83.9.1 problem 1

Internal problem ID [21959]
Book : Differential Equations By Kaj L. Nielsen. Second edition 1966. Barnes and nobel. 66-28306
Section : Chapter III. First order differential equations of the first degree. Ex. X at page 57
Problem number : 1
Date solved : Thursday, October 02, 2025 at 08:20:02 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 14

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

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

✓ Mathematica. Time used: 0.039 (sec). Leaf size: 22

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

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

✓ Sympy. Time used: 0.170 (sec). Leaf size: 10

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

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