Internal problem ID [7448]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 729.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {3 x y^{\prime \prime }-2 \left (3 x -1\right ) y^{\prime }+\left (3 x -2\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 16
dsolve(3*x*diff(y(x),x$2)-2*(3*x-1)*diff(y(x),x)+(3*x-2)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} {\mathrm e}^{x}+c_{2} x^{\frac {1}{3}} {\mathrm e}^{x} \]
✓ Solution by Mathematica
Time used: 0.015 (sec). Leaf size: 21
DSolve[3*x*y''[x]-2*(3*x-1)*y'[x]+(3*x-2)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^x \left (3 c_2 \sqrt [3]{x}+c_1\right ) \\ \end{align*}