Internal problem ID [6687]
Book: Second order enumerated odes
Section: section 2
Problem number: 2.
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 }+\sin \relax (x ) y^{\prime }+y \left (y^{\prime }\right )^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 38
dsolve(diff(y(x),x$2)+sin(x)*diff(y(x),x)+y(x)*diff(y(x),x)^2=0,y(x), singsol=all)
\[ y \relax (x ) = -i \RootOf \left (i \sqrt {2}\, c_{1} \left (\int {\mathrm e}^{\cos \relax (x )}d x \right )+i \sqrt {2}\, c_{2}-\erf \left (\textit {\_Z} \right ) \sqrt {\pi }\right ) \sqrt {2} \]
✓ Solution by Mathematica
Time used: 0.31 (sec). Leaf size: 47
DSolve[y''[x]+Sin[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 \sqrt {\frac {2}{\pi }} \left (\int _1^x-e^{\cos (K[2])} c_1dK[2]+c_2\right )\right ) \\ \end{align*}