Internal problem ID [13976]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 35. Modified Power series solutions and basic method of Frobenius. Additional
Exercises. page 715
Problem number: 35.2 (d).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
\[ \boxed {\left (x +2\right )^{2} y^{\prime \prime }+\left (x +2\right ) y^{\prime }=0} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 34
Order:=6; dsolve((x+2)^2*diff(y(x),x$2)+(x+2)*diff(y(x),x)=0,y(x),type='series',x=0);
\[ y \left (x \right ) = y \left (0\right )+\left (x -\frac {1}{4} x^{2}+\frac {1}{12} x^{3}-\frac {1}{32} x^{4}+\frac {1}{80} x^{5}\right ) D\left (y \right )\left (0\right )+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 39
AsymptoticDSolveValue[(x+2)^2*y''[x]+(x+2)*y'[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_2 \left (\frac {x^5}{80}-\frac {x^4}{32}+\frac {x^3}{12}-\frac {x^2}{4}+x\right )+c_1 \]