Internal problem ID [7144]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 420.
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 \right ) y^{\prime \prime }+\left (3 x +9\right ) y^{\prime }-3 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.11 (sec). Leaf size: 30
dsolve((x^2+6*x)*diff(y(x),x$2)+(3*x+9)*diff(y(x),x)-3*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} \left (3+x \right )+\frac {c_{2} \left (2 x^{2}+12 x +9\right )}{\sqrt {x}\, \sqrt {6+x}} \]
✓ Solution by Mathematica
Time used: 0.015 (sec). Leaf size: 66
DSolve[(x^2+6*x)*y''[x]+(3*x+9)*y'[x]-3*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\sqrt {\frac {2}{3 \pi }} \left (c_1 (2 x (x+6)+9)-\pi c_2 (x+3) \sqrt {-x (x+6)}\right )}{3 \sqrt [4]{-x^2} \sqrt {x+6}} \\ \end{align*}