Internal problem ID [15058]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Section 6. Linear equations of the first order. The Bernoulli equation. Exercises page
54
Problem number: 165.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{\prime }-y \cos \left (x \right )-y^{2} \cos \left (x \right )=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 15
dsolve(diff(y(x),x)-y(x)*cos(x)=y(x)^2*cos(x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {1}{{\mathrm e}^{-\sin \left (x \right )} c_{1} -1} \]
✓ Solution by Mathematica
Time used: 0.359 (sec). Leaf size: 35
DSolve[y'[x]-y[x]*Cos[x]==y[x]^2*Cos[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {e^{\sin (x)+c_1}}{-1+e^{\sin (x)+c_1}} \\ y(x)\to -1 \\ y(x)\to 0 \\ \end{align*}