44.6.6 problem 6

Internal problem ID [7150]
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, February 04, 2025 at 12:40:11 AM
CAS classification : [_linear]

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

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

Time used: 0.062 (sec). Leaf size: 25

DSolve[D[y[x],x]+2*x*y[x]==x^3,y[x],x,IncludeSingularSolutions -> True]
 

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