69.4.20 problem 85

Internal problem ID [18009]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 4. Equations with variables separable and equations reducible to them. Exercises page 38
Problem number : 85
Date solved : Thursday, October 02, 2025 at 02:33:18 PM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 10

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

\[ y = \frac {\pi x}{2}+c_1 \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 27

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

\begin{align*} y(x)&\to -\frac {\pi x}{2}+c_1\\ y(x)&\to \frac {\pi x}{2}+c_1 \end{align*}

✓ Sympy. Time used: 0.098 (sec). Leaf size: 19

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

\[ \left [ y{\left (x \right )} = C_{1} + \frac {\pi x}{2}, \ y{\left (x \right )} = C_{1} + \frac {3 \pi x}{2}\right ] \]