10.5.17 problem 22

Internal problem ID [1209]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.6. Page 100
Problem number : 22
Date solved : Monday, January 27, 2025 at 04:45:17 AM
CAS classification : [_separable]

\begin{align*} \left (x +2\right ) \sin \left (y\right )+x \cos \left (y\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 16

dsolve((2+x)*sin(y(x))+x*cos(y(x))*diff(y(x),x) = 0,y(x), singsol=all)
 

\[ y = \arcsin \left (\frac {{\mathrm e}^{-x}}{c_1 \,x^{2}}\right ) \]

✓ Solution by Mathematica

Time used: 45.553 (sec). Leaf size: 23

DSolve[(2+x)*Sin[y[x]]+x*Cos[y[x]]*D[y[x],x] == 0,y[x],x,IncludeSingularSolutions -> True]
 

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