Internal problem ID [1222]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 7 Series Solutions of Linear Second Equations. 7.2 SERIES SOLUTIONS NEAR AN
ORDINARY POINT I. Exercises 7.2. Page 329
Problem number: 20.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _homogeneous]]
Solve \begin {gather*} \boxed {\left (3 x^{2}+6 x +5\right ) y^{\prime \prime }+9 \left (x +1\right ) y^{\prime }+3 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: 34
Order:=6; dsolve((5+6*x+3*x^2)*diff(y(x),x$2)+9*(x+1)*diff(y(x),x)+3*y(x)=0,y(x),type='series',x=-1);
\[ y \relax (x ) = \left (1-\frac {3 \left (x +1\right )^{2}}{4}+\frac {27 \left (x +1\right )^{4}}{32}\right ) y \left (-1\right )+\left (x +1-\left (x +1\right )^{3}+\frac {6 \left (x +1\right )^{5}}{5}\right ) D\relax (y )\left (-1\right )+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 70
AsymptoticDSolveValue[(5+6*x+2*x^2)*y''[x]+9*(x+1)*y'[x]+3*y[x]==0,y[x],{x,-1,5}]
\[ y(x)\to c_1 \left (-\frac {93}{20} (x+1)^5+\frac {17}{8} (x+1)^4+(x+1)^3-\frac {3}{2} (x+1)^2+1\right )+c_2 \left (\frac {9}{5} (x+1)^5+2 (x+1)^4-2 (x+1)^3+x+1\right ) \]