Internal problem ID [13145]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 8. Review exercises for part of part II. page 143
Problem number: 43.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{\prime }-y^{3}+y^{3} \cos \left (x \right )=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 31
dsolve(diff(y(x),x)=y(x)^3-y(x)^3*cos(x),y(x), singsol=all)
\begin{align*} y \left (x \right ) = \frac {1}{\sqrt {c_{1} -2 x +2 \sin \left (x \right )}} y \left (x \right ) = -\frac {1}{\sqrt {c_{1} -2 x +2 \sin \left (x \right )}} \end{align*}
✓ Solution by Mathematica
Time used: 0.219 (sec). Leaf size: 55
DSolve[y'[x]==y[x]^3-y[x]^3*Cos[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{\sqrt {2} \sqrt {-x+\sin (x)-c_1}} y(x)\to \frac {1}{\sqrt {2} \sqrt {-x+\sin (x)-c_1}} y(x)\to 0 \end{align*}