}^{3} = 0 \]

21976

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

21977

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

21978

\[ {} 2 x +y y^{\prime } \left (4 {y^{\prime }}^{2}+6\right ) = 0 \]

21979

\[ {} 2 {y^{\prime }}^{2}+y y^{\prime }-y^{4} = 0 \]

21980

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

21981

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

21982

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

21983

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

21984

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

21985

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

21986

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

21987

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

21988

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

21989

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

21990

\[ {} y^{\prime \prime }-12 y^{\prime }+35 y = 0 \]

21991

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

21992

\[ {} 9 y^{\prime \prime }-30 y^{\prime }+25 y = 0 \]

21993

\[ {} 3 y^{\prime \prime }-4 y^{\prime }+2 y = 0 \]

21994

\[ {} y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime }+7 y^{\prime \prime }+6 y^{\prime }-8 y = 0 \]

21995

\[ {} y^{\prime \prime \prime }-2 y^{\prime \prime }+3 y^{\prime }-6 y = 0 \]

21996

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

21997

\[ {} y^{\prime \prime \prime \prime }-8 y^{\prime \prime \prime }+42 y^{\prime \prime }-104 y^{\prime }+169 y = 0 \]

21998

\[ {} y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y = 2 x^{2}-3 x -17 \]

21999

\[ {} y^{\prime \prime }-2 y^{\prime }-3 y+8 \,{\mathrm e}^{-x}+3 x = 0 \]

22000

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