Internal problem ID [7246]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 526.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (1-2 x \right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 27
dsolve(2*x^2*diff(y(x),x$2)-x*diff(y(x),x)+(1-2*x)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} \sqrt {x}\, \sinh \left (2 \sqrt {x}\right )+c_{2} \sqrt {x}\, \cosh \left (2 \sqrt {x}\right ) \]
✓ Solution by Mathematica
Time used: 0.016 (sec). Leaf size: 41
DSolve[2*x^2*y''[x]-x*y'[x]+(1-2*x)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} e^{-2 \sqrt {x}} \sqrt {x} \left (2 c_1 e^{4 \sqrt {x}}-c_2\right ) \\ \end{align*}