Internal problem ID [7373]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 654.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [_Lienard]
Solve \begin {gather*} \boxed {z y^{\prime \prime }-2 y^{\prime }+y z=0} \end {gather*}
✓ Solution by Maple
Time used: 0.028 (sec). Leaf size: 25
dsolve(z*diff(y(z),z$2)-2*diff(y(z),z)+z*y(z)=0,y(z), singsol=all)
\[ y \relax (z ) = c_{1} \left (\cos \relax (z ) z -\sin \relax (z )\right )+c_{2} \left (\cos \relax (z )+\sin \relax (z ) z \right ) \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 39
DSolve[z*y''[z]-2*y'[z]+z*y[z]==0,y[z],z,IncludeSingularSolutions -> True]
\begin{align*} y(z)\to -\sqrt {\frac {2}{\pi }} ((c_1 z+c_2) \cos (z)+(c_2 z-c_1) \sin (z)) \\ \end{align*}