44.6.5 problem 5

Internal problem ID [7149]
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, February 04, 2025 at 12:40:07 AM
CAS classification : [_separable]

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

Solution by Maple

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

dsolve(diff(y(x),x)+3*x^2*y(x)=x^2,y(x), singsol=all)
 
\[ y = \frac {1}{3}+c_1 \,{\mathrm e}^{-x^{3}} \]

Solution by Mathematica

Time used: 0.057 (sec). Leaf size: 26

DSolve[D[y[x],x]+3*x^2*y[x]==x^2,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*}