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 : Sunday, March 30, 2025 at 12:34:59 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*}

✓ Maple. Time used: 0.273 (sec). Leaf size: 15

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

\begin{align*} y &= \arccos \left (\sec \left (x \right )\right ) \\ y &= -\arccos \left (\sec \left (x \right )\right ) \\ \end{align*}

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

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

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

✓ Sympy. Time used: 0.588 (sec). Leaf size: 8

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(sin(x)*cos(y(x)) + sin(y(x))*cos(x)*Derivative(y(x), x),0) 
ics = {y(0): 0} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \operatorname {acos}{\left (\frac {1}{\cos {\left (x \right )}} \right )} \]