Internal problem ID [7203]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 482.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x^{2} \left (1-x \right ) y^{\prime \prime }+x \left (x +4\right ) y^{\prime }+\left (-x +2\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 50
dsolve(x^2*(1-x)*diff(y(x),x$2)+x*(4+x)*diff(y(x),x)+(2-x)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1} \left (x^{2}+6 x +3\right )}{x}+\frac {c_{2} \left (\left (3 x^{3}+18 x^{2}+9 x \right ) \ln \relax (x )+51 x^{2}+48 x +1\right )}{x^{2}} \]
✓ Solution by Mathematica
Time used: 0.053 (sec). Leaf size: 51
DSolve[x^2*(1-x)*y''[x]+x*(4+x)*y'[x]+(2-x)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {3 c_1 x (x (x+6)+3)-c_2 \left (51 x^2+48 x+3 (x (x+6)+3) x \log (x)+1\right )}{3 x^2} \\ \end{align*}