Internal problem ID [4505]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {z^{\prime }-x^{2} z=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.001 (sec). Leaf size: 16
Order:=6; dsolve(diff(z(x),x)-x^2*z(x)=0,z(x),type='series',x=0);
\[ z \relax (x ) = \left (1+\frac {x^{3}}{3}\right ) z \relax (0)+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 15
AsymptoticDSolveValue[z'[x]-x^2*z[x]==0,z[x],{x,0,5}]
\[ z(x)\to c_1 \left (\frac {x^3}{3}+1\right ) \]