Internal problem ID [6966]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 235.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {4 x^{2} y^{\prime \prime }-4 y^{\prime } x^{2}+\left (2 x +1\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 20
dsolve(4*x^2*diff(y(x),x$2)-4*x^2*diff(y(x),x)+(1+2*x)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \sqrt {x}\, c_{1}+c_{2} \sqrt {x}\, \expIntegral \left (1, -x \right ) \]
✓ Solution by Mathematica
Time used: 0.026 (sec). Leaf size: 19
DSolve[4*x^2*y''[x]-4*x^2*y'[x]+(1+2*x)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \sqrt {x} (c_2 \text {Ei}(x)+c_1) \\ \end{align*}