Internal problem ID [1414]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 7 Series Solutions of Linear Second Equations. 7.6 THE METHOD OF FROBENIUS
III. Exercises 7.7. Page 389
Problem number: Example 7.7.2 page 383.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x^{2} \left (1-2 x \right ) y^{\prime \prime }+x \left (8-9 x \right ) y^{\prime }+\left (6-3 x \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: 45
Order:=6; dsolve(x^2*(1-2*x)*diff(y(x),x$2)+x*(8-9*x)*diff(y(x),x)+(6-3*x)*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \frac {c_{1} \left (1-\frac {1}{3} x -\frac {1}{14} x^{2}-\frac {1}{28} x^{3}-\frac {25}{1008} x^{4}-\frac {1}{48} x^{5}+\mathrm {O}\left (x^{6}\right )\right )}{x}+\frac {c_{2} \left (2880-23760 x +71280 x^{2}-83160 x^{3}+62370 x^{5}+\mathrm {O}\left (x^{6}\right )\right )}{x^{6}} \]
✓ Solution by Mathematica
Time used: 0.058 (sec). Leaf size: 61
AsymptoticDSolveValue[x^2*(1-2*x)*y''[x]+x*(8-9*x)*y'[x]+(6-3*x)*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_2 \left (-\frac {25 x^3}{1008}-\frac {x^2}{28}-\frac {x}{14}+\frac {1}{x}-\frac {1}{3}\right )+c_1 \left (\frac {1}{x^6}-\frac {33}{4 x^5}+\frac {99}{4 x^4}-\frac {231}{8 x^3}\right ) \]