Internal problem ID [7313]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 593.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {9 x^{2} \left (x +3\right ) y^{\prime \prime }+3 x \left (3+7 x \right ) y^{\prime }+\left (3+4 x \right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.105 (sec). Leaf size: 27
dsolve(9*x^2*(3+x)*diff(y(x),x$2)+3*x*(3+7*x)*diff(y(x),x)+(3+4*x)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1} x^{\frac {1}{3}}}{3+x}+\frac {c_{2} x^{\frac {1}{3}} \ln \relax (x )}{3+x} \]
✓ Solution by Mathematica
Time used: 0.015 (sec). Leaf size: 24
DSolve[9*x^2*(3+x)*y''[x]+3*x*(3+7*x)*y'[x]+(3+4*x)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\sqrt [3]{x} (c_2 \log (x)+c_1)}{x+3} \\ \end{align*}