7.14.26 problem 26

Internal problem ID [451]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 3. Power series methods. Section 3.2 (Series solution near ordinary points). Problems at page 216
Problem number : 26
Date solved : Monday, January 27, 2025 at 02:53:45 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: 0.003 (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}]
 

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