9.7.5 problem problem 5

Internal problem ID [1046]
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
Date solved : Monday, January 27, 2025 at 03:23:05 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=x^{2} y \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(y(x),x)=x^2*y(x),y(x),type='series',x=0);
 

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

✓ Solution by Mathematica

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

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

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