Internal problem ID [2426]
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: 20.
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 y^{\prime } x^{2}+\left (1+2 x \right ) y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.013 (sec). Leaf size: 49
Order:=6; dsolve(4*x^2*diff(y(x),x$2)-4*x^2*diff(y(x),x)+(1+2*x)*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \left (\left (x +\frac {1}{4} x^{2}+\frac {1}{18} x^{3}+\frac {1}{96} x^{4}+\frac {1}{600} x^{5}+\mathrm {O}\left (x^{6}\right )\right ) c_{2}+\left (1+\mathrm {O}\left (x^{6}\right )\right ) \left (\ln \relax (x ) c_{2}+c_{1}\right )\right ) \sqrt {x} \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 60
AsymptoticDSolveValue[4*x^2*y''[x]-4*x^2*y'[x]+(1+2*x)*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_2 \left (\sqrt {x} \left (\frac {x^5}{600}+\frac {x^4}{96}+\frac {x^3}{18}+\frac {x^2}{4}+x\right )+\sqrt {x} \log (x)\right )+c_1 \sqrt {x} \]