Internal problem ID [7579]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 91.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {3 x^{2} y^{\prime \prime }+x \left (1+x \right ) y^{\prime }-y=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 33
dsolve(3*x^2*diff(y(x),x$2)+x*(1+x)*diff(y(x),x)-y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {c_{1} {\mathrm e}^{-\frac {x}{3}}}{x^{\frac {1}{3}}}+\frac {c_{2} {\mathrm e}^{-\frac {x}{3}} \left (\int x^{\frac {1}{3}} {\mathrm e}^{\frac {x}{3}}d x \right )}{x^{\frac {1}{3}}} \]
✓ Solution by Mathematica
Time used: 0.023 (sec). Leaf size: 50
DSolve[3*x^2*y''[x]+x*(1+x)*y'[x]-y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {e^{-x/3} \left (c_2 x^{2/3}-3 \sqrt [3]{3} c_1 (-x)^{2/3} \Gamma \left (\frac {4}{3},-\frac {x}{3}\right )\right )}{x} \]