36.2.12 problem 12

Internal problem ID [6305]
Book : Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson 2018.
Section : Chapter 2, First order differential equations. Section 2.3, Linear equations. Exercises. page 54
Problem number : 12
Date solved : Monday, January 27, 2025 at 01:55:35 PM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }&=x^{2} {\mathrm e}^{-4 x}-4 y \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 17

dsolve(diff(y(x),x)=x^2*exp(-4*x)-4*y(x),y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {\left (x^{3}+3 c_{1} \right ) {\mathrm e}^{-4 x}}{3} \]

✓ Solution by Mathematica

Time used: 0.067 (sec). Leaf size: 22

DSolve[D[y[x],x]==x^2*Exp[-4*x]-4*y[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{3} e^{-4 x} \left (x^3+3 c_1\right ) \]