Internal problem ID [396]
Book: Differential equations and linear algebra, 4th ed., Edwards and Penney
Section: Chapter 11 Power series methods. Section 11.1 Introduction and Review of power series. Page
615
Problem number: problem 5.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-x^{2} y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 16
Order:=6; dsolve(diff(y(x),x)=x^2*y(x),y(x),type='series',x=0);
\[ y \relax (x ) = \left (1+\frac {x^{3}}{3}\right ) y \relax (0)+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 15
AsymptoticDSolveValue[y'[x]==x^2*y[x],y[x],{x,0,5}]
\[ y(x)\to c_1 \left (\frac {x^3}{3}+1\right ) \]