38.5.38 problem 38

Internal problem ID [8386]
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 : 38
Date solved : Tuesday, September 30, 2025 at 05:34:13 PM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (0\right )&=1 \\ \end{align*}

✓ Maple. Time used: 0.278 (sec). Leaf size: 12

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

\[ y = \sqrt {2 \cos \left (x \right )-1} \]

✓ Mathematica. Time used: 0.077 (sec). Leaf size: 25

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

\begin{align*} y(x)&\to \sqrt {2 \int _0^x-\sin (K[1])dK[1]+1} \end{align*}

✓ Sympy. Time used: 0.333 (sec). Leaf size: 12

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

\[ y{\left (x \right )} = \sqrt {2 \cos {\left (x \right )} - 1} \]