23.2.343 problem 391

Internal problem ID [5698]
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 : 391
Date solved : Tuesday, September 30, 2025 at 02:00:24 PM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 18

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

\[ y = \int \operatorname {RootOf}\left (a \cos \left (\textit {\_Z} \right )+\textit {\_Z} b +x \right )d x +c_1 \]

✓ Mathematica. Time used: 0.06 (sec). Leaf size: 42

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

\[ \text {Solve}[\{y(x)=\int K[1] (a \sin (K[1])-b) \, dK[1]+c_1,x=-a \cos (K[1])-b K[1]\},\{y(x),K[1]\}] \]

✗ Sympy

from sympy import * 
x = symbols("x") 
a = symbols("a") 
b = symbols("b") 
y = Function("y") 
ode = Eq(a*cos(Derivative(y(x), x)) + b*Derivative(y(x), 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*b + a*cos(_X0) + x