Internal problem ID [56]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 1.5. Linear first order equations. Page 56
Problem number: 3.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, class A]]
Solve \begin {gather*} \boxed {3 y+y^{\prime }-2 x \,{\mathrm e}^{-3 x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 14
dsolve(3*y(x)+diff(y(x),x) = 2*x/exp(3*x),y(x), singsol=all)
\[ y \relax (x ) = \left (x^{2}+c_{1}\right ) {\mathrm e}^{-3 x} \]
✓ Solution by Mathematica
Time used: 0.051 (sec). Leaf size: 17
DSolve[3*y[x]+y'[x] == 2*x/Exp[3*x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-3 x} \left (x^2+c_1\right ) \\ \end{align*}