9.8.7 problem problem 7

Internal problem ID [1072]
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 7
Date solved : Monday, January 27, 2025 at 04:32:54 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (x^{2}+3\right ) y^{\prime \prime }-7 x y^{\prime }+16 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: 39

Order:=6; 
dsolve((x^2+3)*diff(y(x),x$2)-7*x*diff(y(x),x)+16*y(x)=0,y(x),type='series',x=0);
 

\[ y = \left (1-\frac {8}{3} x^{2}+\frac {8}{27} x^{4}\right ) y \left (0\right )+\left (x -\frac {1}{2} x^{3}+\frac {1}{120} x^{5}\right ) y^{\prime }\left (0\right )+O\left (x^{6}\right ) \]

✓ Solution by Mathematica

Time used: 0.001 (sec). Leaf size: 42

AsymptoticDSolveValue[(x^2+3)*D[y[x],{x,2}]-7*x*D[y[x],x]+16*y[x]==0,y[x],{x,0,"6"-1}]
 

\[ y(x)\to c_2 \left (\frac {x^5}{120}-\frac {x^3}{2}+x\right )+c_1 \left (\frac {8 x^4}{27}-\frac {8 x^2}{3}+1\right ) \]