36.5.2 problem 2

Internal problem ID [6346]
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 : 2
Date solved : Monday, January 27, 2025 at 01:57:47 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

Using series method with expansion around

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

✗ Solution by Maple

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

\[ \text {No solution found} \]

✓ Solution by Mathematica

Time used: 0.032 (sec). Leaf size: 85

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

\[ y(x)\to c_2 e^{3/x} \left (\frac {3001 x^5}{1620}+\frac {613 x^4}{648}+\frac {16 x^3}{27}+\frac {x^2}{2}+\frac {2 x}{3}+1\right ) x^2+c_1 \left (-\frac {23 x^5}{810}+\frac {7 x^4}{216}-\frac {x^3}{27}+\frac {x^2}{6}+1\right ) \]