Internal problem ID [2803]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 2
Problem number: 48.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Riccati]
Solve \begin {gather*} \boxed {y^{\prime }-\cos \relax (x )+\left (\sin \relax (x )-y\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 25
dsolve(diff(y(x),x) = cos(x)-(sin(x)-y(x))*y(x),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: 60.384 (sec). Leaf size: 39
DSolve[y'[x]==Cos[x]-(Sin[x]-y[x])y[x],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*}