Internal problem ID [6696]
Book: Second order enumerated odes
Section: section 2
Problem number: 12.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [_Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]
Solve \begin {gather*} \boxed {3 y^{\prime \prime }+y^{\prime } \cos \relax (x )+\sin \relax (y) \left (y^{\prime }\right )^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 27
dsolve(3*diff(y(x),x$2)+cos(x)*diff(y(x),x)+sin(y(x))*(diff(y(x),x))^2=0,y(x), singsol=all)
\[ \int _{}^{y \relax (x )}{\mathrm e}^{-\frac {\cos \left (\textit {\_a} \right )}{3}}d \textit {\_a} -c_{1} \left (\int {\mathrm e}^{-\frac {\sin \relax (x )}{3}}d x \right )-c_{2} = 0 \]
✓ Solution by Mathematica
Time used: 0.38 (sec). Leaf size: 47
DSolve[3*y''[x]+Cos[x]*y'[x]+Sin[y[x]]*(y'[x])^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}e^{-\frac {1}{3} \cos (K[2])}dK[2]\&\right ]\left [\int _1^x-e^{-\frac {1}{3} \sin (K[3])} c_1dK[3]+c_2\right ] \\ \end{align*}