44.1.22 problem 24

Internal problem ID [6897]
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. Exercises 1.1 at page 12
Problem number : 24
Date solved : Wednesday, March 05, 2025 at 02:49:56 AM
CAS classification : [_linear]

\begin{align*} y^{\prime }+4 x y&=8 x^{3} \end{align*}

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

ode:=diff(y(x),x)+4*x*y(x) = 8*x^3; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.07 (sec). Leaf size: 22

ode=D[y[x],x]+4*x*y[x]==8*x^3; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to 2 x^2+c_1 e^{-2 x^2}-1 \]

✓ Sympy. Time used: 0.319 (sec). Leaf size: 17

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-8*x**3 + 4*x*y(x) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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