38.6.5 problem 5

Internal problem ID [8435]
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 2.3 Linear equations. Exercises 2.3 at page 63
Problem number : 5
Date solved : Tuesday, September 30, 2025 at 05:36:42 PM
CAS classification : [_separable]

\begin{align*} y^{\prime }+3 x^{2} y&=x^{2} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 14

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

\[ y = \frac {1}{3}+{\mathrm e}^{-x^{3}} c_1 \]

✓ Mathematica. Time used: 0.04 (sec). Leaf size: 26

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

\begin{align*} y(x)&\to \frac {1}{3}+c_1 e^{-x^3}\\ y(x)&\to \frac {1}{3} \end{align*}

✓ Sympy. Time used: 0.189 (sec). Leaf size: 12

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

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