Internal problem ID [1424]
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: 8.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x^{2} y^{\prime \prime }+10 y^{\prime } x +\left (14+x \right ) y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 59
Order:=6; dsolve(x^2*diff(y(x),x$2)+10*x*diff(y(x),x)+(14+x)*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \frac {c_{1} \left (1-\frac {1}{6} x +\frac {1}{84} x^{2}-\frac {1}{2016} x^{3}+\frac {1}{72576} x^{4}-\frac {1}{3628800} x^{5}+\mathrm {O}\left (x^{6}\right )\right ) x^{5}+c_{2} \left (\ln \relax (x ) \left (-x^{5}+\mathrm {O}\left (x^{6}\right )\right )+\left (2880+720 x +120 x^{2}+20 x^{3}+5 x^{4}+\mathrm {O}\left (x^{6}\right )\right )\right )}{x^{7}} \]
✓ Solution by Mathematica
Time used: 0.022 (sec). Leaf size: 68
AsymptoticDSolveValue[x^2*y''[x]+10*x*y'[x]+(14+x)*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_2 \left (\frac {x^2}{72576}+\frac {1}{x^2}-\frac {x}{2016}-\frac {1}{6 x}+\frac {1}{84}\right )+c_1 \left (\frac {1}{x^7}+\frac {1}{4 x^6}+\frac {1}{24 x^5}+\frac {1}{144 x^4}+\frac {1}{576 x^3}\right ) \]