Internal problem ID [7408]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 689.
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 x \left (1-x \right ) y^{\prime }+\left (2 x -9\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.145 (sec). Leaf size: 25
dsolve(4*x^2*diff(y(x),x$2)+4*x*(1-x)*diff(y(x),x)+(2*x-9)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1} {\mathrm e}^{x}}{x^{\frac {3}{2}}}+\frac {c_{2} \left (x^{2}+2 x +2\right )}{x^{\frac {3}{2}}} \]
✓ Solution by Mathematica
Time used: 0.018 (sec). Leaf size: 29
DSolve[4*x^2*y''[x]+4*x*(1-x)*y'[x]+(2*x-9)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {c_1 e^x-c_2 (x (x+2)+2)}{x^{3/2}} \\ \end{align*}