Internal problem ID [6910]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 178.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {3 x^{2} \left (x +3\right ) y^{\prime \prime }-x \left (15+x \right ) y^{\prime }-20 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.11 (sec). Leaf size: 33
dsolve(3*x^2*(3+x)*diff(y(x),x$2)-x*(15+x)*diff(y(x),x)-20*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1} \left (x^{2}-36 x -243\right )}{x^{\frac {2}{3}}}+\frac {c_{2} \left (7 x +27\right )}{x^{\frac {2}{3}} \left (3+x \right )^{\frac {1}{3}}} \]
✓ Solution by Mathematica
Time used: 0.122 (sec). Leaf size: 42
DSolve[3*x^2*(3+x)*y''[x]-x*(15+x)*y'[x]-20*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\frac {4 c_1 (7 x+27)}{\sqrt [3]{x+3}}+21 c_2 ((x-36) x-243)}{28 x^{2/3}} \\ \end{align*}