Internal problem ID [7406]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 687.
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 }-x^{2} y^{\prime }-\left (2+3 x \right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.006 (sec). Leaf size: 46
dsolve(x^2*diff(y(x),x$2)-x^2*diff(y(x),x)-(3*x+2)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} x^{2} {\mathrm e}^{x} \left (x +4\right )+\frac {c_{2} \left (-x^{3} {\mathrm e}^{x} \left (x +4\right ) \expIntegral \left (1, x\right )+x^{3}+3 x^{2}-2 x +2\right )}{x} \]
✓ Solution by Mathematica
Time used: 0.038 (sec). Leaf size: 51
DSolve[x^2*y''[x]-x^2*y'[x]-(3*x+2)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {e^x x^3 (x+4) (24 c_1-c_2 \operatorname {Ei}(-x))-c_2 (x (x (x+3)-2)+2)}{24 x} \\ \end{align*}