Internal problem ID [1430]
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: 14.
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 (9+13 x \right ) y^{\prime }+\left (5 x +7\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: 41
Order:=6; dsolve(x^2*(1+2*x)*diff(y(x),x$2)+x*(9+13*x)*diff(y(x),x)+(7+5*x)*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \frac {c_{1} \left (1+\frac {4}{7} x -\frac {5}{28} x^{2}+\frac {5}{42} x^{3}-\frac {5}{48} x^{4}+\frac {7}{66} x^{5}+\mathrm {O}\left (x^{6}\right )\right )}{x}+\frac {c_{2} \left (-86400-449280 x -617760 x^{2}+\mathrm {O}\left (x^{6}\right )\right )}{x^{7}} \]
✓ Solution by Mathematica
Time used: 0.06 (sec). Leaf size: 54
AsymptoticDSolveValue[x^2*(1+2*x)*y''[x]+x*(9+13*x)*y'[x]+(7+5*x)*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_2 \left (-\frac {5 x^3}{48}+\frac {5 x^2}{42}-\frac {5 x}{28}+\frac {1}{x}+\frac {4}{7}\right )+c_1 \left (\frac {1}{x^7}+\frac {26}{5 x^6}+\frac {143}{20 x^5}\right ) \]