Internal problem ID [8026]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 550.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {2 x^{2} \left (1+x \right ) y^{\prime \prime }-x \left (-3 x +1\right ) y^{\prime }+y=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 23
dsolve(2*x^2*(1+x)*diff(y(x),x$2)-x*(1-3*x)*diff(y(x),x)+y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {c_{1} x}{x +1}+\frac {c_{2} \sqrt {x}}{x +1} \]
✓ Solution by Mathematica
Time used: 0.036 (sec). Leaf size: 25
DSolve[2*x^2*(1+x)*y''[x]-x*(1-3*x)*y'[x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {c_1 \sqrt {x}+2 c_2 x}{x+1} \]