Internal problem ID [7305]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 585.
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 }+3 x y^{\prime }+\left (4 x +1\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 33
dsolve(x^2*(1-2*x)*diff(y(x),x$2)+3*x*diff(y(x),x)+(1+4*x)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1}}{x}+\frac {c_{2} \left (-8 x^{3}+18 x^{2}+3 \ln \relax (x )-18 x \right )}{x} \]
✓ Solution by Mathematica
Time used: 0.027 (sec). Leaf size: 35
DSolve[x^2*(1-2*x)*y''[x]+3*x*y'[x]+(1+4*x)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {c_1}{x}-\frac {2}{3} c_2 (x (4 x-9)+9)+\frac {c_2 \log (x)}{x} \\ \end{align*}