Internal problem ID [8173]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 698.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x y^{\prime \prime }+\left (x +n \right ) y^{\prime }+\left (n +1\right ) y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 44
dsolve(x*diff(y(x),x$2)+(x+n)*diff(y(x),x)+(n+1)*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} {\mathrm e}^{-x} \left (-x +n \right )+c_{2} {\mathrm e}^{-x} \left (-x +n \right ) \left (\int \frac {{\mathrm e}^{x} x^{-n}}{\left (-x +n \right )^{2}}d x \right ) \]
✓ Solution by Mathematica
Time used: 0.524 (sec). Leaf size: 48
DSolve[x*y''[x]+(x+n)*y'[x]+(n+1)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-x} (n-x) \left (c_2 \int _1^x\frac {e^{K[1]} K[1]^{-n}}{(n-K[1])^2}dK[1]+c_1\right ) \]