Internal problem ID [437]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\left (x^{2}+6 x \right ) y^{\prime \prime }+\left (3 x +9\right ) y^{\prime }-3 y=0} \end {gather*} With initial conditions \begin {align*} [y \left (-3\right ) = 1, y^{\prime }\left (-3\right ) = 0] \end {align*}
With the expansion point for the power series method at \(x = -3\).
✓ Solution by Maple
Time used: 0.0 (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);
\[ y \relax (x ) = 1-\frac {1}{6} \left (x +3\right )^{2}-\frac {5}{648} \left (x +3\right )^{4}+\mathrm {O}\left (\left (x +3\right )^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 23
AsymptoticDSolveValue[{(x^2+6*x)*y''[x]+(3*x+9)*y'[x]-3*y[x]==0,{y[-3]==1,y'[-3]==0}},y[x],{x,-3,5}]
\[ y(x)\to -\frac {5}{648} (x+3)^4-\frac {1}{6} (x+3)^2+1 \]