Internal problem ID [1344]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 7 Series Solutions of Linear Second Equations. 7.5 THE METHOD OF FROBENIUS
I. Exercises 7.5. Page 358
Problem number: 64.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {9 x^{2} \left (x +5\right ) y^{\prime \prime }+9 x \left (5+9 x \right ) y^{\prime }-\left (5-8 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: 47
Order:=6; dsolve(9*x^2*(5+x)*diff(y(x),x$2)+9*x*(5+9*x)*diff(y(x),x)-(5-8*x)*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \frac {c_{2} x^{\frac {2}{3}} \left (1-\frac {11}{25} x +\frac {11}{50} x^{2}-\frac {1}{10} x^{3}+\frac {29}{700} x^{4}-\frac {4727}{297500} x^{5}+\mathrm {O}\left (x^{6}\right )\right )+c_{1} \left (1+x -\frac {1}{2} x^{2}+\frac {17}{70} x^{3}-\frac {187}{1750} x^{4}+\frac {24497}{568750} x^{5}+\mathrm {O}\left (x^{6}\right )\right )}{x^{\frac {1}{3}}} \]
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 86
AsymptoticDSolveValue[9*x^2*(5+x)*y''[x]+9*x*(5+9*x)*y'[x]-(5-8*x)*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \sqrt [3]{x} \left (-\frac {4727 x^5}{297500}+\frac {29 x^4}{700}-\frac {x^3}{10}+\frac {11 x^2}{50}-\frac {11 x}{25}+1\right )+\frac {c_2 \left (\frac {24497 x^5}{568750}-\frac {187 x^4}{1750}+\frac {17 x^3}{70}-\frac {x^2}{2}+x+1\right )}{\sqrt [3]{x}} \]