44.5.46 problem 42

Internal problem ID [7108]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 2. First order differential equations. Section 2.2 Separable equations. Exercises 2.2 at page 53
Problem number : 42
Date solved : Sunday, March 30, 2025 at 11:42:39 AM
CAS classification : [_separable]

\begin{align*} 2 x \sin \left (y\right )^{2}-\left (x^{2}+10\right ) \cos \left (y\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 19

ode:=2*x*sin(y(x))^2-(x^2+10)*cos(y(x))*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\arcsin \left (\frac {1}{\ln \left (x^{2}+10\right )+2 c_1}\right ) \]

✓ Mathematica. Time used: 0.435 (sec). Leaf size: 24

ode=2*x*Sin[y[x]]^2-(x^2+10)*Cos[y[x]]*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to \csc ^{-1}\left (-\log \left (x^2+10\right )+2 c_1\right ) \\ y(x)\to 0 \\ \end{align*}

✓ Sympy. Time used: 0.531 (sec). Leaf size: 31

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*x*sin(y(x))**2 - (x**2 + 10)*cos(y(x))*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = \operatorname {asin}{\left (\frac {1}{C_{1} + \log {\left (x^{2} + 10 \right )}} \right )} + \pi , \ y{\left (x \right )} = - \operatorname {asin}{\left (\frac {1}{C_{1} + \log {\left (x^{2} + 10 \right )}} \right )}\right ] \]