74.2.18 problem 23

Internal problem ID [15859]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 1. Introduction to Differential Equations. Review exercises, page 23
Problem number : 23
Date solved : Tuesday, January 28, 2025 at 08:10:29 AM
CAS classification : [_quadrature]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.015 (sec). Leaf size: 12

dsolve([diff(y(x),x)=cos(x)^2*sin(x),y(0) = 0],y(x), singsol=all)
 

\[ y = -\frac {\cos \left (x \right )^{3}}{3}+\frac {1}{3} \]

✓ Solution by Mathematica

Time used: 0.005 (sec). Leaf size: 17

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

\[ y(x)\to \frac {1}{3} \left (1-\cos ^3(x)\right ) \]