Internal problem ID [7450]
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]]
\[ \boxed {y^{\prime \prime }+y^{\prime } x +y {y^{\prime }}^{2}=0} \]
✓ Solution by Maple
Time used: 0.016 (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)
\[ y \left (x \right ) = -i \operatorname {RootOf}\left (i \sqrt {\pi }\, \operatorname {erf}\left (\frac {\sqrt {2}\, x}{2}\right ) c_{1} +i \sqrt {2}\, c_{2} -\operatorname {erf}\left (\textit {\_Z} \right ) \sqrt {\pi }\right ) \sqrt {2} \]
✓ Solution by Mathematica
Time used: 0.088 (sec). Leaf size: 44
DSolve[y''[x]+x*y'[x]+y[x]*(y'[x])^2==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -i \sqrt {2} \text {erf}^{-1}\left (i \left (\sqrt {\frac {2}{\pi }} c_2-c_1 \text {erf}\left (\frac {x}{\sqrt {2}}\right )\right )\right ) \]