Internal problem ID [13931]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 33. Power series solutions I: Basic computational methods. Additional Exercises.
page 641
Problem number: 33.5 (i).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }+\left (x +2\right ) y^{\prime }+2 y=0} \] With the expansion point for the power series method at \(x = -2\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 34
Order:=6; dsolve(diff(y(x),x$2)+(x+2)*diff(y(x),x)+2*y(x)=0,y(x),type='series',x=-2);
\[ y \left (x \right ) = \left (1-\left (x +2\right )^{2}+\frac {\left (x +2\right )^{4}}{3}\right ) y \left (-2\right )+\left (x +2-\frac {\left (x +2\right )^{3}}{2}+\frac {\left (x +2\right )^{5}}{8}\right ) D\left (y \right )\left (-2\right )+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 49
AsymptoticDSolveValue[y''[x]+(x+2)*y'[x]+2*y[x]==0,y[x],{x,-2,5}]
\[ y(x)\to c_1 \left (\frac {1}{3} (x+2)^4-(x+2)^2+1\right )+c_2 \left (\frac {1}{8} (x+2)^5-\frac {1}{2} (x+2)^3+x+2\right ) \]