Internal problem ID [7036]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 305.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {2 \left (2-x \right ) x^{2} y^{\prime \prime }-\left (-x +4\right ) x y^{\prime }+\left (3-x \right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 19
dsolve(2*(2-x)*x^2*diff(y(x),x$2)-(4-x)*x*diff(y(x),x)+(3-x)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \sqrt {x}\, c_{1}+c_{2} \sqrt {x \left (x -2\right )} \]
✓ Solution by Mathematica
Time used: 0.036 (sec). Leaf size: 41
DSolve[2*(2-x)*x^2*y''[x]-(4-x)*x*y'[x]+(3-x)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\sqrt [4]{x-2} \sqrt {x} \left (2 c_2 \sqrt {x-2}+c_1\right )}{\sqrt [4]{2-x}} \\ \end{align*}