Internal problem ID [11893]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 6, Series solutions of linear differential equations. Section 6.1. Exercises page
232
Problem number: 10.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _homogeneous]]
\[ \boxed {\left (x +3\right ) y^{\prime \prime }+\left (x +2\right ) y^{\prime }+y=0} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 49
Order:=6; dsolve((x+3)*diff(y(x),x$2)+(x+2)*diff(y(x),x)+y(x)=0,y(x),type='series',x=0);
\[ y \left (x \right ) = \left (1-\frac {1}{6} x^{2}+\frac {1}{18} x^{3}-\frac {1}{216} x^{4}-\frac {7}{3240} x^{5}\right ) y \left (0\right )+\left (x -\frac {1}{3} x^{2}+\frac {1}{36} x^{4}-\frac {1}{108} x^{5}\right ) D\left (y \right )\left (0\right )+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 63
AsymptoticDSolveValue[(x+3)*y''[x]+(x+2)*y'[x]+y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_2 \left (-\frac {x^5}{108}+\frac {x^4}{36}-\frac {x^2}{3}+x\right )+c_1 \left (-\frac {7 x^5}{3240}-\frac {x^4}{216}+\frac {x^3}{18}-\frac {x^2}{6}+1\right ) \]