Internal problem ID [2027]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 11, page 45
Problem number: 17.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Bernoulli]
\[ \boxed {y^{\prime }+y \cos \left (x \right )-y^{3} \sin \left (x \right )=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 96
dsolve(diff(y(x),x)+y(x)*cos(x)=y(x)^3*sin(x),y(x), singsol=all)
\begin{align*} y = \frac {\sqrt {-\left (-c_{1} +2 \left (\int {\mathrm e}^{-2 \sin \left (x \right )} \sin \left (x \right )d x \right )\right ) {\mathrm e}^{-2 \sin \left (x \right )}}}{-c_{1} +2 \left (\int {\mathrm e}^{-2 \sin \left (x \right )} \sin \left (x \right )d x \right )} y = -\frac {\sqrt {-\left (-c_{1} +2 \left (\int {\mathrm e}^{-2 \sin \left (x \right )} \sin \left (x \right )d x \right )\right ) {\mathrm e}^{-2 \sin \left (x \right )}}}{-c_{1} +2 \left (\int {\mathrm e}^{-2 \sin \left (x \right )} \sin \left (x \right )d x \right )} \end{align*}
✓ Solution by Mathematica
Time used: 10.83 (sec). Leaf size: 84
DSolve[y'[x]+y[x]*Cos[x]==y[x]^3*Sin[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{\sqrt {e^{2 \sin (x)} \left (-2 \int _1^xe^{-2 \sin (K[1])} \sin (K[1])dK[1]+c_1\right )}} y(x)\to \frac {1}{\sqrt {e^{2 \sin (x)} \left (-2 \int _1^xe^{-2 \sin (K[1])} \sin (K[1])dK[1]+c_1\right )}} y(x)\to 0 \end{align*}