4.7.21 Problems 2001 to 2100

Table 4.789: Solved using series method

#

ODE

Mathematica

Maple

Sympy

22341

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

22342

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

22937

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

22938

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

22939

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

22940

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

22941

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

22942

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

22943

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

22944

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

22945

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

22946

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

22947

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

22948

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

22949

\[ {} \left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+6 y = 0 \]

22950

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

22951

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

22952

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

22953

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

22954

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

22955

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

22956

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

22957

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

22958

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

22959

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

22960

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

22961

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

22962

\[ {} \left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+6 y = 0 \]

22963

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

22964

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

22965

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

22966

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

22967

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

22968

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

22969

\[ {} \left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+12 y = 0 \]

22970

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

22971

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

22972

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

22973

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

22974

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

22975

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

22976

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

22977

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

22978

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

22979

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

22980

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

22981

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

22982

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

22983

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

22984

\[ {} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{9}\right ) y = 0 \]

22985

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

22986

\[ {} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-8\right ) y = 0 \]

22987

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

22988

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

22989

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

22990

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

22991

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

22992

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

22993

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

22994

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

22995

\[ {} \left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+6 y = 0 \]

22996

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

22997

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

23549

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

23550

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

23551

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

23552

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

23553

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

23554

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

23555

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

23556

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

23557

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

23558

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

23559

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

23560

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

23561

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

23562

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

23563

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

23564

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

23565

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

23566

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

23567

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

23568

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

23569

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

23782

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

23783

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

23784

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

23785

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

23786

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

23787

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

23788

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

23789

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

23790

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

23791

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

23792

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

23793

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

23794

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

23795

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

23796

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

23797

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