60.1.346 problem 353

Internal problem ID [10360]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 353
Date solved : Sunday, March 30, 2025 at 04:25:52 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.006 (sec). Leaf size: 12

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

\[ y = \arcsin \left (\frac {1}{x c_1}\right ) \]

✓ Mathematica. Time used: 11.816 (sec). Leaf size: 19

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

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

✓ Sympy. Time used: 0.326 (sec). Leaf size: 15

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

\[ \left [ y{\left (x \right )} = \pi - \operatorname {asin}{\left (\frac {C_{1}}{x} \right )}, \ y{\left (x \right )} = \operatorname {asin}{\left (\frac {C_{1}}{x} \right )}\right ] \]