Internal problem ID [2458]
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: 25.
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 (1-x \right ) y^{\prime }+\left (1-x \right ) 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: 43
Order:=6; dsolve(x^2*diff(y(x),x$2)-x*(1-x)*diff(y(x),x)+(1-x)*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \left (\left (1+\mathrm {O}\left (x^{6}\right )\right ) \left (c_{2} \ln \relax (x )+c_{1}\right )+\left (-x +\frac {1}{4} x^{2}-\frac {1}{18} x^{3}+\frac {1}{96} x^{4}-\frac {1}{600} x^{5}+\mathrm {O}\left (x^{6}\right )\right ) c_{2}\right ) x \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 50
AsymptoticDSolveValue[x^2*y''[x]-x*(1-x)*y'[x]+(1-x)*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_2 \left (x \left (-\frac {x^5}{600}+\frac {x^4}{96}-\frac {x^3}{18}+\frac {x^2}{4}-x\right )+x \log (x)\right )+c_1 x \]