Internal problem ID [8004]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 528.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {2 x^{2} \left (x +3\right ) y^{\prime \prime }+x \left (1+5 x \right ) y^{\prime }+\left (1+x \right ) y=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 36
dsolve(2*x^2*(3+x)*diff(y(x),x$2)+x*(1+5*x)*diff(y(x),x)+(1+x)*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {c_{1} x^{\frac {1}{3}}}{\left (x +3\right )^{\frac {4}{3}}}+\frac {c_{2} x^{\frac {1}{3}} \left (\int \frac {\left (x +3\right )^{\frac {1}{3}}}{x^{\frac {5}{6}}}d x \right )}{\left (x +3\right )^{\frac {4}{3}}} \]
✓ Solution by Mathematica
Time used: 0.071 (sec). Leaf size: 50
DSolve[2*x^2*(3+x)*y''[x]+x*(1+5*x)*y'[x]+(1+x)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {\sqrt [3]{x} \left (6 \sqrt [3]{3} c_2 \sqrt [6]{x} \operatorname {Hypergeometric2F1}\left (-\frac {1}{3},\frac {1}{6},\frac {7}{6},-\frac {x}{3}\right )+c_1\right )}{(x+3)^{4/3}} \]