73.5.11 problem 6.5 (c)

Internal problem ID [15122]
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)
Date solved : Tuesday, January 28, 2025 at 07:33:56 AM
CAS classification : [_Bernoulli]

\begin{align*} y^{\prime }+3 \cot \left (x \right ) y&=6 \cos \left (x \right ) y^{{2}/{3}} \end{align*}

✓ Solution by Maple

Time used: 0.018 (sec). Leaf size: 17

dsolve(diff(y(x),x)+3*cot(x)*y(x)=6*cos(x)*y(x)^(2/3),y(x), singsol=all)
 

\[ y^{{1}/{3}}-\sin \left (x \right )-\csc \left (x \right ) c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.285 (sec). Leaf size: 34

DSolve[D[y[x],x]+3*Cot[x]*y[x]==6*Cos[x]*y[x]^(2/3),y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{27} \csc ^3(x) \left (\int _1^x3 \sin (2 K[1])dK[1]+3 c_1\right ){}^3 \]