40.2.23 problem 48

Internal problem ID [6601]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 4. Equations of first order and first degree (Variable separable). Supplemetary problems. Page 22
Problem number : 48
Date solved : Monday, January 27, 2025 at 02:15:24 PM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (0\right )&=\frac {\pi }{4} \end{align*}

✓ Solution by Maple

Time used: 0.023 (sec). Leaf size: 14

dsolve([cos(y(x))+(1+exp(-x))*sin(y(x))*diff(y(x),x)= 0,y(0) = 1/4*Pi],y(x), singsol=all)
 

\[ y = \arccos \left (\frac {\sqrt {2}\, \left ({\mathrm e}^{x}+1\right )}{4}\right ) \]

✓ Solution by Mathematica

Time used: 52.488 (sec). Leaf size: 20

DSolve[{Cos[y[x]]+(1+Exp[-x])*Sin[y[x]]*D[y[x],x]== 0,{y[0]==Pi/4}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \arccos \left (\frac {e^x+1}{2 \sqrt {2}}\right ) \]