Internal problem ID [7113]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 384.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x^{2} y^{\prime \prime }+\left (3 x^{2}+2 x \right ) y^{\prime }-2 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 29
dsolve(x^2*diff(y(x), x, x) + (2*x+3*x^2)*diff(y(x),x)-2*y(x) = 0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1} {\mathrm e}^{-3 x}}{x^{2}}+\frac {c_{2} \left (9 x^{2}-6 x +2\right )}{x^{2}} \]
✓ Solution by Mathematica
Time used: 0.018 (sec). Leaf size: 35
DSolve[x^2*y''[x]+(2*x+3*x^2)*y'[x]-2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {c_1 \left (9 x^2-6 x+2\right )+27 c_2 e^{-3 x}}{27 x^2} \\ \end{align*}