Internal problem ID [7492]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 775.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x y^{\prime \prime }+\left (-6+x \right ) y^{\prime }-3 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 39
dsolve(x*diff(y(x),x$2)+(x-6)*diff(y(x),x)-3*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} \left (x^{3}-12 x^{2}+60 x -120\right )+c_{2} {\mathrm e}^{-x} \left (x^{3}+12 x^{2}+60 x +120\right ) \]
✓ Solution by Mathematica
Time used: 0.012 (sec). Leaf size: 92
DSolve[x*y''[x]+(x-6)*y'[x]-3*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {2 e^{-x/2} \sqrt {x} \left (\left (c_1 x \left (x^2+60\right )+12 i c_2 \left (x^2+10\right )\right ) \cosh \left (\frac {x}{2}\right )-\left (12 c_1 \left (x^2+10\right )+i c_2 x \left (x^2+60\right )\right ) \sinh \left (\frac {x}{2}\right )\right )}{\sqrt {\pi } \sqrt {-i x}} \\ \end{align*}