Internal problem ID [6828]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 96.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {2 x^{2} y^{\prime \prime }+5 x y^{\prime }+\left (x +1\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 31
dsolve(2*x^2*diff(y(x),x$2)+5*x*diff(y(x),x)+(1+x)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1} \sin \left (\sqrt {2}\, \sqrt {x}\right )}{x}+\frac {c_{2} \cos \left (\sqrt {2}\, \sqrt {x}\right )}{x} \]
✓ Solution by Mathematica
Time used: 0.058 (sec). Leaf size: 60
DSolve[2*x^2*y''[x]+5*x*y'[x]+(1+x)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {2 c_1 e^{i \sqrt {2} \sqrt {x}}+i \sqrt {2} c_2 e^{-i \sqrt {2} \sqrt {x}}}{2 x} \\ \end{align*}