Internal problem ID [7143]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 419.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\left (x^{2}-6 x +10\right ) y^{\prime \prime }-4 \left (x -3\right ) y^{\prime }+6 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (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)
\[ y \relax (x ) = c_{1} \left (x^{3}-30 x +60\right )+c_{2} \left (\frac {26}{3}+x^{2}-6 x \right ) \]
✓ Solution by Mathematica
Time used: 0.036 (sec). Leaf size: 34
DSolve[(x^2-6*x+10)*y''[x]-4*(x-3)*y'[x]+6*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{3} i \left (3 c_1 (x-(3+i))^3+c_2 (3 (x-6) x+26)\right ) \\ \end{align*}