Internal problem ID [6894]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 162.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x^{2} \left (4+3 x \right ) y^{\prime \prime }-x \left (4-3 x \right ) y^{\prime }+4 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 27
dsolve(x^2*(4+3*x)*diff(y(x),x$2)-x*(4-3*x)*diff(y(x),x)+4*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1} x}{3 x +4}+\frac {c_{2} x \ln \relax (x )}{3 x +4} \]
✓ Solution by Mathematica
Time used: 0.012 (sec). Leaf size: 22
DSolve[x^2*(4+3*x)*y''[x]-x*(4-3*x)*y'[x]+4*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x (c_2 \log (x)+c_1)}{3 x+4} \\ \end{align*}