68.1.58 problem 80

Internal problem ID [17125]
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 : Thursday, October 02, 2025 at 01:44:07 PM
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*}

✓ Maple. Time used: 0.024 (sec). Leaf size: 20

ode:=diff(y(x),x) = sin(x)^4; 
ic:=[y(0) = 0]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.009 (sec). Leaf size: 17

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

\begin{align*} y(x)&\to \int _0^x\sin ^4(K[1])dK[1] \end{align*}

✓ Sympy. Time used: 0.095 (sec). Leaf size: 27

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-sin(x)**4 + Derivative(y(x), x),0) 
ics = {y(0): 0} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {3 x}{8} - \frac {\sin ^{3}{\left (x \right )} \cos {\left (x \right )}}{4} - \frac {3 \sin {\left (x \right )} \cos {\left (x \right )}}{8} \]