Internal problem ID [1195]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 7 Series Solutions of Linear Second Equations. 7.1 Exercises. Page 318
Problem number: 16.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x y^{\prime \prime }+\left (2 x +4\right ) y^{\prime }+\left (2+x \right ) y=0} \end {gather*} With the expansion point for the power series method at \(x = -1\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 52
Order:=6; dsolve(x*diff(y(x),x$2)+(4+2*x)*diff(y(x),x)+(2+x)*y(x)=0,y(x),type='series',x=-1);
\[ y \relax (x ) = \left (1+\frac {\left (x +1\right )^{2}}{2}+\frac {2 \left (x +1\right )^{3}}{3}+\frac {7 \left (x +1\right )^{4}}{8}+\frac {17 \left (x +1\right )^{5}}{15}\right ) y \left (-1\right )+\left (x +1+\left (x +1\right )^{2}+\frac {3 \left (x +1\right )^{3}}{2}+2 \left (x +1\right )^{4}+\frac {103 \left (x +1\right )^{5}}{40}\right ) D\relax (y )\left (-1\right )+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 81
AsymptoticDSolveValue[(x)*y''[x]+(4+2*x)*y'[x]+(2+x)*y[x]==0,y[x],{x,-1,5}]
\[ y(x)\to c_1 \left (\frac {17}{15} (x+1)^5+\frac {7}{8} (x+1)^4+\frac {2}{3} (x+1)^3+\frac {1}{2} (x+1)^2+1\right )+c_2 \left (\frac {103}{40} (x+1)^5+2 (x+1)^4+\frac {3}{2} (x+1)^3+(x+1)^2+x+1\right ) \]