Internal problem ID [7307]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 587.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x^{2} \left (1-x \right ) y^{\prime \prime }-x \left (3-5 x \right ) y^{\prime }+\left (4-5 x \right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 49
dsolve(x^2*(1-x)*diff(y(x),x$2)-x*(3-5*x)*diff(y(x),x)+(4-5*x)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} x^{2} \left (x -1\right )^{3}+c_{2} \left (-\left (x -1\right )^{3} \ln \left (x -1\right )+\left (x -1\right )^{3} \ln \relax (x )-x^{2}+\frac {5 x}{2}-\frac {11}{6}\right ) x^{2} \]
✓ Solution by Mathematica
Time used: 0.035 (sec). Leaf size: 53
DSolve[x^2*(1-x)*y''[x]-x*(3-5*x)*y'[x]+(4-5*x)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{6} x^2 \left (-6 c_1 (x-1)^3+c_2 (3 x (2 x-5)+11)+6 c_2 (x-1)^3 (\log (x-1)-\log (x))\right ) \\ \end{align*}