Internal problem ID [7112]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 383.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
Solve \begin {gather*} \boxed {2 x^{2} y^{\prime \prime }+3 x y^{\prime }-y x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.138 (sec). Leaf size: 31
dsolve(2*x^2*diff(y(x),x$2)+3*x*diff(y(x),x)-x*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1} \sinh \left (\sqrt {2}\, \sqrt {x}\right )}{\sqrt {x}}+\frac {c_{2} \cosh \left (\sqrt {2}\, \sqrt {x}\right )}{\sqrt {x}} \]
✓ Solution by Mathematica
Time used: 0.036 (sec). Leaf size: 56
DSolve[2*x^2*y''[x]+3*x*y'[x]-x*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} 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}} \\ \end{align*}