15.1.23 problem 23

Internal problem ID [2863]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 5, page 21
Problem number : 23
Date solved : Monday, January 27, 2025 at 06:20:37 AM
CAS classification : [_separable]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.188 (sec). Leaf size: 23

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

\begin{align*} y &= \frac {\pi }{2}-\arcsin \left (\sec \left (x \right )\right ) \\ y &= -\frac {\pi }{2}+\arcsin \left (\sec \left (x \right )\right ) \\ \end{align*}

✓ Solution by Mathematica

Time used: 5.957 (sec). Leaf size: 17

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

\begin{align*} y(x)\to -\arccos (\sec (x)) \\ y(x)\to \arccos (\sec (x)) \\ \end{align*}