23.2.342 problem 390

Internal problem ID [5697]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 2. THE DIFFERENTIAL EQUATION IS OF FIRST ORDER AND OF SECOND OR HIGHER DEGREE, page 278
Problem number : 390
Date solved : Tuesday, September 30, 2025 at 02:00:22 PM
CAS classification : [_Clairaut]

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

✓ Maple. Time used: 0.005 (sec). Leaf size: 27

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

\begin{align*} y &= \arcsin \left (x \right ) x +\sqrt {-x^{2}+1} \\ y &= \cos \left (c_1 \right )+c_1 x \\ \end{align*}

✓ Mathematica. Time used: 0.02 (sec). Leaf size: 18

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

\begin{align*} y(x)&\to c_1 x+\cos (c_1)\\ y(x)&\to 1 \end{align*}

✗ Sympy

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

NotImplementedError : multiple generators [_X0, cos(_X0)] 
No algorithms are implemented to solve equation _X0*x - y(x) + cos(_X0)