Internal problem ID [4193]
Book: A treatise on ordinary and partial differential equations by William Woolsey Johnson.
1913
Section: Chapter VII, Solutions in series. Examples XIV. page 177
Problem number: 7.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x^{4} y^{\prime \prime }+y^{\prime } x +y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✗ Solution by Maple
Order:=6; dsolve(x^4*diff(y(x),x$2)+x*diff(y(x),x)+y(x)=0,y(x),type='series',x=0);
\[ \text {No solution found} \]
✓ Solution by Mathematica
Time used: 0.034 (sec). Leaf size: 49
AsymptoticDSolveValue[x^4*y''[x]+x*y'[x]+y[x]==0,y[x],{x,0,5}]
\[ y(x)\to \frac {c_1 \left (1-x^2\right )}{x}+c_2 e^{\frac {1}{2 x^2}} \left (420 x^6+45 x^4+6 x^2+1\right ) x^4 \]