Internal problem ID [8182]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 707.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{2} y^{\prime \prime }-\left (x^{2}+4 x \right ) y^{\prime }+4 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 32
dsolve(x^2*diff(y(x),x$2)-(x^2+4*x)*diff(y(x),x)+4*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} {\mathrm e}^{x} x^{4}+c_{2} x \left ({\mathrm e}^{x} x^{3} \operatorname {Ei}_{1}\left (x \right )-x^{2}+x -2\right ) \]
✓ Solution by Mathematica
Time used: 0.017 (sec). Leaf size: 41
DSolve[x^2*y''[x]-(x^2+4*x)*y'[x]+4*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_2 e^x x^4-\frac {1}{6} c_1 x \left (e^x x^3 \operatorname {ExpIntegralEi}(-x)+x^2-x+2\right ) \]