Internal problem ID [6689]
Book: Second order enumerated odes
Section: section 2
Problem number: 4.
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 {y^{\prime \prime }+\left (\sin \relax (x )+2 x \right ) y^{\prime }+\cos \relax (y) y \left (y^{\prime }\right )^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 34
dsolve(diff(y(x),x$2)+(sin(x)+2*x)*diff(y(x),x)+cos(y(x))*y(x)*diff(y(x),x)^2=0,y(x), singsol=all)
\[ \int _{}^{y \relax (x )}{\mathrm e}^{\cos \left (\textit {\_a} \right )+\textit {\_a} \sin \left (\textit {\_a} \right )}d \textit {\_a} -c_{1} \left (\int {\mathrm e}^{-x^{2}+\cos \relax (x )}d x \right )-c_{2} = 0 \]
✓ Solution by Mathematica
Time used: 0.585 (sec). Leaf size: 53
DSolve[y''[x]+(Sin[x]+2*x)*y'[x]+Cos[y[x]]*y[x]*(y'[x])^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}e^{\cos (K[2])+K[2] \sin (K[2])}dK[2]\&\right ]\left [\int _1^x-e^{\cos (K[3])-K[3]^2} c_1dK[3]+c_2\right ] \\ \end{align*}