64.5.3 problem 3

Internal problem ID [13316]
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 : 3
Date solved : Tuesday, January 28, 2025 at 05:21:58 AM
CAS classification : [[_linear, `class A`]]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 14

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

\[ y = \left (x^{3}+c_{1} \right ) {\mathrm e}^{-3 x} \]

✓ Solution by Mathematica

Time used: 0.071 (sec). Leaf size: 17

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

\[ y(x)\to e^{-3 x} \left (x^3+c_1\right ) \]