Internal problem ID [8248]
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]]
\[ \boxed {x y^{\prime \prime }+\left (x -6\right ) y^{\prime }-3 y=0} \]
✓ Solution by Maple
Time used: 0.0 (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)
\[ y \left (x \right ) = c_{1} \left (x^{3}-12 x^{2}+60 x -120\right )+c_{2} {\mathrm e}^{-x} \left (x^{3}+12 x^{2}+60 x +120\right ) \]
✓ Solution by Mathematica
Time used: 0.069 (sec). Leaf size: 98
DSolve[x*y''[x]+(x-6)*y'[x]-3*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {2 e^{-x/2} \sqrt {x} \left (\left (c_1 x^3+12 i c_2 x^2+60 c_1 x+120 i c_2\right ) \cosh \left (\frac {x}{2}\right )-\left (12 c_1 \left (x^2+10\right )+i c_2 x \left (x^2+60\right )\right ) \sinh \left (\frac {x}{2}\right )\right )}{\sqrt {\pi } \sqrt {-i x}} \]