9.8.22 problem problem 22

Internal problem ID [1087]
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 22
Date solved : Monday, January 27, 2025 at 04:33:08 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (x^{2}+6 x \right ) y^{\prime \prime }+\left (3 x +9\right ) y^{\prime }-3 y&=0 \end{align*}

Using series method with expansion around

\begin{align*} -3 \end{align*}

With initial conditions

\begin{align*} y \left (-3\right )&=1\\ y^{\prime }\left (-3\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 14

Order:=6; 
dsolve([(x^2+6*x)*diff(y(x),x$2)+(3*x+9)*diff(y(x),x)-3*y(x)=0,y(-3) = 1, D(y)(-3) = 0],y(x),type='series',x=-3);
 

\[ y = 1-\frac {1}{6} \left (x +3\right )^{2}-\frac {5}{648} \left (x +3\right )^{4}+\operatorname {O}\left (\left (x +3\right )^{6}\right ) \]

✓ Solution by Mathematica

Time used: 0.001 (sec). Leaf size: 23

AsymptoticDSolveValue[{(x^2+6*x)*D[y[x],{x,2}]+(3*x+9)*D[y[x],x]-3*y[x]==0,{y[-3]==1,Derivative[1][y][-3 ]==0}},y[x],{x,-3,"6"-1}]
 

\[ y(x)\to -\frac {5}{648} (x+3)^4-\frac {1}{6} (x+3)^2+1 \]