Internal problem ID [8127]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 652.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {4 z y^{\prime \prime }+2 \left (1-z \right ) y^{\prime }-y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 27
dsolve(4*z*diff(y(z),z$2)+2*(1-z)*diff(y(z),z)-y(z)=0,y(z), singsol=all)
\[ y \left (z \right ) = c_{1} {\mathrm e}^{\frac {z}{2}}+c_{2} {\mathrm e}^{\frac {z}{2}} \left (\int \frac {{\mathrm e}^{-\frac {z}{2}}}{\sqrt {z}}d z \right ) \]
✓ Solution by Mathematica
Time used: 0.04 (sec). Leaf size: 34
DSolve[4*z*y''[z]+2*(1-z)*y'[z]-y[z]==0,y[z],z,IncludeSingularSolutions -> True]
\[ y(z)\to e^{z/2} \left (c_1-\sqrt {2} c_2 \Gamma \left (\frac {1}{2},\frac {z}{2}\right )\right ) \]