44.1.18 problem 20

Internal problem ID [6893]
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 : Monday, January 27, 2025 at 02:34:12 PM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 25

dsolve(2*diff(y(x),x)=y(x)^3*cos(x),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*}

✓ Solution by Mathematica

Time used: 0.270 (sec). Leaf size: 42

DSolve[2*D[y[x],x]==y[x]^3*Cos[x],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {1}{\sqrt {-\sin (x)-2 c_1}} \\ y(x)\to \frac {1}{\sqrt {-\sin (x)-2 c_1}} \\ y(x)\to 0 \\ \end{align*}