59.1.751 problem 773

Internal problem ID [9923]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 773
Date solved : Monday, January 27, 2025 at 06:15:49 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x y^{\prime \prime }+2 y^{\prime }-y x&=0 \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 17

dsolve(x*diff(y(x),x$2)+2*diff(y(x),x)-x*y(x)=0,y(x), singsol=all)
 

\[ y = \frac {c_{1} \sinh \left (x \right )+c_{2} \cosh \left (x \right )}{x} \]

✓ Solution by Mathematica

Time used: 0.026 (sec). Leaf size: 28

DSolve[x*D[y[x],{x,2}]+2*D[y[x],x]-x*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {2 c_1 e^{-x}+c_2 e^x}{2 x} \]