Internal problem ID [2456]
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: 23.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {4 x^{2} y^{\prime \prime }+4 x \left (1-x \right ) y^{\prime }+\left (2 x -9\right ) y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 47
Order:=6; dsolve(4*x^2*diff(y(x),x$2)+4*x*(1-x)*diff(y(x),x)+(2*x-9)*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \frac {c_{1} x^{3} \left (1+\frac {1}{4} x +\frac {1}{20} x^{2}+\frac {1}{120} x^{3}+\frac {1}{840} x^{4}+\frac {1}{6720} x^{5}+\mathrm {O}\left (x^{6}\right )\right )+c_{2} \left (12+12 x +6 x^{2}+2 x^{3}+\frac {1}{2} x^{4}+\frac {1}{10} x^{5}+\mathrm {O}\left (x^{6}\right )\right )}{x^{\frac {3}{2}}} \]
✓ Solution by Mathematica
Time used: 0.029 (sec). Leaf size: 90
AsymptoticDSolveValue[4*x^2*y''[x]+4*x*(1-x)*y'[x]+(2*x-9)*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (\frac {x^{5/2}}{24}+\frac {x^{3/2}}{6}+\frac {1}{x^{3/2}}+\frac {\sqrt {x}}{2}+\frac {1}{\sqrt {x}}\right )+c_2 \left (\frac {x^{11/2}}{840}+\frac {x^{9/2}}{120}+\frac {x^{7/2}}{20}+\frac {x^{5/2}}{4}+x^{3/2}\right ) \]