40.16.7 problem 14

Internal problem ID [6798]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 25. Integration in series. Supplemetary problems. Page 205
Problem number : 14
Date solved : Monday, January 27, 2025 at 02:30:43 PM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} y^{\prime \prime }+2 x^{2} y&=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)+2*x^2*y(x)=0,y(x),type='series',x=0);
 

\[ y = \left (1-\frac {x^{4}}{6}\right ) y \left (0\right )+\left (x -\frac {1}{10} x^{5}\right ) y^{\prime }\left (0\right )+O\left (x^{6}\right ) \]

✓ Solution by Mathematica

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

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

\[ y(x)\to c_2 \left (x-\frac {x^5}{10}\right )+c_1 \left (1-\frac {x^4}{6}\right ) \]