85.15.5 problem 1 (e)

Internal problem ID [22530]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter two. First order and simple higher order ordinary differential equations. A Exercises at page 47
Problem number : 1 (e)
Date solved : Thursday, October 02, 2025 at 08:46:44 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)]`], [_Abel, `2nd type`, `class A`]]

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

✓ Maple. Time used: 0.007 (sec). Leaf size: 45

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

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

✓ Mathematica. Time used: 0.122 (sec). Leaf size: 49

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

\begin{align*} y(x)&\to -\sin (x)-\sqrt {x^2+\sin ^2(x)+c_1}\\ y(x)&\to -\sin (x)+\sqrt {x^2+\sin ^2(x)+c_1} \end{align*}

✗ Sympy

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

Timed Out