38.6.6 problem 6

Internal problem ID [8436]
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 : 6
Date solved : Tuesday, September 30, 2025 at 05:36:43 PM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 19

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

\[ y = \frac {x^{2}}{2}-\frac {1}{2}+{\mathrm e}^{-x^{2}} c_1 \]

✓ Mathematica. Time used: 0.019 (sec). Leaf size: 25

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

\begin{align*} y(x)&\to \frac {1}{2} \left (x^2-1\right )+c_1 e^{-x^2} \end{align*}

✓ Sympy. Time used: 0.162 (sec). Leaf size: 17

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

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