64.5.4 problem 4

Internal problem ID [13317]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 2, section 2.3 (Linear equations). Exercises page 56
Problem number : 4
Date solved : Tuesday, January 28, 2025 at 05:22:00 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 14

dsolve(diff(y(x),x)+4*x*y(x)=8*x,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.037 (sec). Leaf size: 22

DSolve[D[y[x],x]+4*x*y[x]==8*x,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to 2+c_1 e^{-2 x^2} \\ y(x)\to 2 \\ \end{align*}