68.4.41 problem 41

Internal problem ID [17221]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.2, page 39
Problem number : 41
Date solved : Thursday, October 02, 2025 at 01:58:46 PM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=x^{3} \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.028 (sec). Leaf size: 9

ode:=diff(y(x),x) = x^3; 
ic:=[y(0) = 0]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \frac {x^{4}}{4} \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 12

ode=D[y[x],x]==x^3; 
ic={y[0]==0}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {x^4}{4} \end{align*}

✓ Sympy. Time used: 0.067 (sec). Leaf size: 7

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x**3 + Derivative(y(x), x),0) 
ics = {y(0): 0} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {x^{4}}{4} \]