44.5.2 problem 2

Internal problem ID [7064]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 2. First order differential equations. Section 2.2 Separable equations. Exercises 2.2 at page 53
Problem number : 2
Date solved : Sunday, March 30, 2025 at 11:37:22 AM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 16

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

\[ y = \frac {1}{3} x^{3}+x^{2}+x +\frac {1}{3}+c_1 \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 19

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

\[ y(x)\to \frac {x^3}{3}+x^2+x+c_1 \]

✓ Sympy. Time used: 0.172 (sec). Leaf size: 14

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

\[ y{\left (x \right )} = C_{1} + \frac {x^{3}}{3} + x^{2} + x \]