Internal problem ID [6952]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 221.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {z y^{\prime \prime }+\left (2 z -3\right ) y^{\prime }+\frac {4 y}{z}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 39
dsolve(z*diff(y(z),z$2)+(2*z-3)*diff(y(z),z)+4/z*y(z)=0,y(z), singsol=all)
\[ y \relax (z ) = c_{1} z^{2} {\mathrm e}^{-2 z} \left (2 z -1\right )+c_{2} \left (\frac {1}{2}+{\mathrm e}^{-2 z} \left (z -\frac {1}{2}\right ) \expIntegral \left (1, -2 z \right )\right ) z^{2} \]
✓ Solution by Mathematica
Time used: 0.269 (sec). Leaf size: 39
DSolve[z*y''[z]+(2*z-3)*y'[z]+4/z*y[z]==0,y[z],z,IncludeSingularSolutions -> True]
\begin{align*} y(z)\to \frac {1}{2} z^2 \left (e^{-2 z} (2 z-1) (4 c_2 \text {Ei}(2 z)+c_1)-4 c_2\right ) \\ \end{align*}