Internal problem ID [7191]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 469.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x y^{\prime \prime }-\left (2 x +2\right ) y^{\prime }+\left (x +2\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 16
dsolve(x*diff(y(x),x$2)-(2*x+2)*diff(y(x),x)+(x+2)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} {\mathrm e}^{x}+c_{2} {\mathrm e}^{x} x^{3} \]
✓ Solution by Mathematica
Time used: 0.021 (sec). Leaf size: 29
DSolve[x*y''[x]-(2*x+2)*y'[x]+(x+2)*y[x]==6*x^3*Exp[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{6} e^x \left (9 x^4+2 c_2 x^3+6 c_1\right ) \\ \end{align*}