Internal problem ID [6827]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 95.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x^{2} \left (x +4\right ) y^{\prime \prime }-x \left (1-3 x \right ) y^{\prime }+y=0} \end {gather*}
✓ Solution by Maple
Time used: 13.312 (sec). Leaf size: 27
dsolve(x^2*(4+x)*diff(y(x),x$2)-x*(1-3*x)*diff(y(x),x)+y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1} x^{\frac {1}{4}}}{\left (4+x \right )^{\frac {9}{4}}}+c_{2} \hypergeom \left (\left [1, 3\right ], \left [\frac {7}{4}\right ], -\frac {x}{4}\right ) x \]
✓ Solution by Mathematica
Time used: 0.291 (sec). Leaf size: 87
DSolve[x^2*(4+x)*y''[x]-x*(1-3*x)*y'[x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {10 c_2 \sqrt [4]{x} \left (\tanh ^{-1}\left (\sqrt [4]{\frac {x}{x+4}}\right )-\text {ArcTan}\left (\sqrt [4]{\frac {x}{x+4}}\right )\right )+c_2 \sqrt [4]{x+4} x^2+9 c_2 \sqrt [4]{x+4} x+2 c_1 \sqrt [4]{x}}{2 (x+4)^{9/4}} \\ \end{align*}