59.1.804 problem 827

Internal problem ID [9976]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 827
Date solved : Monday, January 27, 2025 at 06:16:20 PM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} 2 x^{2} y^{\prime \prime }+3 x y^{\prime }-y x&=0 \end{align*}

✓ Solution by Maple

Time used: 0.061 (sec). Leaf size: 29

dsolve(2*x^2*diff(y(x),x$2)+3*x*diff(y(x),x)-x*y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.058 (sec). Leaf size: 56

DSolve[2*x^2*D[y[x],{x,2}]+3*x*D[y[x],x]-x*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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