Internal problem ID [13494]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 13. Higher order equations: Extending first order concepts. Additional exercises
page 259
Problem number: 13.4 (c).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]
\[ \boxed {\sin \left (y\right ) y^{\prime \prime }+\cos \left (y\right ) {y^{\prime }}^{2}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 14
dsolve(sin(y(x))*diff(y(x),x$2)+cos(y(x))*diff(y(x),x)^2=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {\pi }{2}+\arcsin \left (c_{1} x +c_{2} \right ) \]
✓ Solution by Mathematica
Time used: 11.859 (sec). Leaf size: 29
DSolve[Sin[y[x]]*y''[x]+Cos[y[x]]*y'[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\arccos (-c_1 (x+c_2)) \\ y(x)\to \arccos (-c_1 (x+c_2)) \\ \end{align*}