Internal problem ID [1435]
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: 19.
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 }-2 x \left (3+14 x \right ) y^{\prime }+\left (6+100 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: 43
Order:=6; dsolve(x^2*(1+2*x)*diff(y(x),x$2)-2*x*(3+14*x)*diff(y(x),x)+(6+100*x)*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = c_{1} x^{6} \left (1+\frac {4}{3} x +\frac {8}{7} x^{2}+\frac {4}{7} x^{3}+\frac {8}{63} x^{4}+\mathrm {O}\left (x^{6}\right )\right )+c_{2} x \left (2880+51840 x +414720 x^{2}+1935360 x^{3}+5806080 x^{4}+11612160 x^{5}+\mathrm {O}\left (x^{6}\right )\right ) \]
✓ Solution by Mathematica
Time used: 0.048 (sec). Leaf size: 64
AsymptoticDSolveValue[x^2*(1+2*x)*y''[x]-2*x*(3+14*x)*y'[x]+(6+100*x)*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (2016 x^5+672 x^4+144 x^3+18 x^2+x\right )+c_2 \left (\frac {8 x^{10}}{63}+\frac {4 x^9}{7}+\frac {8 x^8}{7}+\frac {4 x^7}{3}+x^6\right ) \]