Internal problem ID [6145]
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: 10.
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 x y^{\prime }+5 y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 44
Order:=8; dsolve(diff(y(x),x$2)+2*x*diff(y(x),x)+5*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \left (1-\frac {5}{2} x^{2}+\frac {15}{8} x^{4}-\frac {13}{16} x^{6}\right ) y \relax (0)+\left (x -\frac {7}{6} x^{3}+\frac {77}{120} x^{5}-\frac {11}{48} x^{7}\right ) D\relax (y )\relax (0)+O\left (x^{8}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 56
AsymptoticDSolveValue[y''[x]+2*x*y'[x]+5*y[x]==0,y[x],{x,0,7}]
\[ y(x)\to c_2 \left (-\frac {11 x^7}{48}+\frac {77 x^5}{120}-\frac {7 x^3}{6}+x\right )+c_1 \left (-\frac {13 x^6}{16}+\frac {15 x^4}{8}-\frac {5 x^2}{2}+1\right ) \]