Internal problem ID [7602]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 21.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Riccati]
Solve \begin {gather*} \boxed {y^{\prime }-y^{2}+y \sin \relax (x )-\cos \relax (x )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 25
dsolve(diff(y(x),x) - y(x)^2 +y(x)*sin(x) - cos(x)=0,y(x), singsol=all)
\[ y \relax (x ) = -\frac {{\mathrm e}^{-\cos \relax (x )}}{c_{1}+\int {\mathrm e}^{-\cos \relax (x )}d x}+\sin \relax (x ) \]
✓ Solution by Mathematica
Time used: 60.487 (sec). Leaf size: 39
DSolve[y'[x] - y[x]^2 +y[x]*Sin[x] - Cos[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \sin (x)-\frac {c_1 e^{-\cos (x)}}{1+c_1 \int _1^xe^{-\cos (K[1])}dK[1]} \\ \end{align*}