Internal problem ID [2417]
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: 11.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {6 x^{2} y^{\prime \prime }+x \left (1+18 x \right ) y^{\prime }+\left (12 x +1\right ) y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 47
Order:=6; dsolve(6*x^2*diff(y(x),x$2)+x*(1+18*x)*diff(y(x),x)+(1+12*x)*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = c_{1} x^{\frac {1}{3}} \left (1-\frac {18}{5} x +\frac {324}{55} x^{2}-\frac {5832}{935} x^{3}+\frac {104976}{21505} x^{4}-\frac {1889568}{623645} x^{5}+\mathrm {O}\left (x^{6}\right )\right )+c_{2} \sqrt {x}\, \left (1-3 x +\frac {9}{2} x^{2}-\frac {9}{2} x^{3}+\frac {27}{8} x^{4}-\frac {81}{40} x^{5}+\mathrm {O}\left (x^{6}\right )\right ) \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 88
AsymptoticDSolveValue[6*x^2*y''[x]+x*(1+18*x)*y'[x]+(1+12*x)*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \sqrt {x} \left (-\frac {81 x^5}{40}+\frac {27 x^4}{8}-\frac {9 x^3}{2}+\frac {9 x^2}{2}-3 x+1\right )+c_2 \sqrt [3]{x} \left (-\frac {1889568 x^5}{623645}+\frac {104976 x^4}{21505}-\frac {5832 x^3}{935}+\frac {324 x^2}{55}-\frac {18 x}{5}+1\right ) \]