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 : Monday, January 27, 2025 at 02:34:22 PM
CAS classification : [_linear]

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

Solution by Maple

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

dsolve(diff(y(x),x)+4*x*y(x)=8*x^3,y(x), singsol=all)
 
\[ y = 2 x^{2}-1+{\mathrm e}^{-2 x^{2}} c_{1} \]

Solution by Mathematica

Time used: 0.070 (sec). Leaf size: 22

DSolve[D[y[x],x]+4*x*y[x]==8*x^3,y[x],x,IncludeSingularSolutions -> True]
 
\[ y(x)\to 2 x^2+c_1 e^{-2 x^2}-1 \]