Internal problem ID [7283]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 563.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {9 x^{2} y^{\prime \prime }+3 x \left (-2 x^{2}+3 x +5\right ) y^{\prime }+\left (-14 x^{2}+12 x +1\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.969 (sec). Leaf size: 42
dsolve(9*x^2*diff(y(x),x$2)+3*x*(5+3*x-2*x^2)*diff(y(x),x)+(1+12*x-14*x^2)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1} {\mathrm e}^{\frac {x \left (x -3\right )}{3}}}{x^{\frac {1}{3}}}+\frac {c_{2} {\mathrm e}^{\frac {x \left (x -3\right )}{3}} \left (\int \frac {{\mathrm e}^{-\frac {x \left (x -3\right )}{3}}}{x}d x \right )}{x^{\frac {1}{3}}} \]
✓ Solution by Mathematica
Time used: 0.132 (sec). Leaf size: 52
DSolve[9*x^2*y''[x]+3*x*(5+3*x-2*x^2)*y'[x]+(1+12*x-14*x^2)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {e^{\frac {1}{3} (x-3) x} \left (c_2 \int _1^x\frac {e^{K[1]-\frac {K[1]^2}{3}}}{K[1]}dK[1]+c_1\right )}{\sqrt [3]{x}} \\ \end{align*}