Internal problem ID [7034]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 304.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{2} \left (1+x \right ) y^{\prime \prime }-\left (2 x +1\right ) \left (y^{\prime } x -y\right )=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 15
dsolve(x^2*(1+x)*diff(y(x),x$2)-(1+2*x)*(x*diff(y(x),x)-y(x))=0,y(x), singsol=all)
\[ y \left (x \right ) = x c_{1} +c_{2} x \left (x +\ln \left (x \right )\right ) \]
✓ Solution by Mathematica
Time used: 0.084 (sec). Leaf size: 132
DSolve[x^2*(1+x)*y''[x]-(1+2*x)*(x*y'[x]+y[x])==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_2 x^{1+\sqrt {2}} \operatorname {Hypergeometric2F1}\left (-\frac {1}{2}+\sqrt {2}-\frac {\sqrt {17}}{2},\frac {1}{2} \left (-1+2 \sqrt {2}+\sqrt {17}\right ),1+2 \sqrt {2},-x\right )+c_1 x^{1-\sqrt {2}} \operatorname {Hypergeometric2F1}\left (\frac {1}{2} \left (-1-2 \sqrt {2}-\sqrt {17}\right ),\frac {1}{2} \left (-1-2 \sqrt {2}+\sqrt {17}\right ),1-2 \sqrt {2},-x\right ) \\ \end{align*}