Internal problem ID [4453]
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]]
Solve \begin {gather*} \boxed {y^{\prime }-x^{2} {\mathrm e}^{-4 x}+4 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.001 (sec). Leaf size: 16
dsolve(diff(y(x),x)=x^2*exp(-4*x)-4*y(x),y(x), singsol=all)
\[ y \relax (x ) = \left (\frac {x^{3}}{3}+c_{1}\right ) {\mathrm e}^{-4 x} \]
✓ Solution by Mathematica
Time used: 0.066 (sec). Leaf size: 22
DSolve[y'[x]==x^2*Exp[-4*x]-4*y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{3} e^{-4 x} \left (x^3+3 c_1\right ) \\ \end{align*}