Internal problem ID [2449]
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: 16.
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 }+\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: 0.012 (sec). Leaf size: 69
Order:=6; dsolve(4*x^2*diff(y(x),x$2)+(1-4*x)*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \left (\left (\ln \relax (x ) c_{2}+c_{1}\right ) \left (1+x +\frac {1}{4} x^{2}+\frac {1}{36} x^{3}+\frac {1}{576} x^{4}+\frac {1}{14400} x^{5}+\mathrm {O}\left (x^{6}\right )\right )+\left (\left (-2\right ) x -\frac {3}{4} x^{2}-\frac {11}{108} x^{3}-\frac {25}{3456} x^{4}-\frac {137}{432000} x^{5}+\mathrm {O}\left (x^{6}\right )\right ) c_{2}\right ) \sqrt {x} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 124
AsymptoticDSolveValue[4*x^2*y''[x]+(1-4*x)*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \sqrt {x} \left (\frac {x^5}{14400}+\frac {x^4}{576}+\frac {x^3}{36}+\frac {x^2}{4}+x+1\right )+c_2 \left (\sqrt {x} \left (-\frac {137 x^5}{432000}-\frac {25 x^4}{3456}-\frac {11 x^3}{108}-\frac {3 x^2}{4}-2 x\right )+\sqrt {x} \left (\frac {x^5}{14400}+\frac {x^4}{576}+\frac {x^3}{36}+\frac {x^2}{4}+x+1\right ) \log (x)\right ) \]