74.1.58 problem 80

Internal problem ID [15838]
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 : 80
Date solved : Tuesday, January 28, 2025 at 08:09:13 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=\sin \left (x \right )^{4} \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.065 (sec). Leaf size: 20

dsolve([diff(y(x),x)=sin(x)^4,y(0) = 0],y(x), singsol=all)
 

\[ y = \frac {3 x}{8}-\frac {\sin \left (2 x \right )}{4}+\frac {\sin \left (4 x \right )}{32} \]

✓ Solution by Mathematica

Time used: 0.013 (sec). Leaf size: 17

DSolve[{D[y[x],x]==Sin[x]^4,{y[0]==0}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \int _0^x\sin ^4(K[1])dK[1] \]