Internal problem ID [1436]
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: 20.
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 (6+11 x \right ) y^{\prime }+\left (6+32 x \right ) 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: 37
Order:=6; dsolve(x^2*(1+x)*diff(y(x),x$2)-x*(6+11*x)*diff(y(x),x)+(6+32*x)*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = c_{1} x^{6} \left (1+\frac {2}{3} x +\frac {1}{7} x^{2}+\mathrm {O}\left (x^{6}\right )\right )+c_{2} x \left (2880+15120 x +30240 x^{2}+25200 x^{3}-15120 x^{5}+\mathrm {O}\left (x^{6}\right )\right ) \]
✓ Solution by Mathematica
Time used: 0.048 (sec). Leaf size: 51
AsymptoticDSolveValue[x^2*(1+x)*y''[x]-x*(6+11*x)*y'[x]+(6+32*x)*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_2 \left (\frac {x^8}{7}+\frac {2 x^7}{3}+x^6\right )+c_1 \left (\frac {35 x^4}{4}+\frac {21 x^3}{2}+\frac {21 x^2}{4}+x\right ) \]