Internal problem ID [2652]
Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth
edition, 2015
Section: Chapter 1, First-Order Differential Equations. Section 1.6, First-Order Linear Differential
Equations. page 59
Problem number: Problem 14.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, `class A`]]
\[ \boxed {y^{\prime }+\alpha y={\mathrm e}^{\beta x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 27
dsolve(diff(y(x),x)+alpha*y(x)=exp(beta*x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {{\mathrm e}^{-\alpha x} \left ({\mathrm e}^{x \left (\alpha +\beta \right )}+c_{1} \left (\alpha +\beta \right )\right )}{\alpha +\beta } \]
✓ Solution by Mathematica
Time used: 0.055 (sec). Leaf size: 31
DSolve[y'[x]+\[Alpha]*y[x]==Exp[\[Beta]*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {e^{\alpha (-x)} \left (e^{x (\alpha +\beta )}+c_1 (\alpha +\beta )\right )}{\alpha +\beta } \]