9.8.26 problem problem 26

Internal problem ID [1091]
Book : Differential equations and linear algebra, 4th ed., Edwards and Penney
Section : Chapter 11 Power series methods. Section 11.2 Power series solutions. Page 624
Problem number : problem 26
Date solved : Monday, January 27, 2025 at 04:33:12 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (x^{3}+1\right ) y^{\prime \prime }+x^{4} y&=0 \end{align*}

Using series method with expansion around

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

✓ Solution by Maple

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

Order:=6; 
dsolve((1+x^3)*diff(y(x),x$2)+x^4*y(x)=0,y(x),type='series',x=0);
 

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

✓ Solution by Mathematica

Time used: 0.001 (sec). Leaf size: 10

AsymptoticDSolveValue[(1+x^3)*D[y[x],{x,2}]+x^4*y[x]==0,y[x],{x,0,"6"-1}]
 

\[ y(x)\to c_2 x+c_1 \]