Internal problem ID [6463]
Book: Own collection of miscellaneous problems
Section: section 3.0
Problem number: 26.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+\sin \relax (y) \left (y^{\prime }\right )^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 21
dsolve(diff(y(x),x$2)+sin(y(x))*diff(y(x),x)^2=0,y(x), singsol=all)
\[ \int _{}^{y \relax (x )}{\mathrm e}^{-\cos \left (\textit {\_a} \right )}d \textit {\_a} -c_{1} x -c_{2} = 0 \]
✓ Solution by Mathematica
Time used: 0.324 (sec). Leaf size: 37
DSolve[y''[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}}\frac {e^{\sin (K[1])-\cos (K[1]) K[1]}}{c_1}dK[1]\&\right ][x+c_2] \\ \end{align*}