4.7.19 Problems 1801 to 1900

Table 4.785: Solved using series method

#

ODE

Mathematica

Maple

Sympy

19730

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

19731

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

19732

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

19733

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

19734

\[ {} \left (x^{2}-x -6\right ) y^{\prime \prime }+\left (5+3 x \right ) y^{\prime }+y = 0 \]

19735

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

19736

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

19737

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

20261

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

20262

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

20263

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

20264

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

20265

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

20266

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

20997

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

20998

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

20999

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

21000

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

21001

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

21002

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

21003

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

21004

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

21005

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

21006

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

21007

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

21008

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

21009

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

21010

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

21011

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

21012

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

21013

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

21014

\[ {} \frac {y^{\prime \prime }}{x}+\frac {3 \left (x -4\right ) y^{\prime }}{x +6}+\frac {x^{2} \left (x -2\right ) y}{x -1} = 0 \]

21015

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

21016

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

21017

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

21018

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

21019

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

21020

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

21021

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

21022

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

21023

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

21024

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

21025

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

21026

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

21027

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

21028

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

21102

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

21103

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

21104

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

21383

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

21384

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

21385

\[ {} t x^{\prime \prime } = t x+1 \]

21386

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

21387

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

21388

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

21389

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

21390

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

21743

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

21744

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

21745

\[ {} 2 x^{2} y^{\prime \prime }+7 x \left (1+x \right ) y^{\prime }-3 y = 0 \]

21746

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

21747

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

21748

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

21749

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

21750

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

21751

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

21752

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

21753

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

21754

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

21755

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

21756

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

21757

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

21758

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

21759

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

21760

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

21761

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

21762

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

21763

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

21764

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

21765

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

21766

\[ {} -4 y-6 x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime } = 0 \]

21767

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

21768

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

21769

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

21770

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

21771

\[ {} \left (x^{2}+2\right ) y^{\prime \prime }+\left (2 x +\frac {2}{x}\right ) y^{\prime }+2 x^{2} y = \frac {4 x^{2}+2 x +10}{x^{4}} \]

21772

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

21773

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

21774

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

21775

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

21776

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

21777

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

21778

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

21779

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

21780

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

21781

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

21782

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

21783

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

21784

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

21785

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