Internal problem ID [6161]
Book: Elementary differential equations. Rainville, Bedient, Bedient. Prentice Hall. NJ. 8th edition.
1997.
Section: CHAPTER 17. Power series solutions. 17.5. Solutions Near an Ordinary Point. Exercises page
355
Problem number: 26.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-2 \left (x +3\right ) y^{\prime }-3 y=0} \end {gather*} With the expansion point for the power series method at \(x = -3\).
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 44
Order:=8; dsolve(diff(y(x),x$2)-2*(x+3)*diff(y(x),x)-3*y(x)=0,y(x),type='series',x=-3);
\[ y \relax (x ) = \left (1+\frac {3 \left (3+x \right )^{2}}{2}+\frac {7 \left (3+x \right )^{4}}{8}+\frac {77 \left (3+x \right )^{6}}{240}\right ) y \left (-3\right )+\left (3+x +\frac {5 \left (3+x \right )^{3}}{6}+\frac {3 \left (3+x \right )^{5}}{8}+\frac {13 \left (3+x \right )^{7}}{112}\right ) D\relax (y )\left (-3\right )+O\left (x^{8}\right ) \]
✓ Solution by Mathematica
Time used: 0.002 (sec). Leaf size: 69
AsymptoticDSolveValue[y''[x]-2*(x+3)*y'[x]-3*y[x]==0,y[x],{x,-3,7}]
\[ y(x)\to c_1 \left (\frac {77}{240} (x+3)^6+\frac {7}{8} (x+3)^4+\frac {3}{2} (x+3)^2+1\right )+c_2 \left (\frac {13}{112} (x+3)^7+\frac {3}{8} (x+3)^5+\frac {5}{6} (x+3)^3+x+3\right ) \]