60.1.348 problem 355

Internal problem ID [10362]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 355
Date solved : Sunday, March 30, 2025 at 04:26:04 PM
CAS classification : [_exact]

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

✓ Maple. Time used: 0.014 (sec). Leaf size: 15

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

\[ \cos \left (x \right ) y+x \sin \left (y\right )+c_1 = 0 \]

✓ Mathematica. Time used: 0.139 (sec). Leaf size: 59

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

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

✗ Sympy

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

Timed Out