23.1.741 problem 741

Internal problem ID [5348]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 1. THE DIFFERENTIAL EQUATION IS OF FIRST ORDER AND OF FIRST DEGREE, page 223
Problem number : 741
Date solved : Tuesday, September 30, 2025 at 12:33:45 PM
CAS classification : [_exact]

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

✓ Maple. Time used: 0.018 (sec). Leaf size: 36

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

\[ y = \frac {-a x +\operatorname {RootOf}\left (-a^{2} x +b^{2} x +\arcsin \left (\cos \left (\textit {\_Z} \right )+c_1 \right ) b +\textit {\_Z} a \right )}{b} \]

✓ Mathematica. Time used: 0.339 (sec). Leaf size: 108

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

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

✗ Sympy

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

Timed Out