Internal problem ID [7418]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 699.
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 }+x y^{\prime }+y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.025 (sec). Leaf size: 50
dsolve(x^4*diff(y(x),x$2)+x*diff(y(x),x)+y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} \left (\frac {\erfi \left (\frac {\sqrt {2}}{2 x}\right ) \left (x^{2}-1\right ) \sqrt {2}\, \sqrt {\pi }}{x}+2 \,{\mathrm e}^{\frac {1}{2 x^{2}}}\right )+\frac {c_{2} \left (x^{2}-1\right )}{x} \]
✓ Solution by Mathematica
Time used: 0.068 (sec). Leaf size: 59
DSolve[x^4*y''[x]+x*y'[x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\left (x^2-1\right ) \left (4 c_1-\sqrt {2 \pi } c_2 \operatorname {Erfi}\left (\frac {1}{\sqrt {2} x}\right )\right )-2 c_2 e^{\frac {1}{2 x^2}} x}{4 x} \\ \end{align*}