9.8.21 problem problem 21

Internal problem ID [1086]
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 21
Date solved : Monday, January 27, 2025 at 04:33:07 AM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

\begin{align*} \left (4 x^{2}+16 x +17\right ) y^{\prime \prime }&=8 y \end{align*}

Using series method with expansion around

\begin{align*} -2 \end{align*}

With initial conditions

\begin{align*} y \left (-2\right )&=1\\ y^{\prime }\left (-2\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 14

Order:=6; 
dsolve([(4*x^2+16*x+17)*diff(y(x),x$2)=8*y(x),y(-2) = 1, D(y)(-2) = 0],y(x),type='series',x=-2);
 

\[ y = 4 x^{2}+16 x +17 \]

✓ Solution by Mathematica

Time used: 0.001 (sec). Leaf size: 12

AsymptoticDSolveValue[{(4*x^2+16*x+17)*D[y[x],{x,2}]==8*y[x],{y[-2]==1,Derivative[1][y][-2]==0}},y[x],{x,-2,"6"-1}]
 

\[ y(x)\to 4 (x+2)^2+1 \]