73.23.16 problem 33.5 (d)

Internal problem ID [15662]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 33. Power series solutions I: Basic computational methods. Additional Exercises. page 641
Problem number : 33.5 (d)
Date solved : Tuesday, January 28, 2025 at 08:03:49 AM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} y^{\prime \prime }-3 x^{2} y&=0 \end{align*}

Using series method with expansion around

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 29

Order:=6; 
dsolve(diff(y(x),x$2)-3*x^2*y(x)=0,y(x),type='series',x=0);
 

\[ y = \left (1+\frac {x^{4}}{4}\right ) y \left (0\right )+\left (x +\frac {3}{20} x^{5}\right ) y^{\prime }\left (0\right )+O\left (x^{6}\right ) \]

✓ Solution by Mathematica

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

AsymptoticDSolveValue[D[y[x],{x,2}]-3*x^2*y[x]==0,y[x],{x,0,"6"-1}]
 

\[ y(x)\to c_2 \left (\frac {3 x^5}{20}+x\right )+c_1 \left (\frac {x^4}{4}+1\right ) \]