Internal problem ID [7395]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 676.
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 \left (3+x \right ) y^{\prime }+\left (4-x \right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 44
dsolve(x^2*diff(y(x),x$2)-x*(3+x)*diff(y(x),x)+(4-x)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} {\mathrm e}^{x} x^{2} \left (x^{2}+4 x +2\right )+c_{2} \left ({\mathrm e}^{x} \left (x^{2}+4 x +2\right ) \expIntegral \left (1, x\right )-x -3\right ) x^{2} \]
✓ Solution by Mathematica
Time used: 0.094 (sec). Leaf size: 42
DSolve[x^2*y''[x]-x*(3+x)*y'[x]+(4-x)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{4} x^2 \left (e^x (x (x+4)+2) (c_2 \text {Ei}(-x)+4 c_1)+c_2 (x+3)\right ) \\ \end{align*}