6.200 Problems 19901 to 20000

Table 6.399: Main lookup table sequentially arranged

#

ODE

Mathematica

Maple

Sympy

19901

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

19902

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

19903

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

19904

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

19905

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

19906

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

19907

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

19908

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

19909

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

19910

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

19911

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

19912

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

19913

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

19914

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

19915

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

19916

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

19917

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

19918

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

19919

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

19920

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

19921

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

19922

\[ {} x^{3}-3 x^{2} y+5 x y^{2}-7 y^{3}+\left (y^{4}+2 y^{2}-x^{3}+5 x^{2} y-21 x y^{2}\right ) y^{\prime } = 0 \]

19923

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

19924

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

19925

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

19926

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

19927

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

19928

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

19929

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

19930

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

19931

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

19932

\[ {} \left (3 x +2 y-7\right ) y^{\prime } = 2 x -3 y+6 \]

19933

\[ {} \left (6 x -5 y+4\right ) y^{\prime } = 1+2 x -y \]

19934

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

19935

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

19936

\[ {} \left (x -3 y+4\right ) y^{\prime } = 2 x -6 y+7 \]

19937

\[ {} \left (5 x -2 y+7\right ) y^{\prime } = 10 x -4 y+6 \]

19938

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

19939

\[ {} \left (6 x -4 y+1\right ) y^{\prime } = 3 x -2 y+1 \]

19940

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

19941

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

19942

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

19943

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

19944

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

19945

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

19946

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

19947

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

19948

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

19949

\[ {} y^{\prime \prime }+4 y^{\prime }+3 y = 2 \,{\mathrm e}^{2 x} \]

19950

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

19951

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

19952

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

19953

\[ {} y^{\prime \prime \prime }+5 y^{\prime \prime }+6 y^{\prime } = x \]

19954

\[ {} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y = x \]

19955

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

19956

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

19957

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

19958

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

19959

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

19960

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

19961

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

19962

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

19963

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

19964

\[ {} e y^{\prime \prime } = \frac {w \left (\frac {L^{2}}{4}-x^{2}\right )}{2} \]

19965

\[ {} e y^{\prime \prime } = -\frac {\left (w L +P \right ) x}{2}-\frac {w \,x^{2}}{2} \]

19966

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

19967

\[ {} e y^{\prime \prime } = -P L +\left (w L +P \right ) x -\frac {w \left (L^{2}+x^{2}\right )}{2} \]

19968

\[ {} e y^{\prime \prime } = P \left (a -y\right ) \]

19969

\[ {} x^{3} y^{\prime \prime \prime }+7 x^{2} y^{\prime \prime }+8 x y^{\prime } = \ln \left (x \right )^{2} \]

19970

\[ {} x^{2} y^{\prime \prime }+3 x y^{\prime }-8 y = x \]

19971

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

19972

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

19973

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

19974

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

19975

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

19976

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

19977

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

19978

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

19979

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

19980

\[ {} \left (3 x^{2}+x \right ) y^{\prime \prime }+2 \left (1+6 x \right ) y^{\prime }+6 y = \sin \left (x \right ) \]

19981

\[ {} \left (x^{3}+x^{2}-3 x +1\right ) y^{\prime \prime \prime }+\left (9 x^{2}+6 x -9\right ) y^{\prime \prime }+\left (18 x +6\right ) y^{\prime }+6 y = x^{3} \]

19982

\[ {} 4 y^{\prime }+5 x y^{\prime \prime }+x^{2} y^{\prime \prime \prime } = -\frac {1}{x^{2}} \]

19983

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

19984

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

19985

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

19986

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

19987

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

19988

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

19989

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

19990

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

19991

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

19992

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

19993

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

19994

\[ {} V^{\prime \prime }+\frac {2 V^{\prime }}{r} = 0 \]

19995

\[ {} V^{\prime \prime }+\frac {V^{\prime }}{r} = 0 \]

19996

\[ {} [z^{\prime }\left (x \right )+7 y \left (x \right )-3 z \left (x \right ) = 0, 7 y^{\prime }\left (x \right )+63 y \left (x \right )-36 z \left (x \right ) = 0] \]

19997

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

19998

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

19999

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

20000

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