Internal problem ID [7959]
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]]
\[ \boxed {x^{2} \left (1-x \right ) y^{\prime \prime }+x \left (4+x \right ) y^{\prime }+\left (-x +2\right ) y=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 53
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)
\[ y \left (x \right ) = \frac {c_{1} \left (x^{2}+6 x +3\right )}{x}+\frac {c_{2} \left (3 x^{3} \ln \left (x \right )+18 x^{2} \ln \left (x \right )+9 x \ln \left (x \right )+51 x^{2}+48 x +1\right )}{3 x^{2}} \]
✓ Solution by Mathematica
Time used: 0.07 (sec). Leaf size: 53
DSolve[x^2*(1-x)*y''[x]+x*(4+x)*y'[x]+(2-x)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {3 c_1 x \left (x^2+6 x+3\right )-c_2 \left (51 x^2+3 \left (x^2+6 x+3\right ) x \log (x)+48 x+1\right )}{3 x^2} \]