9.8.25 problem problem 25

Internal problem ID [1090]
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 25
Date solved : Monday, January 27, 2025 at 04:33:11 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+x^{2} y^{\prime }+x^{2} 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: 34

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

\[ y = \left (1-\frac {x^{4}}{12}\right ) y \left (0\right )+\left (x -\frac {1}{12} x^{4}-\frac {1}{20} x^{5}\right ) y^{\prime }\left (0\right )+O\left (x^{6}\right ) \]

✓ Solution by Mathematica

Time used: 0.001 (sec). Leaf size: 35

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

\[ y(x)\to c_1 \left (1-\frac {x^4}{12}\right )+c_2 \left (-\frac {x^5}{20}-\frac {x^4}{12}+x\right ) \]