Internal problem ID [8577]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 997.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_symmetry_[F(x),G(x)]], _Riccati]
Solve \begin {gather*} \boxed {y^{\prime }-\left (y+\cos \relax (x )\right )^{2}-\sin \relax (x )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 16
dsolve(diff(y(x),x) = (y(x)+cos(x))^2+sin(x),y(x), singsol=all)
\[ y \relax (x ) = -\cos \relax (x )+\frac {1}{c_{1}-x} \]
✓ Solution by Mathematica
Time used: 0.18 (sec). Leaf size: 26
DSolve[y'[x] == Sin[x] + (Cos[x] + y[x])^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\cos (x)+\frac {1}{-x+c_1} \\ y(x)\to -\cos (x) \\ \end{align*}