Internal problem ID [7174]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 451.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {2 x y^{\prime \prime }+\left (4 x +1\right ) y^{\prime }+\left (2 x +1\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 20
dsolve(2*x*diff(y(x),x$2)+(4*x+1)*diff(y(x),x)+(2*x+1)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{-x} c_{1}+c_{2} \sqrt {x}\, {\mathrm e}^{-x} \]
✓ Solution by Mathematica
Time used: 0.009 (sec). Leaf size: 23
DSolve[2*x*y''[x]+(4*x+1)*y'[x]+(2*x+1)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-x} \left (2 c_2 \sqrt {x}+c_1\right ) \\ \end{align*}