Internal problem ID [2429]
Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition,
2015
Section: Chapter 11, Series Solutions to Linear Differential Equations. Exercises for 11.5. page
771
Problem number: Example 11.5.4 page 765.
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 }+x \left (-x +3\right ) y^{\prime }+y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 53
Order:=6; dsolve(x^2*diff(y(x),x$2)+x*(3-x)*diff(y(x),x)+y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \frac {\left (3 x -\frac {1}{4} x^{2}-\frac {1}{36} x^{3}-\frac {1}{288} x^{4}-\frac {1}{2400} x^{5}+\mathrm {O}\left (x^{6}\right )\right ) c_{2}+\left (1-x +\mathrm {O}\left (x^{6}\right )\right ) \left (c_{2} \ln \relax (x )+c_{1}\right )}{x} \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 66
AsymptoticDSolveValue[x^2*y''[x]+x*(3-x)*y'[x]+y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_2 \left (\frac {-\frac {x^5}{2400}-\frac {x^4}{288}-\frac {x^3}{36}-\frac {x^2}{4}+3 x}{x}+\frac {(1-x) \log (x)}{x}\right )+\frac {c_1 (1-x)}{x} \]