Internal problem ID [7173]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 450.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\left (1-2 x \right ) y^{\prime \prime }+2 y^{\prime }+\left (2 x -3\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 16
dsolve((1-2*x)*diff(y(x),x$2)+2*diff(y(x),x)+(2*x-3)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} {\mathrm e}^{x}+c_{2} x \,{\mathrm e}^{-x} \]
✓ Solution by Mathematica
Time used: 0.076 (sec). Leaf size: 48
DSolve[(1-2*x)*y''[x]+2*y'[x]+(2*x-3)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {e^{-x-\frac {1}{2}} \sqrt {1-2 x} \left (c_1 e^{2 x}-e c_2 x\right )}{\sqrt {2 x-1}} \\ \end{align*}