38.2.22 problem 22

Internal problem ID [8240]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 1. Introduction to differential equations. Section 1.2 Initial value problems. Exercises 1.2 at page 19
Problem number : 22
Date solved : Tuesday, September 30, 2025 at 05:19:42 PM
CAS classification : [_separable]

\begin{align*} \left (1+y^{3}\right ) y^{\prime }&=x^{2} \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 20

ode:=(1+y(x)^3)*diff(y(x),x) = x^2; 
dsolve(ode,y(x), singsol=all);
 

\[ \frac {x^{3}}{3}-\frac {y^{4}}{4}-y+c_1 = 0 \]

✓ Mathematica. Time used: 60.08 (sec). Leaf size: 871

ode=(1+y[x]^3)*D[y[x],x]==x^2; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} \text {Solution too large to show}\end{align*}

✓ Sympy. Time used: 74.550 (sec). Leaf size: 2003

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x**2 + (y(x)**3 + 1)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \text {Solution too large to show} \]