Internal problem ID [7500]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 10.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {\left (x^{2}-6 x +10\right ) y^{\prime \prime }-4 \left (x -3\right ) y^{\prime }+6 y=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 25
dsolve((x^2-6*x+10)*diff(y(x),x$2)-4*(x-3)*diff(y(x),x)+6*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} \left (x^{3}-30 x +60\right )+c_{2} \left (\frac {26}{3}+x^{2}-6 x \right ) \]
✓ Solution by Mathematica
Time used: 0.086 (sec). Leaf size: 36
DSolve[(x^2-6*x+10)*y''[x]-4*(x-3)*y'[x]+6*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {1}{3} i \left (c_2 \left (3 x^2-18 x+26\right )+3 c_1 (x-(3+i))^3\right ) \]