Internal problem ID [1438]
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: 22.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, _with_symmetry_[0,F(x)]]]
Solve \begin {gather*} \boxed {x^{2} \left (1+2 x \right ) y^{\prime \prime }-x \left (9+8 x \right ) y^{\prime }-12 y x=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 44
Order:=6; dsolve(x^2*(1+2*x)*diff(y(x),x$2)-x*(9+8*x)*diff(y(x),x)-12*x*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = c_{1} x^{10} \left (1-8 x +40 x^{2}-160 x^{3}+560 x^{4}-1792 x^{5}+\mathrm {O}\left (x^{6}\right )\right )+c_{2} \left (-1316818944000+1755758592000 x -2194698240000 x^{2}+2508226560000 x^{3}-2508226560000 x^{4}+2006581248000 x^{5}+\mathrm {O}\left (x^{6}\right )\right ) \]
✓ Solution by Mathematica
Time used: 0.047 (sec). Leaf size: 62
AsymptoticDSolveValue[x^2*(1+2*x)*y''[x]-x*(9+8*x)*y'[x]-12*x*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (\frac {40 x^4}{21}-\frac {40 x^3}{21}+\frac {5 x^2}{3}-\frac {4 x}{3}+1\right )+c_2 \left (560 x^{14}-160 x^{13}+40 x^{12}-8 x^{11}+x^{10}\right ) \]