Internal problem ID [436]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _homogeneous]]
Solve \begin {gather*} \boxed {\left (4 x^{2}+16 x +17\right ) y^{\prime \prime }-8 y=0} \end {gather*} With initial conditions \begin {align*} [y \left (-2\right ) = 1, y^{\prime }\left (-2\right ) = 0] \end {align*}
With the expansion point for the power series method at \(x = -2\).
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 13
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);
\[ y \relax (x ) = 4 x^{2}+16 x +17 \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 12
AsymptoticDSolveValue[{(4*x^2+16*x+17)*y''[x]==8*y[x],{y[-2]==1,y'[-2]==0}},y[x],{x,-2,5}]
\[ y(x)\to 4 (x+2)^2+1 \]