73.23.20 problem 33.5 (h)

Internal problem ID [15666]
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 (h)
Date solved : Tuesday, January 28, 2025 at 08:03:52 AM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

\begin{align*} \left (x^{2}-6 x \right ) y^{\prime \prime }+4 \left (x -3\right ) y^{\prime }+2 y&=0 \end{align*}

Using series method with expansion around

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

✓ Solution by Maple

Time used: 0.083 (sec). Leaf size: 44

Order:=6; 
dsolve((x^2-6*x)*diff(y(x),x$2)+4*(x-3)*diff(y(x),x)+2*y(x)=0,y(x),type='series',x=0);
 

\[ y = c_{1} \left (1+\frac {1}{6} x +\frac {1}{36} x^{2}+\frac {1}{216} x^{3}+\frac {1}{1296} x^{4}+\frac {1}{7776} x^{5}+\operatorname {O}\left (x^{6}\right )\right )+\frac {c_{2} \left (1+\frac {1}{3} x +\frac {1}{18} x^{2}+\frac {1}{108} x^{3}+\frac {1}{648} x^{4}+\frac {1}{3888} x^{5}+\operatorname {O}\left (x^{6}\right )\right )}{x} \]

✓ Solution by Mathematica

Time used: 0.039 (sec). Leaf size: 64

AsymptoticDSolveValue[(x^2-6*x)*D[y[x],{x,2}]+4*(x-3)*D[y[x],x]+2*y[x]==0,y[x],{x,0,"6"-1}]
 

\[ y(x)\to c_1 \left (\frac {x^3}{1296}+\frac {x^2}{216}+\frac {x}{36}+\frac {1}{x}+\frac {1}{6}\right )+c_2 \left (\frac {x^4}{1296}+\frac {x^3}{216}+\frac {x^2}{36}+\frac {x}{6}+1\right ) \]