73.23.9 problem 33.3 (i)

Internal problem ID [15655]
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 : 33.3 (i)
Date solved : Tuesday, January 28, 2025 at 08:03:43 AM
CAS classification : [_separable]

\begin{align*} \left (-x^{3}+2\right ) y^{\prime }-3 x^{2} y&=0 \end{align*}

Using series method with expansion around

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

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 19

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

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

✓ Solution by Mathematica

Time used: 0.001 (sec). Leaf size: 15

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

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