Internal problem ID [7670]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 182.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{2} \left (1+x \right ) y^{\prime \prime }-x \left (6+11 x \right ) y^{\prime }+\left (6+32 x \right ) y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 40
dsolve(x^2*(1+x)*diff(y(x),x$2)-x*(6+11*x)*diff(y(x),x)+(6+32*x)*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} x \left (35 x^{3}+42 x^{2}+21 x +4\right )+c_{2} x \left (x^{7}+\frac {14}{3} x^{6}+7 x^{5}\right ) \]
✓ Solution by Mathematica
Time used: 0.074 (sec). Leaf size: 45
DSolve[x^2*(1+x)*y''[x]-x*(6+11*x)*y'[x]+(6+32*x)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{3} c_1 x (x+1)^6 (3 x-4)-\frac {1}{140} c_2 x \left (35 x^3+42 x^2+21 x+4\right ) \]