73.7.20 problem 20

Internal problem ID [15178]
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 : 20
Date solved : Tuesday, January 28, 2025 at 07:40:11 AM
CAS classification : [_separable]

\begin{align*} \sin \left (y\right )+\left (1+x \right ) \cos \left (y\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.041 (sec). Leaf size: 14

dsolve(sin(y(x))+(1+x)*cos(y(x))*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y = \arcsin \left (\frac {1}{c_{1} \left (x +1\right )}\right ) \]

✓ Solution by Mathematica

Time used: 17.623 (sec). Leaf size: 21

DSolve[Sin[y[x]]+(1+x)*Cos[y[x]]*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \arcsin \left (\frac {e^{c_1}}{x+1}\right ) \\ y(x)\to 0 \\ \end{align*}