12.3.2 problem 2

Internal problem ID [1579]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 2, First order equations. separable equations. Section 2.2 Page 52
Problem number : 2
Date solved : Monday, January 27, 2025 at 05:09:06 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.040 (sec). Leaf size: 12

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

\[ y = \arcsin \left (\frac {{\mathrm e}^{\cos \left (x \right )}}{c_1}\right ) \]

✓ Solution by Mathematica

Time used: 27.860 (sec). Leaf size: 22

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

\begin{align*} y(x)\to \arcsin \left (e^{\cos (x)+\frac {c_1}{2}}\right ) \\ y(x)\to 0 \\ \end{align*}