Internal problem ID [8203]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 728.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x y^{\prime \prime }-2 \left (1+x \right ) y^{\prime }+\left (x +2\right ) y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 16
dsolve(x*diff(y(x),x$2)-2*(x+1)*diff(y(x),x)+(x+2)*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} {\mathrm e}^{x}+c_{2} {\mathrm e}^{x} x^{3} \]
✓ Solution by Mathematica
Time used: 0.026 (sec). Leaf size: 23
DSolve[x*y''[x]-2*(x+1)*y'[x]+(x+2)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{3} e^x \left (c_2 x^3+3 c_1\right ) \]