73.25.4 problem 35.2 (d)

Internal problem ID [15712]
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)
Date solved : Tuesday, January 28, 2025 at 08:05:47 AM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} \left (x +2\right )^{2} y^{\prime \prime }+\left (x +2\right ) y^{\prime }&=0 \end{align*}

Using series method with expansion around

\begin{align*} 0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 36

Order:=6; 
dsolve((x+2)^2*diff(y(x),x$2)+(x+2)*diff(y(x),x)=0,y(x),type='series',x=0);
 

\[ y = y \left (0\right )+\left (x -\frac {1}{4} x^{2}+\frac {1}{12} x^{3}-\frac {1}{32} x^{4}+\frac {1}{80} x^{5}\right ) y^{\prime }\left (0\right )+O\left (x^{6}\right ) \]

✓ Solution by Mathematica

Time used: 0.001 (sec). Leaf size: 39

AsymptoticDSolveValue[(x+2)^2*D[y[x],{x,2}]+(x+2)*D[y[x],x]==0,y[x],{x,0,"6"-1}]
 

\[ y(x)\to c_2 \left (\frac {x^5}{80}-\frac {x^4}{32}+\frac {x^3}{12}-\frac {x^2}{4}+x\right )+c_1 \]