1.2 problem 7.2.2

Internal problem ID [4751]

Book: Notes on Diffy Qs. Differential Equations for Engineers. By by Jiri Lebl, 2013.
Section: Chapter 7. POWER SERIES METHODS. 7.2.1 Exercises. page 290
Problem number: 7.2.2.
ODE order: 2.
ODE degree: 1.

CAS Maple gives this as type [[_Emden, _Fowler]]

Solve \begin {gather*} \boxed {y^{\prime \prime }+4 x y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).

Solution by Maple

Time used: 0.001 (sec). Leaf size: 24

Order:=6; 
dsolve(diff(y(x),x$2)+4*x*y(x)=0,y(x),type='series',x=0);
 

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

Solution by Mathematica

Time used: 0.001 (sec). Leaf size: 28

AsymptoticDSolveValue[y''[x]+4*x*y[x]==0,y[x],{x,0,5}]
 

\[ y(x)\to c_2 \left (x-\frac {x^4}{3}\right )+c_1 \left (1-\frac {2 x^3}{3}\right ) \]