Internal problem ID [2062]
Book: Differential equations and linear algebra, Stephen W. Goode, second edition, 2000
Section: 1.6, page 50
Problem number: 13.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, `class A`]]
\[ \boxed {y^{\prime }+\alpha y-{\mathrm e}^{\beta x}=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 24
dsolve(diff(y(x),x)+alpha*y(x)=exp(beta*x),y(x), singsol=all)
\[ y \left (x \right ) = \left (\frac {{\mathrm e}^{x \left (\alpha +\beta \right )}}{\alpha +\beta }+c_{1} \right ) {\mathrm e}^{-\alpha x} \]
✓ Solution by Mathematica
Time used: 0.062 (sec). Leaf size: 31
DSolve[y'[x]+\[Alpha]*y[x]==Exp[\[Beta]*x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {e^{\alpha (-x)} \left (e^{x (\alpha +\beta )}+c_1 (\alpha +\beta )\right )}{\alpha +\beta } \\ \end{align*}