73.7.43 problem 43

Internal problem ID [15201]
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
Date solved : Tuesday, January 28, 2025 at 07:41:56 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=y^{3}-y^{3} \cos \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 31

dsolve(diff(y(x),x)=y(x)^3-y(x)^3*cos(x),y(x), singsol=all)
 

\begin{align*} y &= \frac {1}{\sqrt {c_{1} -2 x +2 \sin \left (x \right )}} \\ y &= -\frac {1}{\sqrt {c_{1} -2 x +2 \sin \left (x \right )}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.179 (sec). Leaf size: 77

DSolve[D[y[x],x]==y[x]^3-y[x]^3*Cos[x],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {1}{\sqrt {2} \sqrt {-\int _1^x(1-\cos (K[1]))dK[1]-c_1}} \\ y(x)\to \frac {1}{\sqrt {2} \sqrt {-\int _1^x(1-\cos (K[1]))dK[1]-c_1}} \\ y(x)\to 0 \\ \end{align*}