Internal problem ID [14123]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {y^{\prime }=\cos \left (x \right )^{2} \sin \left (x \right )} \] With initial conditions \begin {align*} [y \left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 12
dsolve([diff(y(x),x)=cos(x)^2*sin(x),y(0) = 0],y(x), singsol=all)
\[ y \left (x \right ) = -\frac {\cos \left (x \right )^{3}}{3}+\frac {1}{3} \]
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 17
DSolve[{y'[x]==Cos[x]^2*Sin[x],{y[0]==0}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{3} \left (1-\cos ^3(x)\right ) \]