44.8.15 problem 2(g)

Internal problem ID [9217]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 1. What is a differential equation. Problems for Review and Discovery. Page 53
Problem number : 2(g)
Date solved : Tuesday, September 30, 2025 at 06:15:12 PM
CAS classification : [_separable]

\begin{align*} 2 x \cos \left (y\right )-x^{2} \sin \left (y\right ) y^{\prime }&=0 \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=1 \\ \end{align*}

✓ Maple. Time used: 0.303 (sec). Leaf size: 11

ode:=2*x*cos(y(x))-x^2*sin(y(x))*diff(y(x),x) = 0; 
ic:=[y(1) = 1]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \arccos \left (\frac {\cos \left (1\right )}{x^{2}}\right ) \]

✓ Mathematica. Time used: 27.883 (sec). Leaf size: 12

ode=2*x*Cos[y[x]]-x^2*Sin[y[x]]*D[y[x],x]==0; 
ic={y[1]==1}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \arccos \left (\frac {\cos (1)}{x^2}\right ) \end{align*}

✓ Sympy. Time used: 0.235 (sec). Leaf size: 10

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x**2*sin(y(x))*Derivative(y(x), x) + 2*x*cos(y(x)),0) 
ics = {y(1): 1} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \operatorname {acos}{\left (\frac {\cos {\left (1 \right )}}{x^{2}} \right )} \]