Internal problem ID [1433]
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: 17.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (1-10 x \right ) y^{\prime }-\left (9-10 x \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: 45
Order:=6; dsolve(x^2*(1+x)*diff(y(x),x$2)+x*(1-10*x)*diff(y(x),x)-(9-10*x)*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = c_{1} x^{3} \left (1+2 x +\frac {9}{4} x^{2}+\frac {5}{3} x^{3}+\frac {5}{6} x^{4}+\frac {3}{11} x^{5}+\mathrm {O}\left (x^{6}\right )\right )+\frac {c_{2} \left (-86400-898560 x -4043520 x^{2}-9884160 x^{3}-12355200 x^{4}+\mathrm {O}\left (x^{6}\right )\right )}{x^{3}} \]
✓ Solution by Mathematica
Time used: 0.043 (sec). Leaf size: 64
AsymptoticDSolveValue[x^2*(1+x)*y''[x]+x*(1-10*x)*y'[x]-(9-10*x)*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (\frac {1}{x^3}+\frac {52}{5 x^2}+143 x+\frac {234}{5 x}+\frac {572}{5}\right )+c_2 \left (\frac {5 x^7}{6}+\frac {5 x^6}{3}+\frac {9 x^5}{4}+2 x^4+x^3\right ) \]