76.1.3 problem 3

Internal problem ID [17302]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 2. First order differential equations. Section 2.1 (Separable equations). Problems at page 44
Problem number : 3
Date solved : Tuesday, January 28, 2025 at 09:59:07 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }+y^{3} \sin \left (x \right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 25

dsolve(diff(y(x),x)+y(x)^3*sin(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.195 (sec). Leaf size: 73

DSolve[D[y[x],x]+y[x]^3*Sin[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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