Internal problem ID [1432]
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: 16.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {3 x^{2} \left (x +3\right ) y^{\prime \prime }-x \left (15+x \right ) y^{\prime }-20 y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.012 (sec). Leaf size: 45
Order:=6; dsolve(3*x^2*(3+x)*diff(y(x),x$2)-x*(15+x)*diff(y(x),x)-20*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \frac {c_{1} x^{4} \left (1-\frac {4}{9} x +\frac {13}{81} x^{2}-\frac {832}{15309} x^{3}+\frac {2470}{137781} x^{4}-\frac {21736}{3720087} x^{5}+\mathrm {O}\left (x^{6}\right )\right )+c_{2} \left (-144-\frac {64}{3} x +\frac {16}{27} x^{2}-\frac {112}{6561} x^{4}+\frac {448}{59049} x^{5}+\mathrm {O}\left (x^{6}\right )\right )}{x^{\frac {2}{3}}} \]
✓ Solution by Mathematica
Time used: 0.041 (sec). Leaf size: 85
AsymptoticDSolveValue[3*x^2*(3+x)*y''[x]-x*(15+x)*y'[x]-20*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (\frac {7 x^{10/3}}{59049}-\frac {x^{4/3}}{243}+\frac {1}{x^{2/3}}+\frac {4 \sqrt [3]{x}}{27}\right )+c_2 \left (\frac {2470 x^{22/3}}{137781}-\frac {832 x^{19/3}}{15309}+\frac {13 x^{16/3}}{81}-\frac {4 x^{13/3}}{9}+x^{10/3}\right ) \]