Internal problem ID [8206]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 731.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {\left (x^{2}+2 x \right ) y^{\prime \prime }-2 \left (1+x \right ) y^{\prime }+2 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 15
dsolve((x^2+2*x)*diff(y(x),x$2)-2*(x+1)*diff(y(x),x)+2*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} \left (x +1\right )+c_{2} x^{2} \]
✓ Solution by Mathematica
Time used: 0.032 (sec). Leaf size: 19
DSolve[(x^2+2*x)*y''[x]-2*(x+1)*y'[x]+2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_1 x^2-c_2 (x+1) \]