59.1.635 problem 652

Internal problem ID [9807]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 652
Date solved : Monday, January 27, 2025 at 06:14:30 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 4 z y^{\prime \prime }+2 \left (1-z \right ) y^{\prime }-y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.031 (sec). Leaf size: 22

dsolve(4*z*diff(y(z),z$2)+2*(1-z)*diff(y(z),z)-y(z)=0,y(z), singsol=all)
 

\[ y \left (z \right ) = {\mathrm e}^{\frac {z}{2}} \left (\operatorname {erf}\left (\frac {\sqrt {2}\, \sqrt {z}}{2}\right ) c_{1} +c_{2} \right ) \]

✓ Solution by Mathematica

Time used: 0.066 (sec). Leaf size: 44

DSolve[4*z*D[y[z],{z,2}]+2*(1-z)*D[y[z],z]-y[z]==0,y[z],z,IncludeSingularSolutions -> True]
 

\[ y(z)\to e^{\frac {z}{2}-\frac {1}{4}} \left (\sqrt {e} c_1-\sqrt {2} c_2 \Gamma \left (\frac {1}{2},\frac {z}{2}\right )\right ) \]