Internal problem ID [1304]
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: 10.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {10 x^{2} \left (2 x^{2}+x +1\right ) y^{\prime \prime }+x \left (66 x^{2}+13 x +13\right ) y^{\prime }-\left (10 x^{2}+4 x +1\right ) y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 47
Order:=6; dsolve(10*x^2*(1+x+2*x^2)*diff(y(x),x$2)+x*(13+13*x+66*x^2)*diff(y(x),x)-(1+4*x+10*x^2)*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \frac {c_{2} x^{\frac {7}{10}} \left (1+\frac {3}{17} x -\frac {7}{153} x^{2}-\frac {547}{5661} x^{3}+\frac {26942}{266067} x^{4}+\frac {200432}{3991005} x^{5}+\mathrm {O}\left (x^{6}\right )\right )+c_{1} \left (1+x +\frac {14}{13} x^{2}-\frac {556}{897} x^{3}-\frac {5314}{9867} x^{4}+\frac {2092186}{2121405} x^{5}+\mathrm {O}\left (x^{6}\right )\right )}{\sqrt {x}} \]
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 86
AsymptoticDSolveValue[10*x^2*(1+x+2*x^2)*y''[x]+x*(13+13*x+66*x^2)*y'[x]-(1+4*x+10*x^2)*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \sqrt [5]{x} \left (\frac {200432 x^5}{3991005}+\frac {26942 x^4}{266067}-\frac {547 x^3}{5661}-\frac {7 x^2}{153}+\frac {3 x}{17}+1\right )+\frac {c_2 \left (\frac {2092186 x^5}{2121405}-\frac {5314 x^4}{9867}-\frac {556 x^3}{897}+\frac {14 x^2}{13}+x+1\right )}{\sqrt {x}} \]