20.26.3 problem Example 11.5.5 page 768

Internal problem ID [4028]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 11, Series Solutions to Linear Differential Equations. Exercises for 11.5. page 771
Problem number : Example 11.5.5 page 768
Date solved : Monday, January 27, 2025 at 08:06:32 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }-\left (4+x \right ) y&=0 \end{align*}

Using series method with expansion around

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

✓ Solution by Maple

Time used: 0.016 (sec). Leaf size: 58

Order:=6; 
dsolve(x^2*diff(y(x),x$2)+x*diff(y(x),x)-(4+x)*y(x)=0,y(x),type='series',x=0);
 

\[ y \left (x \right ) = \frac {c_{1} x^{4} \left (1+\frac {1}{5} x +\frac {1}{60} x^{2}+\frac {1}{1260} x^{3}+\frac {1}{40320} x^{4}+\frac {1}{1814400} x^{5}+\operatorname {O}\left (x^{6}\right )\right )+c_{2} \left (\ln \left (x \right ) \left (x^{4}+\frac {1}{5} x^{5}+\operatorname {O}\left (x^{6}\right )\right )+\left (-144+48 x -12 x^{2}+4 x^{3}-\frac {6}{25} x^{5}+\operatorname {O}\left (x^{6}\right )\right )\right )}{x^{2}} \]

✓ Solution by Mathematica

Time used: 0.022 (sec). Leaf size: 77

AsymptoticDSolveValue[x^2*D[y[x],{x,2}]+x*D[y[x],x]-(4+x)*y[x]==0,y[x],{x,0,"6"-1}]
 

\[ y(x)\to c_1 \left (\frac {x^4-16 x^3+48 x^2-192 x+576}{576 x^2}-\frac {1}{144} x^2 \log (x)\right )+c_2 \left (\frac {x^6}{40320}+\frac {x^5}{1260}+\frac {x^4}{60}+\frac {x^3}{5}+x^2\right ) \]