Internal problem ID [1416]
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: Example 7.7.4 page 387.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x^{2} \left (-2 x^{2}+1\right ) y^{\prime \prime }+x \left (-13 x^{2}+7\right ) y^{\prime }-14 x^{2} 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: 32
Order:=6; dsolve(x^2*(1-2*x^2)*diff(y(x),x$2)+x*(7-13*x^2)*diff(y(x),x)-14*x^2*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = c_{1} \left (1+\frac {7}{8} x^{2}+\frac {77}{80} x^{4}+\mathrm {O}\left (x^{6}\right )\right )+\frac {c_{2} \left (-86400+216000 x^{2}-54000 x^{4}+\mathrm {O}\left (x^{6}\right )\right )}{x^{6}} \]
✓ Solution by Mathematica
Time used: 0.013 (sec). Leaf size: 44
AsymptoticDSolveValue[x^2*(1-2*x^2)*y''[x]+x*(7-13*x^2)*y'[x]-14*x^2*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_2 \left (\frac {77 x^4}{80}+\frac {7 x^2}{8}+1\right )+c_1 \left (\frac {1}{x^6}-\frac {5}{2 x^4}+\frac {5}{8 x^2}\right ) \]