Internal problem ID [13066]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 6. Simplifying through simplifiction. Additional exercises. page 114
Problem number: 6.5 (c).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Bernoulli]
\[ \boxed {y^{\prime }+3 \cot \left (x \right ) y-6 \cos \left (x \right ) y^{\frac {2}{3}}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 19
dsolve(diff(y(x),x)+3*cot(x)*y(x)=6*cos(x)*y(x)^(2/3),y(x), singsol=all)
\[ -\sin \left (x \right )-\frac {c_{1}}{\sin \left (x \right )}+y^{\frac {1}{3}} = 0 \]
✓ Solution by Mathematica
Time used: 0.305 (sec). Leaf size: 24
DSolve[y'[x]+3*Cot[x]*y[x]==6*Cos[x]*y[x]^(2/3),y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {1}{8} \csc ^3(x) (\cos (2 x)-2 c_1){}^3 \]