Internal problem ID [6694]
Book: Second order enumerated odes
Section: section 2
Problem number: 10.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [_Liouville, [_2nd_order, _reducible, _mu_xy]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+x y^{\prime }+y \left (y^{\prime }\right )^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.053 (sec). Leaf size: 40
dsolve(diff(y(x),x$2)+x*diff(y(x),x)+y(x)*(diff(y(x),x))^2=0,y(x), singsol=all)
\[ y \relax (x ) = -i \RootOf \left (i \erf \left (\frac {x \sqrt {2}}{2}\right ) \sqrt {\pi }\, c_{1}+i \sqrt {2}\, c_{2}-\erf \left (\textit {\_Z} \right ) \sqrt {\pi }\right ) \sqrt {2} \]
✓ Solution by Mathematica
Time used: 0.049 (sec). Leaf size: 44
DSolve[y''[x]+x*y'[x]+y[x]*(y'[x])^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -i \sqrt {2} \text {erf}^{-1}\left (i \left (\sqrt {\frac {2}{\pi }} c_2-c_1 \text {Erf}\left (\frac {x}{\sqrt {2}}\right )\right )\right ) \\ \end{align*}