9.8.4 problem problem 4

Internal problem ID [1069]
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 4
Date solved : Monday, January 27, 2025 at 04:32:51 AM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+6 x y^{\prime }+4 y&=0 \end{align*}

Using series method with expansion around

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 39

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

\[ y = \left (3 x^{4}-2 x^{2}+1\right ) y \left (0\right )+\left (x -\frac {5}{3} x^{3}+\frac {7}{3} x^{5}\right ) y^{\prime }\left (0\right )+O\left (x^{6}\right ) \]

✓ Solution by Mathematica

Time used: 0.001 (sec). Leaf size: 60

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

\[ y(x)\to c_1 \left (4 x^5-5 x^4+4 x^3-2 x^2+1\right )+c_2 \left (\frac {77 x^5}{15}-\frac {13 x^4}{2}+\frac {16 x^3}{3}-3 x^2+x\right ) \]