7.7.15 problem 15

Internal problem ID [193]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Review problems at page 98
Problem number : 15
Date solved : Friday, February 07, 2025 at 08:04:16 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)
 

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

✓ Solution by Mathematica

Time used: 0.075 (sec). Leaf size: 17

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

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