Internal problem ID [2459]
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: 26.
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+2 x \right ) y^{\prime }+\left (4 x -1\right ) y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.026 (sec). Leaf size: 47
Order:=6; dsolve(4*x^2*diff(y(x),x$2)+4*x*(1+2*x)*diff(y(x),x)+(4*x-1)*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \frac {c_{1} x \left (1-x +\frac {2}{3} x^{2}-\frac {1}{3} x^{3}+\frac {2}{15} x^{4}-\frac {2}{45} x^{5}+\mathrm {O}\left (x^{6}\right )\right )+c_{2} \left (1-2 x +2 x^{2}-\frac {4}{3} x^{3}+\frac {2}{3} x^{4}-\frac {4}{15} x^{5}+\mathrm {O}\left (x^{6}\right )\right )}{\sqrt {x}} \]
✓ Solution by Mathematica
Time used: 0.024 (sec). Leaf size: 88
AsymptoticDSolveValue[4*x^2*y''[x]+4*x*(1+2*x)*y'[x]+(4*x-1)*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (\frac {2 x^{7/2}}{3}-\frac {4 x^{5/2}}{3}+2 x^{3/2}-2 \sqrt {x}+\frac {1}{\sqrt {x}}\right )+c_2 \left (\frac {2 x^{9/2}}{15}-\frac {x^{7/2}}{3}+\frac {2 x^{5/2}}{3}-x^{3/2}+\sqrt {x}\right ) \]