23.1.453 problem 443

Internal problem ID [5060]
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 : 443
Date solved : Tuesday, September 30, 2025 at 11:30:56 AM
CAS classification : [[_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]

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

✓ Maple. Time used: 0.075 (sec). Leaf size: 16

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

\[ x +\cot \left (y\right )+y-c_1 \csc \left (y\right ) = 0 \]

✓ Mathematica. Time used: 0.129 (sec). Leaf size: 31

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

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

✓ Sympy. Time used: 5.199 (sec). Leaf size: 22

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

\[ C_{1} + x \sin {\left (y{\left (x \right )} \right )} + y{\left (x \right )} \sin {\left (y{\left (x \right )} \right )} + \cos {\left (y{\left (x \right )} \right )} = 0 \]