Internal problem ID [7798]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 311.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x \left (x +2\right ) y^{\prime \prime }+2 \left (1+x \right ) y^{\prime }-2 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 36
dsolve(x*(x+2)*diff(y(x),x$2)+2*(x+1)*diff(y(x),x)-2*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} \left (x +1\right )+c_{2} \left (\frac {x \ln \left (x \right )}{2}-\frac {\ln \left (x +2\right ) x}{2}+\frac {\ln \left (x \right )}{2}-\frac {\ln \left (x +2\right )}{2}+1\right ) \]
✓ Solution by Mathematica
Time used: 0.026 (sec). Leaf size: 37
DSolve[x*(x+2)*y''[x]+2*(x+1)*y'[x]-2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_1 (x+1)-\frac {1}{2} c_2 ((x+1) \log (-x)-(x+1) \log (x+2)+2) \]