Internal problem ID [8005]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 529.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{2} \left (4+x \right ) y^{\prime \prime }-x \left (-3 x +1\right ) y^{\prime }+y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 36
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)
\[ y \left (x \right ) = \frac {c_{1} x^{\frac {1}{4}}}{\left (x +4\right )^{\frac {9}{4}}}+\frac {c_{2} x^{\frac {1}{4}} \left (\int \frac {\left (x +4\right )^{\frac {5}{4}}}{x^{\frac {1}{4}}}d x \right )}{\left (x +4\right )^{\frac {9}{4}}} \]
✓ Solution by Mathematica
Time used: 0.102 (sec). Leaf size: 89
DSolve[x^2*(4+x)*y''[x]-x*(1-3*x)*y'[x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {\sqrt [4]{x} \left (-10 c_2 \arctan \left (\sqrt [4]{\frac {x}{x+4}}\right )+10 c_2 \text {arctanh}\left (\sqrt [4]{\frac {x}{x+4}}\right )+c_2 \sqrt [4]{x+4} x^{7/4}+9 c_2 \sqrt [4]{x+4} x^{3/4}+2 c_1\right )}{2 (x+4)^{9/4}} \]