Internal problem ID [4510]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\left (2 x -3\right ) y^{\prime \prime }-x y^{\prime }+y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 34
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);
\[ y \relax (x ) = \left (1+\frac {1}{6} x^{2}+\frac {1}{27} x^{3}+\frac {5}{648} x^{4}+\frac {1}{540} x^{5}\right ) y \relax (0)+D\relax (y )\relax (0) x +O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.002 (sec). Leaf size: 41
AsymptoticDSolveValue[(2*x-3)*y''[x]-x*y'[x]+y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (\frac {x^5}{540}+\frac {5 x^4}{648}+\frac {x^3}{27}+\frac {x^2}{6}+1\right )+c_2 x \]