Internal problem ID [6695]
Book: Second order enumerated odes
Section: section 2
Problem number: 11.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y], _Liouville, [_2nd_order, _reducible, _mu_xy]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+\sin \relax (x ) y^{\prime }+\left (y^{\prime }\right )^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 14
dsolve(diff(y(x),x$2)+sin(x)*diff(y(x),x)+(diff(y(x),x))^2=0,y(x), singsol=all)
\[ y \relax (x ) = \ln \left (c_{1} \left (\int {\mathrm e}^{\cos \relax (x )}d x \right )+c_{2}\right ) \]
✓ Solution by Mathematica
Time used: 60.149 (sec). Leaf size: 43
DSolve[y''[x]+Sin[x]*y'[x]+(y'[x])^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \int _1^x\frac {e^{\cos (K[2])}}{c_1-\int _1^{K[2]}-e^{\cos (K[1])}dK[1]}dK[2]+c_2 \\ \end{align*}