Internal problem ID [7034]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 303.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x \left (-x^{2}+2\right ) y^{\prime \prime }-\left (x^{2}+4 x +2\right ) \left (\left (1-x \right ) y^{\prime }+y\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.006 (sec). Leaf size: 17
dsolve(x*(2-x^2)*diff(y(x),x$2)-(x^2+4*x+2)*((1-x)*diff(y(x),x)+y(x))=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} \left (x -1\right )+c_{2} {\mathrm e}^{x} x^{2} \]
✓ Solution by Mathematica
Time used: 0.059 (sec). Leaf size: 21
DSolve[x*(2-x^2)*y''[x]-(x^2+4*x+2)*((1-x)*y'[x]+y[x])==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 e^x x^2+c_2 (x-1) \\ \end{align*}