80.3.24 problem 25

Internal problem ID [21188]
Book : A Textbook on Ordinary Differential Equations by Shair Ahmad and Antonio Ambrosetti. Second edition. ISBN 978-3-319-16407-6. Springer 2015
Section : Chapter 3. First order nonlinear differential equations. Excercise 3.7 at page 67
Problem number : 25
Date solved : Saturday, October 04, 2025 at 05:35:37 PM
CAS classification : [_exact]

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

With initial conditions

\begin{align*} y \left (2\right )&=\pi \\ \end{align*}

✓ Maple. Time used: 0.041 (sec). Leaf size: 17

ode:=x+sin(y(x))+x*cos(y(x))*diff(y(x),x) = 0; 
ic:=[y(2) = Pi]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \arcsin \left (\frac {x^{2}-4}{2 x}\right )+\pi \]

✗ Mathematica

ode=(x+Sin[y[x]])+(x*Cos[y[x]])*D[y[x],x]==0; 
ic={y[2]==Pi}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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✓ Sympy. Time used: 1.078 (sec). Leaf size: 12

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*cos(y(x))*Derivative(y(x), x) + x + sin(y(x)),0) 
ics = {y(2): pi} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \operatorname {asin}{\left (\frac {x}{2} - \frac {2}{x} \right )} + \pi \]