36.5.12 problem 13

Internal problem ID [6356]
Book : Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson 2018.
Section : Chapter 8, Series solutions of differential equations. Section 8.3. page 443
Problem number : 13
Date solved : Monday, January 27, 2025 at 01:58:04 PM
CAS classification : [_separable]

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

Using series method with expansion around

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 19

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

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

✓ Solution by Mathematica

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

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

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