60.1.351 problem 358

Internal problem ID [10365]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 358
Date solved : Wednesday, March 05, 2025 at 10:37:39 AM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.179 (sec). Leaf size: 9

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

\[ y = \arccos \left (\sec \left (x \right ) c_{1} \right ) \]

✓ Mathematica. Time used: 0.136 (sec). Leaf size: 82

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

\[ \text {Solve}\left [\int _1^x(-\sin (K[1]-y(x))-\sin (K[1]+y(x)))dK[1]+\int _1^{y(x)}\left (\sin (x-K[2])-\sin (x+K[2])-\int _1^x(\cos (K[1]-K[2])-\cos (K[1]+K[2]))dK[1]\right )dK[2]=c_1,y(x)\right ] \]

✓ Sympy. Time used: 0.580 (sec). Leaf size: 20

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 = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = - \operatorname {acos}{\left (\frac {C_{1}}{\cos {\left (x \right )}} \right )} + 2 \pi , \ y{\left (x \right )} = \operatorname {acos}{\left (\frac {C_{1}}{\cos {\left (x \right )}} \right )}\right ] \]