Internal problem ID [2421]
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 11.4. page
758
Problem number: 15.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {2 x^{2} y^{\prime \prime }-x \left (1+2 x \right ) y^{\prime }+2 \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: 0.016 (sec). Leaf size: 41
Order:=6; dsolve(2*x^2*diff(y(x),x$2)-x*(1+2*x)*diff(y(x),x)+2*(4*x-1)*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \frac {c_{2} x^{\frac {5}{2}} \left (1-\frac {4}{7} x +\frac {4}{63} x^{2}+\mathrm {O}\left (x^{6}\right )\right )+c_{1} \left (1+3 x +\frac {21}{2} x^{2}-\frac {35}{2} x^{3}+\frac {35}{8} x^{4}-\frac {7}{40} x^{5}+\mathrm {O}\left (x^{6}\right )\right )}{\sqrt {x}} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 65
AsymptoticDSolveValue[2*x^2*y''[x]-x*(1+2*x)*y'[x]+2*(4*x-1)*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (\frac {4 x^2}{63}-\frac {4 x}{7}+1\right ) x^2+\frac {c_2 \left (-\frac {7 x^5}{40}+\frac {35 x^4}{8}-\frac {35 x^3}{2}+\frac {21 x^2}{2}+3 x+1\right )}{\sqrt {x}} \]