74.1.39 problem 46

Internal problem ID [15819]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 1. Introduction to Differential Equations. Exercises 1.1, page 10
Problem number : 46
Date solved : Tuesday, January 28, 2025 at 08:08:08 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 22

dsolve(diff(y(x),x)=sin(x)^3*tan(x),y(x), singsol=all)
 

\[ y = -\frac {\sin \left (x \right )^{3}}{3}-\sin \left (x \right )+\ln \left (\sec \left (x \right )+\tan \left (x \right )\right )+c_{1} \]

✓ Solution by Mathematica

Time used: 0.012 (sec). Leaf size: 23

DSolve[D[y[x],x]==Sin[x]^3*Tan[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \text {arctanh}(\sin (x))-\frac {1}{3} \sin ^3(x)-\sin (x)+c_1 \]