Internal problem ID [7175]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 452.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x y^{\prime \prime }-\left (2 x +1\right ) y^{\prime }+\left (x +1\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 16
dsolve(x*diff(y(x),x$2)-(2*x+1)*diff(y(x),x)+(x+1)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} {\mathrm e}^{x}+c_{2} {\mathrm e}^{x} x^{2} \]
✓ Solution by Mathematica
Time used: 0.013 (sec). Leaf size: 23
DSolve[x*y''[x]-(2*x+1)*y'[x]+(x+1)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} e^x \left (c_2 x^2+2 c_1\right ) \\ \end{align*}