Internal problem ID [8130]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 655.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {z y^{\prime \prime }+\left (2 z -3\right ) y^{\prime }+\frac {4 y}{z}=0} \]
✓ Solution by Maple
Time used: 0.016 (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)
\[ y \left (z \right ) = c_{1} z^{2} {\mathrm e}^{-2 z} \left (2 z -1\right )+c_{2} z^{2} \left (\frac {1}{2}+{\mathrm e}^{-2 z} \left (z -\frac {1}{2}\right ) \operatorname {Ei}_{1}\left (-2 z \right )\right ) \]
✓ Solution by Mathematica
Time used: 0.087 (sec). Leaf size: 47
DSolve[z*y''[z]+(2*z-3)*y'[z]+4/z*y[z]==0,y[z],z,IncludeSingularSolutions -> True]
\[ y(z)\to -\frac {1}{2} e^{-2 z} z^2 \left (4 c_2 (1-2 z) \operatorname {ExpIntegralEi}(2 z)-2 c_1 z+4 c_2 e^{2 z}+c_1\right ) \]