29.26.4 problem 737

Internal problem ID [5325]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 26
Problem number : 737
Date solved : Sunday, March 30, 2025 at 07:58:00 AM
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: 0.661 (sec). Leaf size: 50

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]
 

\[ \text {Solve}[\sin (a x) \sin (b y(x))-\cos (a x) \cos (b y(x))-\sin (b x) \cos (a y(x))-\cos (b x) \sin (a y(x))=c_1,y(x)] \]

✗ 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