Internal problem ID [6871]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 139.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x^{2} \left (1-2 x \right ) y^{\prime \prime }-x \left (4 x +5\right ) y^{\prime }+\left (9+4 x \right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 61
dsolve(x^2*(1-2*x)*diff(y(x),x$2)-x*(5+4*x)*diff(y(x),x)+(9+4*x)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1} \left (8 x^{4}+x^{3}\right )}{\left (2 x -1\right )^{6}}+\frac {c_{2} \left (\left (-6 x -\frac {3}{4}\right ) \ln \relax (x )+x^{4}-4 x^{3}+9 x^{2}+\frac {609 x}{512}-\frac {9375}{4096}\right ) x^{3}}{\left (2 x -1\right )^{6}} \]
✓ Solution by Mathematica
Time used: 0.062 (sec). Leaf size: 61
DSolve[x^2*(1-2*x)*y''[x]-x*(5+4*x)*y'[x]+(9+4*x)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x^3 (-8 (8 x+1) (c_2 x (8 x (8 x-33)+609)-6 c_1)+3072 c_2 (8 x+1) \log (x)+9375 c_2)}{384 (1-2 x)^6} \\ \end{align*}