Internal problem ID [7095]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 366.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {u^{\prime \prime }-\left (2 x +1\right ) u^{\prime }+\left (x^{2}+x -1\right ) u=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 22
dsolve(diff(u(x),x$2)-(2*x+1)*diff(u(x),x)+(x^2+x-1)*u(x)=0,u(x), singsol=all)
\[ u \relax (x ) = {\mathrm e}^{\frac {x^{2}}{2}} c_{1}+c_{2} {\mathrm e}^{\frac {x \left (x +2\right )}{2}} \]
✓ Solution by Mathematica
Time used: 0.011 (sec). Leaf size: 24
DSolve[u''[x]-(2*x+1)*u'[x]+(x^2+x-1)*u[x]==0,u[x],x,IncludeSingularSolutions -> True]
\begin{align*} u(x)\to e^{\frac {x^2}{2}} \left (c_2 e^x+c_1\right ) \\ \end{align*}