60.1.75 problem 76

Internal problem ID [10089]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 76
Date solved : Sunday, March 30, 2025 at 03:13:55 PM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.009 (sec). Leaf size: 41

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

\[ y = 2 \arctan \left (\frac {\tanh \left (\frac {\sqrt {a^{2}-b^{2}}\, \left (c_1 +x \right )}{2}\right ) \sqrt {a^{2}-b^{2}}}{a +b}\right ) \]

✓ Mathematica. Time used: 0.265 (sec). Leaf size: 53

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

\begin{align*} y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{b-a \cos (K[1])}dK[1]\&\right ][-x+c_1] \\ y(x)\to -\arccos \left (\frac {b}{a}\right ) \\ y(x)\to \arccos \left (\frac {b}{a}\right ) \\ \end{align*}

✗ Sympy

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

TypeError : < not supported between instances of NoneType and y