Internal problem ID [4495]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x^{2} y^{\prime \prime }+3 y^{\prime }-y x=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✗ 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: 0.041 (sec). Leaf size: 85
AsymptoticDSolveValue[x^2*y''[x]+3*y'[x]-x*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_2 e^{3/x} \left (\frac {3001 x^5}{1620}+\frac {613 x^4}{648}+\frac {16 x^3}{27}+\frac {x^2}{2}+\frac {2 x}{3}+1\right ) x^2+c_1 \left (-\frac {23 x^5}{810}+\frac {7 x^4}{216}-\frac {x^3}{27}+\frac {x^2}{6}+1\right ) \]