36.5.17 problem 18

Internal problem ID [6361]
Book : Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson 2018.
Section : Chapter 8, Series solutions of differential equations. Section 8.3. page 443
Problem number : 18
Date solved : Monday, January 27, 2025 at 01:58:09 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

Using series method with expansion around

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 38

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

\[ y = \left (1+\frac {1}{6} x^{2}+\frac {1}{27} x^{3}+\frac {5}{648} x^{4}+\frac {1}{540} x^{5}\right ) y \left (0\right )+y^{\prime }\left (0\right ) x +O\left (x^{6}\right ) \]

✓ Solution by Mathematica

Time used: 0.002 (sec). Leaf size: 41

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

\[ y(x)\to c_1 \left (\frac {x^5}{540}+\frac {5 x^4}{648}+\frac {x^3}{27}+\frac {x^2}{6}+1\right )+c_2 x \]