38.1.18 problem 20

Internal problem ID [8179]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 1. Introduction to differential equations. Exercises 1.1 at page 12
Problem number : 20
Date solved : Tuesday, September 30, 2025 at 05:18:17 PM
CAS classification : [_separable]

\begin{align*} 2 y^{\prime }&=y^{3} \cos \left (x \right ) \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 25

ode:=2*diff(y(x),x) = y(x)^3*cos(x); 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= \frac {1}{\sqrt {c_1 -\sin \left (x \right )}} \\ y &= -\frac {1}{\sqrt {c_1 -\sin \left (x \right )}} \\ \end{align*}

✓ Mathematica. Time used: 0.115 (sec). Leaf size: 77

ode=2*D[y[x],x]==y[x]^3*Cos[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\frac {1}{\sqrt {2} \sqrt {-\int _1^x\frac {1}{2} \cos (K[1])dK[1]-c_1}}\\ y(x)&\to \frac {1}{\sqrt {2} \sqrt {-\int _1^x\frac {1}{2} \cos (K[1])dK[1]-c_1}}\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.521 (sec). Leaf size: 29

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-y(x)**3*cos(x) + 2*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = - \sqrt {- \frac {1}{C_{1} + \sin {\left (x \right )}}}, \ y{\left (x \right )} = \sqrt {- \frac {1}{C_{1} + \sin {\left (x \right )}}}\right ] \]