Internal problem ID [7747]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 260.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{4} y^{\prime \prime }+x y^{\prime }+y=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 47
dsolve(x^4*diff(y(x),x$2)+x*diff(y(x),x)+y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {c_{1} \left (x^{2}-1\right )}{x}+\frac {c_{2} \left (x^{2}-1\right ) \left (\int \frac {x^{2} {\mathrm e}^{\frac {1}{2 x^{2}}}}{\left (x +1\right )^{2} \left (x -1\right )^{2}}d x \right )}{x} \]
✓ Solution by Mathematica
Time used: 0.218 (sec). Leaf size: 61
DSolve[x^4*y''[x]+x*y'[x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {\sqrt {2 \pi } c_2 \left (x^2-1\right ) \text {erfi}\left (\frac {1}{\sqrt {2} x}\right )-4 c_1 \left (x^2-1\right )+2 c_2 e^{\frac {1}{2 x^2}} x}{4 x} \]