20.2 problem 2

Internal problem ID [2466]

Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section: Chapter 11, Series Solutions to Linear Differential Equations. Additional problems. Section 11.7. page 788
Problem number: 2.
ODE order: 2.
ODE degree: 1.

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

Solve \begin {gather*} \boxed {y^{\prime \prime }-y x^{2}=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).

Solution by Maple

Time used: 0.003 (sec). Leaf size: 24

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

\[ y \relax (x ) = \left (1+\frac {x^{4}}{12}\right ) y \relax (0)+\left (x +\frac {1}{20} x^{5}\right ) D\relax (y )\relax (0)+O\left (x^{6}\right ) \]

Solution by Mathematica

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

AsymptoticDSolveValue[y''[x]-x^2*y[x]==0,y[x],{x,0,5}]
 

\[ y(x)\to c_2 \left (\frac {x^5}{20}+x\right )+c_1 \left (\frac {x^4}{12}+1\right ) \]