Internal problem ID [8283]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 810.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {u^{\prime \prime }-\left (2 x +1\right ) u^{\prime }+\left (x^{2}+x -1\right ) u=0} \]
✓ 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)
\[ u \left (x \right ) = c_{1} {\mathrm e}^{\frac {x^{2}}{2}}+c_{2} {\mathrm e}^{\frac {x \left (x +2\right )}{2}} \]
✓ Solution by Mathematica
Time used: 0.025 (sec). Leaf size: 24
DSolve[u''[x]-(2*x+1)*u'[x]+(x^2+x-1)*u[x]==0,u[x],x,IncludeSingularSolutions -> True]
\[ u(x)\to e^{\frac {x^2}{2}} \left (c_2 e^x+c_1\right ) \]