Internal problem ID [6962]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 231.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {4 x y^{\prime \prime }-x y^{\prime }+2 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 40
dsolve(4*x*diff(y(x),x$2)-x*diff(y(x),x)+2*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} \left (x^{2}-8 x \right )+c_{2} \left (\frac {\left (x^{2}-8 x \right ) \expIntegral \left (1, -\frac {x}{4}\right )}{128}+\frac {{\mathrm e}^{\frac {x}{4}} \left (x -4\right )}{32}\right ) \]
✓ Solution by Mathematica
Time used: 0.053 (sec). Leaf size: 43
DSolve[4*x*y''[x]-x*y'[x]+2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{128} c_2 \left ((x-8) x \operatorname {Ei}\left (\frac {x}{4}\right )-4 e^{x/4} (x-4)\right )+c_1 (x-8) x \\ \end{align*}