Internal problem ID [15119]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Section 9. The Riccati equation. Exercises page 75
Problem number: 233.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, `_with_symmetry_[F(x),G(x)]`], _Riccati]
\[ \boxed {y^{\prime }+y^{2}-2 y \sin \left (x \right )=-\sin \left (x \right )^{2}+\cos \left (x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 14
dsolve(diff(y(x),x)+y(x)^2-2*y(x)*sin(x)+sin(x)^2-cos(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \sin \left (x \right )+\frac {1}{x -c_{1}} \]
✓ Solution by Mathematica
Time used: 0.257 (sec). Leaf size: 20
DSolve[y'[x]+y[x]^2-2*y[x]*Sin[x]+Sin[x]^2-Cos[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \sin (x)+\frac {1}{x+c_1} \\ y(x)\to \sin (x) \\ \end{align*}