Internal problem ID [4961]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, `class A`]]
\[ \boxed {y^{\prime }+4 y=x^{2} {\mathrm e}^{-4 x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 16
dsolve(diff(y(x),x)=x^2*exp(-4*x)-4*y(x),y(x), singsol=all)
\[ y \left (x \right ) = \left (\frac {x^{3}}{3}+c_{1} \right ) {\mathrm e}^{-4 x} \]
✓ Solution by Mathematica
Time used: 0.058 (sec). Leaf size: 22
DSolve[y'[x]==x^2*Exp[-4*x]-4*y[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{3} e^{-4 x} \left (x^3+3 c_1\right ) \]