Internal problem ID [4768]
Book: Notes on Diffy Qs. Differential Equations for Engineers. By by Jiri Lebl, 2013.
Section: Chapter 7. POWER SERIES METHODS. 7.3.2 The method of Frobenius. Exercises. page
300
Problem number: 7.3.8 (b).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x^{2} y^{\prime \prime }+y^{\prime }+y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✗ Solution by Maple
Order:=6; dsolve(x^2*diff(y(x),x$2)+diff(y(x),x)+y(x)=0,y(x),type='series',x=0);
\[ \text {No solution found} \]
✓ Solution by Mathematica
Time used: 0.033 (sec). Leaf size: 84
AsymptoticDSolveValue[x^2*y''[x]+y'[x]+y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_2 e^{\frac {1}{x}} \left (\frac {59241 x^5}{40}+\frac {1911 x^4}{8}+\frac {91 x^3}{2}+\frac {21 x^2}{2}+3 x+1\right ) x^2+c_1 \left (-\frac {91 x^5}{40}+\frac {7 x^4}{8}-\frac {x^3}{2}+\frac {x^2}{2}-x+1\right ) \]