66.2.15 problem Problem 15

Internal problem ID [13914]
Book : Differential equations and the calculus of variations by L. ElSGOLTS. MIR PUBLISHERS, MOSCOW, Third printing 1977.
Section : Chapter 2, DIFFERENTIAL EQUATIONS OF THE SECOND ORDER AND HIGHER. Problems page 172
Problem number : Problem 15
Date solved : Tuesday, January 28, 2025 at 06:08:24 AM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} y^{\prime \prime }+4 y x&=0 \end{align*}

Using series method with expansion around

\begin{align*} 0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 29

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

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

✓ Solution by Mathematica

Time used: 0.010 (sec). Leaf size: 28

AsymptoticDSolveValue[D[y[x],{x,2}]+4*x*y[x]==0,y[x],{x,0,"6"-1}]
 

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